**Part 3**

**Properties and Applications** 

24 Will-be-set-by-IN-TECH

332 Smart Nanoparticles Technology

Landau, L. D. & Lifshitz, E. M. (1980). *Statistical Physics,* part 1, third edn, Pergamon Press,

Lifshitz, E. M. & Pitaevskii, L. (1980). *Statistical physics : pt. 2: theory of the condensed state*, Vol. 9 of *Course of Theoretical Physics*, third edn, Pergamon Press, Ltd., New York.

Lukosz, W. & Kunz, R. E. (1977). Light emission by magnetic and electric dipoles close to a plane interface. i. total radiated power, *J. Opt. Soc. Am.* 67(12): 1607–1615. URL: *http://www.opticsinfobase.org/abstract.cfm?URI=josa-67-12-1607*

Macklin, J. J., Trautman, J. K., Harris, T. D. & Brus, L. E. (1996). Imaging and time-resolved spectroscopy of single molecules at an interface, *Science* 272(5259): 255–258.

Milonni, P. & Knight, P. (1973). Spontaneous emission between mirrors, *Optics Communications*

Omont, A. (1977). *Irreducible components of the density matrix: application to optical pumping*, 5

Purcell, E. M. (1946). Spontaneous emission probabilities at radio frequencies, *Phys. Rev.*

Ruppin, R. (1982). Decay of an excited molecule near a small metal sphere, *J. Chem. Phys.*

Snoeks, E., Lagendijk, A. & Polman, A. (1995). Measuring and modifying the spontaneous emission rate of erbium near an interface, *Phys. Rev. Lett.* 74: 2459–2462.

Sobelman, I. I. (1972). *Introduction to the theory of atomic spectra*, Vol. 40 of *International series of monographs in natural philosophy*, Pergamon Press, Oxford, New York. Steiner, M., Schleifenbaum, F., Stupperich, C., Failla, A. V., Hartschuh, A. & Meixner,

Vallée, R., Tomczak, N., Gersen, H., van Dijk, E., García-Parajó, M., Vancso, G. & van Hulst,

Wylie, J. M. & Sipe, J. E. (1984). Quantum electrodynamics near an interface, *Phys. Rev. A*

Wylie, J. M. & Sipe, J. E. (1985). Quantum electrodynamics near an interface. II, *Phys. Rev. A*

Yeung, M. S. & Gustafson, T. K. (1996). Spontaneous emission near an absorbing dielectric

URL: *http://www.sciencedirect.com/science/article/pii/S0009261401011198* Varshalovich, D. A., Moskalev, A. N. & Khersonskii, V. K. (1988). *Quantum Theory of Angular*

A. J. (2005). Microcavity-controlled single-molecule fluorescence, *Chem. Phys. Chem.*

N. (2001). On the role of electromagnetic boundary conditions in single molecule fluorescence lifetime studies of dyes embedded in thin films, *Chemical Physics Letters*

URL: *http://www.sciencedirect.com/science/article/pii/0030401873902393* Nikolaev, G. N. (2006). Effective transfer of light energy to a nanoparticle by means of a

in *Progress in quantum electronics*, Pergamon Press, pp. 69–138 .

URL: *http://books.google.com/books?id=TmrRQgAACAAJ*

URL: *http://link.aps.org/doi/10.1103/PhysRevLett.74.2459*

Loisell, W. H. (1973). *Quantum Statistical Properties of Radiation*, Wiley, New York.

URL: *http://www.sciencemag.org/content/272/5259/255.abstract*

resonance atomic lens, *JETP* 102(3): 394–405.

Ltd., New York.

9(2): 119 – 122.

69(11-12): 681.

6: 2190 – 2196.

348(3–4): 161–167.

30(3): 1185–1193.

32(4): 2030–2043.

*Momentum*, World Scientific Pub Co Inc.

surface, *Phys. Rev. A* 54: 5227–5242.

URL: *http://link.aps.org/doi/10.1103/PhysRevA.54.5227*

76(4): 1681.

**0**

**15**

Fei Duan

*Singapore*

**Thermal Property Measurement**

*School of Mechanical and Aerospace Engineering, Nanyang Technological University*

Fluids have been applied in the cooling in the most important industries including microelectronics, manufacturing, metrology, etc. With increasing thermal loads that require advances in cooling the new higher power output devices with faster speeds and smaller feature, the conventional heat transfer fluids, such as water, engine oil, ethylene glycol, etc., demonstrate the relative low heat transfer performance. The use of solid particles as an additive suspended in the base fluid is a potential alternative technique for the heat transfer enhancement, i.e. thermal conductivity of metallic or nonmetallic solids might have two orders of magnitude higher than the conventional fluids. The enhancement of thermal conductivity of conventional fluids with the suspension of solid particles, such as micrometer-sized particles, has been well known for more than 100 years (Choi, 1995). However, the conventional micrometer-sized particle liquid suspensions require high concentrations (>10%) of particles to achieve such an enhancement. Because they have the rheological and stability problems such as sedimentation, erosion, fouling, and pressure drop in flow channels, the fluids with the micrometer-sized particle have not been of interest for practical applications. The recent advance in materials technology has made it possible to produce nanometer-sized particles that can overcome these above problems. The innovative fluids suspended with nanometer-sized solid particles can change the transport and thermal

Modern nanotechnology can produce materials with average particle sizes below 50 nm. All solid nanoparticles with high thermal conductivity can be used as additives of nanofluids. These nanoparticles that have been usually used in the nanofluids include: metallic particles (Cu, Al, Fe, Au, Ag, etc.), and nonmetallic particles (Al2O3, CuO, Fe3O4, TiO2, SiC, carbon nanotube, etc.). The base media of nanofluids are usually water, oil, acetone, decene, ethylene glycol, etc. (Li et al., 2009). A 40% increase in thermal conductivity was found in the Cu oil-based nanofluids with 0.3% volume concentration, while the Al2O3 water-based nanofluids exhibited a 29% enhancement of thermal conductivity for the 5%

The Al2O3 nanoparticles were selected to prepare the water-based nanofluids in this study due to their chemical stability. Preparation of nanofluids is the key step in the use of nanoparticles for stable nanofluids. Two kinds of methods have been employed in producing nanofluids: the single-step method and the two-step method. The single-step method is a process combining the preparation of nanoparticles with the synthesis of nanofluids, for which the nanoparticles are directly prepared by the physical vapor deposition technique

properties of the base fluid, and make the fluid stable.

volume concentration nanofluids (Eastman et al., 1997).

**1. Introduction**

**of Al**2**O**3**-Water Nanofluids**

## **Thermal Property Measurement of Al**2**O**3**-Water Nanofluids**

Fei Duan

*School of Mechanical and Aerospace Engineering, Nanyang Technological University Singapore*

#### **1. Introduction**

Fluids have been applied in the cooling in the most important industries including microelectronics, manufacturing, metrology, etc. With increasing thermal loads that require advances in cooling the new higher power output devices with faster speeds and smaller feature, the conventional heat transfer fluids, such as water, engine oil, ethylene glycol, etc., demonstrate the relative low heat transfer performance. The use of solid particles as an additive suspended in the base fluid is a potential alternative technique for the heat transfer enhancement, i.e. thermal conductivity of metallic or nonmetallic solids might have two orders of magnitude higher than the conventional fluids. The enhancement of thermal conductivity of conventional fluids with the suspension of solid particles, such as micrometer-sized particles, has been well known for more than 100 years (Choi, 1995). However, the conventional micrometer-sized particle liquid suspensions require high concentrations (>10%) of particles to achieve such an enhancement. Because they have the rheological and stability problems such as sedimentation, erosion, fouling, and pressure drop in flow channels, the fluids with the micrometer-sized particle have not been of interest for practical applications. The recent advance in materials technology has made it possible to produce nanometer-sized particles that can overcome these above problems. The innovative fluids suspended with nanometer-sized solid particles can change the transport and thermal properties of the base fluid, and make the fluid stable.

Modern nanotechnology can produce materials with average particle sizes below 50 nm. All solid nanoparticles with high thermal conductivity can be used as additives of nanofluids. These nanoparticles that have been usually used in the nanofluids include: metallic particles (Cu, Al, Fe, Au, Ag, etc.), and nonmetallic particles (Al2O3, CuO, Fe3O4, TiO2, SiC, carbon nanotube, etc.). The base media of nanofluids are usually water, oil, acetone, decene, ethylene glycol, etc. (Li et al., 2009). A 40% increase in thermal conductivity was found in the Cu oil-based nanofluids with 0.3% volume concentration, while the Al2O3 water-based nanofluids exhibited a 29% enhancement of thermal conductivity for the 5% volume concentration nanofluids (Eastman et al., 1997).

The Al2O3 nanoparticles were selected to prepare the water-based nanofluids in this study due to their chemical stability. Preparation of nanofluids is the key step in the use of nanoparticles for stable nanofluids. Two kinds of methods have been employed in producing nanofluids: the single-step method and the two-step method. The single-step method is a process combining the preparation of nanoparticles with the synthesis of nanofluids, for which the nanoparticles are directly prepared by the physical vapor deposition technique

models were found to be unable to predict the anomalously high thermal conductivity of nanofluids. This might be because these models do not include the effects of particle size, interfacial layer at the particle/liquid interface, and the Brownian motion of particles (Jang & Choi, 2004; Keblinski et al., 2002; Wang et al., 1999; Yu & Choi, 2003). Recently, Yu & Choi (2003) proposed a modified Maxwell model to account for the effect of the nano-layer by replacing the thermal conductivity of solid particles with the modified thermal conductivity of particles, which is based on the so called effective medium theory (Schwartz et al., 1995). The model can predict the presence of thin nano-layers less than 10 nm in thickness. Yu & Choi (2004) proposed a modified Hamilton-Crosser model to include the particle-liquid interfacial layer for nonspherical particles. The model can predict the thermal conductivity of the carbon nanotube-in-oil nanofluids reasonably well. However, it fails to predict the nonlinear behavior of the effective thermal conductivity of general oxide and metal based nanofluids. Xue (2003) presented a model for the effective thermal conductivity of nanofluids considering the effect of the interface between the solid particles and the base fluid based on the Maxwell model and the average polarization theory. Xue (2003) demonstrated that the model predictions were in a good agreement with the experiments of the nanotube oil-based nanofluids at high thermal conductivity and nonlinearity. However, Yu & Choi (2004) found that the predicted values from the model by Xue are inaccurate by using two incorrect parameters, as same as the finding of Kim et al. (2004). Xue & Xu (2005) obtained an equation for the effective thermal conductivity based on the Bruggeman model (Bruggeman, 1935). The equation takes account of the effect of interfacial shells by replacing the thermal conductivity of nanoparticles with the assumed value of the "complex nanoparticles", which introduces interfacial shells between the nanoparticles and the base fluids. The model can explain the size dependence of the thermal conductivity of nanofluids (Xuan & Li, 2000). Xie et al. (2001) considered the interfacial nano-layer with the linear thermal conductivity distribution and proposed an effective thermal conductivity model to account for the effects of nano-layer thickness, nanoparticles size, volume fraction, and thermal conductivities of fluids, and nanoparticles. They claimed that the calculated values could agree well with some available experimental

Thermal Property Measurement of Al2O3-Water Nanofluids 337

Temperature is one of the important factors influencing the thermal conductivity of nanofluids (Das et al., 2003; Li & Peterson, 2006; Yang & Han, 2006). Xuan et al. (2003) considered the Brownian motion of suspended nanoparticles on the basis of the Maxwell model. The prediction from the model is in an agreement with the experiment results, especially when the effect of nanoparticle aggregation is taken into account. But the model may be not accurate for the second term in the equation. Wang et al. (2003) proposed a fractal model for predicting the thermal conductivity of nanofluids based on the effective medium approximation and the fractal theory, developed firstly by Mandelbrot (1982). It can describe the disorder and stochastic process of clustering and polarization of nanoparticles within the mesoscale limit. A comprehensive model considering a large enhancement of thermal conductivity in nanofluids and its strong temperature dependence was deduced from the Stokes-Einstein formula by Kumar et al. (2004). The thermal conductivity enhancement takes into account of the Brownian motion of the particles. However, the validity of the model in the molecular size regime has to be explored and it may not be suitable for a large concentration of the particles where interactions of particles become important. Bhattacharya et al. (2004) developed a technique to compute the effective thermal conductivity of a nanofluid using the Brownian motion simulation. They combined the liquid conductivity and particle conductivity. The model showed a good agreement of the thermal conductivity of nanofluids. Jang & Choi (2004) combined four modes of energy transport in the nanofluids, collision between base fluid molecules, thermal diffusion of nanoparticles in fluids, collision between nanoparticles

data.

or the liquid chemical method (Choi, 1995; Eastman et al., 1997). The processes of drying, storage, transportation, and dispersion of nanoparticles can be avoided, so the aggregation of nanoparticles is minimized and the stability of fluids is increased. But a disadvantage of the method is that only low vapor pressure fluids are compatible with the process. It limits the applications of the method. The two-step method for preparing nanofluids is a process by dispersing nanoparticles into base liquids. Eastman et al. (1997), Lee et al. (1999), and Wang et al. (1999) used this method to produce the Al2O3 nanofluids. Nanoparticles used in the method are firstly produced as a dry powder by inert gas condensation, chemical vapor deposition, mechanical alloying, or the other suitable techniques before the nano-sized powder is then dispersed into a fluid in the second processing step. This step-by-step method isolates the preparation of the nanofluids from the preparation of nanoparticles. As a result, aggregation of nanoparticles may take place in both the steps, especially in the process of drying, storage, and transportation of nanoparticles. The aggregation would not only result in the settlement and clogging, but also affect the thermal properties. The techniques such as ultrasonic agitation or the addition of surfactant into the fluids are often used to minimize particle aggregation and improve dispersion behavior. Since nanopowder synthesis techniques have already been commercialized, there are potential economic advantages in using the two-step synthesis method. But an important problem that needs to be solved is the stabilization of the suspension to be prepared.

Nanofluids are a new class of solid-liquid composite materials consisting of solid nanoparticles, with sizes typically in the order of 1 - 100 nm, suspending in a heat transfer liquid. Nanofluids are expected to have superior properties compared to conventional heat transfer fluids. The much larger relative surface area of nanoparticles should not only significantly improve heat transfer capabilities (Xie et al., 2001), but also increase the stability of the suspensions. In addition, nanofluids can improve abrasion-related properties as compared to the conventional solid/fluid mixtures. Successful applications of nanofluids would support the current trend toward component miniaturization by enabling the design of smaller but higher-power heat exchanger systems (Keblinski et al., 2005). The thermal properties including thermal conductivity, viscosity, and surface tension have been investigated.

#### **1.1 Thermal conductivity of nanofluids**

Since the model reported by Maxwell (1892), the classical models have been derived by Hamilton & Crosser (1962), Bruggeman (1935), and Xuan & Li (2000) for predicting the effective thermal conductivity of a continuum mixture with the assumed well-dispersed solid particles in the base fluid. The Maxwell model was developed to determine the effective thermal conductivity of liquid-solid suspensions for a low volumetric concentration of spherical particles. This model is applicable to statistically homogeneous low volume fraction liquid-solid suspensions with randomly dispersed and uniform spherical particles in size. For non-spherical particles, the thermal conductivity of the nanofluids depends not only on the volume fraction of the particles, but also on the shape of the particles. Hamilton & Crosser (1962) modified the Maxwell model to determine the effective thermal conductivity of nonspherical particles by applying a shape factor for the effective thermal conductivity of two-component mixtures. The Hamilton-Crosser model considers the nanoparticle aggregation. For spherical particles, the Hamilton-Crosser model reduces to the Maxwell model. In the Bruggeman model, the mean field approach is used to analyze the interactions among the randomly distributed particles (Bruggeman, 1935). The model by Xuan & Li (2000) is not specified for any particular shape of particles. However, the classical 2 Will-be-set-by-IN-TECH

or the liquid chemical method (Choi, 1995; Eastman et al., 1997). The processes of drying, storage, transportation, and dispersion of nanoparticles can be avoided, so the aggregation of nanoparticles is minimized and the stability of fluids is increased. But a disadvantage of the method is that only low vapor pressure fluids are compatible with the process. It limits the applications of the method. The two-step method for preparing nanofluids is a process by dispersing nanoparticles into base liquids. Eastman et al. (1997), Lee et al. (1999), and Wang et al. (1999) used this method to produce the Al2O3 nanofluids. Nanoparticles used in the method are firstly produced as a dry powder by inert gas condensation, chemical vapor deposition, mechanical alloying, or the other suitable techniques before the nano-sized powder is then dispersed into a fluid in the second processing step. This step-by-step method isolates the preparation of the nanofluids from the preparation of nanoparticles. As a result, aggregation of nanoparticles may take place in both the steps, especially in the process of drying, storage, and transportation of nanoparticles. The aggregation would not only result in the settlement and clogging, but also affect the thermal properties. The techniques such as ultrasonic agitation or the addition of surfactant into the fluids are often used to minimize particle aggregation and improve dispersion behavior. Since nanopowder synthesis techniques have already been commercialized, there are potential economic advantages in using the two-step synthesis method. But an important problem that needs to be solved is the

Nanofluids are a new class of solid-liquid composite materials consisting of solid nanoparticles, with sizes typically in the order of 1 - 100 nm, suspending in a heat transfer liquid. Nanofluids are expected to have superior properties compared to conventional heat transfer fluids. The much larger relative surface area of nanoparticles should not only significantly improve heat transfer capabilities (Xie et al., 2001), but also increase the stability of the suspensions. In addition, nanofluids can improve abrasion-related properties as compared to the conventional solid/fluid mixtures. Successful applications of nanofluids would support the current trend toward component miniaturization by enabling the design of smaller but higher-power heat exchanger systems (Keblinski et al., 2005). The thermal properties including thermal conductivity, viscosity, and surface tension have been

Since the model reported by Maxwell (1892), the classical models have been derived by Hamilton & Crosser (1962), Bruggeman (1935), and Xuan & Li (2000) for predicting the effective thermal conductivity of a continuum mixture with the assumed well-dispersed solid particles in the base fluid. The Maxwell model was developed to determine the effective thermal conductivity of liquid-solid suspensions for a low volumetric concentration of spherical particles. This model is applicable to statistically homogeneous low volume fraction liquid-solid suspensions with randomly dispersed and uniform spherical particles in size. For non-spherical particles, the thermal conductivity of the nanofluids depends not only on the volume fraction of the particles, but also on the shape of the particles. Hamilton & Crosser (1962) modified the Maxwell model to determine the effective thermal conductivity of nonspherical particles by applying a shape factor for the effective thermal conductivity of two-component mixtures. The Hamilton-Crosser model considers the nanoparticle aggregation. For spherical particles, the Hamilton-Crosser model reduces to the Maxwell model. In the Bruggeman model, the mean field approach is used to analyze the interactions among the randomly distributed particles (Bruggeman, 1935). The model by Xuan & Li (2000) is not specified for any particular shape of particles. However, the classical

stabilization of the suspension to be prepared.

**1.1 Thermal conductivity of nanofluids**

investigated.

models were found to be unable to predict the anomalously high thermal conductivity of nanofluids. This might be because these models do not include the effects of particle size, interfacial layer at the particle/liquid interface, and the Brownian motion of particles (Jang & Choi, 2004; Keblinski et al., 2002; Wang et al., 1999; Yu & Choi, 2003). Recently, Yu & Choi (2003) proposed a modified Maxwell model to account for the effect of the nano-layer by replacing the thermal conductivity of solid particles with the modified thermal conductivity of particles, which is based on the so called effective medium theory (Schwartz et al., 1995). The model can predict the presence of thin nano-layers less than 10 nm in thickness. Yu & Choi (2004) proposed a modified Hamilton-Crosser model to include the particle-liquid interfacial layer for nonspherical particles. The model can predict the thermal conductivity of the carbon nanotube-in-oil nanofluids reasonably well. However, it fails to predict the nonlinear behavior of the effective thermal conductivity of general oxide and metal based nanofluids. Xue (2003) presented a model for the effective thermal conductivity of nanofluids considering the effect of the interface between the solid particles and the base fluid based on the Maxwell model and the average polarization theory. Xue (2003) demonstrated that the model predictions were in a good agreement with the experiments of the nanotube oil-based nanofluids at high thermal conductivity and nonlinearity. However, Yu & Choi (2004) found that the predicted values from the model by Xue are inaccurate by using two incorrect parameters, as same as the finding of Kim et al. (2004). Xue & Xu (2005) obtained an equation for the effective thermal conductivity based on the Bruggeman model (Bruggeman, 1935). The equation takes account of the effect of interfacial shells by replacing the thermal conductivity of nanoparticles with the assumed value of the "complex nanoparticles", which introduces interfacial shells between the nanoparticles and the base fluids. The model can explain the size dependence of the thermal conductivity of nanofluids (Xuan & Li, 2000). Xie et al. (2001) considered the interfacial nano-layer with the linear thermal conductivity distribution and proposed an effective thermal conductivity model to account for the effects of nano-layer thickness, nanoparticles size, volume fraction, and thermal conductivities of fluids, and nanoparticles. They claimed that the calculated values could agree well with some available experimental data.

Temperature is one of the important factors influencing the thermal conductivity of nanofluids (Das et al., 2003; Li & Peterson, 2006; Yang & Han, 2006). Xuan et al. (2003) considered the Brownian motion of suspended nanoparticles on the basis of the Maxwell model. The prediction from the model is in an agreement with the experiment results, especially when the effect of nanoparticle aggregation is taken into account. But the model may be not accurate for the second term in the equation. Wang et al. (2003) proposed a fractal model for predicting the thermal conductivity of nanofluids based on the effective medium approximation and the fractal theory, developed firstly by Mandelbrot (1982). It can describe the disorder and stochastic process of clustering and polarization of nanoparticles within the mesoscale limit. A comprehensive model considering a large enhancement of thermal conductivity in nanofluids and its strong temperature dependence was deduced from the Stokes-Einstein formula by Kumar et al. (2004). The thermal conductivity enhancement takes into account of the Brownian motion of the particles. However, the validity of the model in the molecular size regime has to be explored and it may not be suitable for a large concentration of the particles where interactions of particles become important. Bhattacharya et al. (2004) developed a technique to compute the effective thermal conductivity of a nanofluid using the Brownian motion simulation. They combined the liquid conductivity and particle conductivity. The model showed a good agreement of the thermal conductivity of nanofluids. Jang & Choi (2004) combined four modes of energy transport in the nanofluids, collision between base fluid molecules, thermal diffusion of nanoparticles in fluids, collision between nanoparticles

**1.2 Viscosity of nanofluids**

viscosity of nanofluids.

Viscosity of nanofluids is an important parameter in the fluid transporting. However, the data collected showed that no theoretical models (Batchelor, 1977; Brinkman, 1952; Einstein, 1906; Frankel & Acrivos, 1967; Graham, 1981; Lundgren, 1967) succeed in predicting the viscosity of nanofluids accurately until now. A few theoretical models were used to estimate particle suspension viscosities. Almost all the formulae were derived from the pioneering work of Einstein (1906), which is based on the assumption of a linearly viscous fluid containing the dilute, suspended, and spherical particles. The Einstein formula is found to be valid for relatively low particle volume fractions less than 0.01. Beyond this value, it underestimates the effective viscosity of the mixture. Later, many works have been devoted to the "correction" of his formula. Brinkman (1952) has extended the Einstein formula for use with moderate particle concentration. Lundgren (1967) proposed an equation under the form of a Taylor series. Batchelor (1977) considered the effect of the Brownian motion of particles on the bulk stress of an approximately isotropic suspension of rigid and spherical particles. Graham (1981) generalized the work of Frankel & Acrivos (1967), but the correlation was presented for low concentrations. Almost no model mentioned could predict the viscosity of nanofluids in a wide range of nanoparticle volume fraction so far. According to these correlations the effective viscosity depends only on the viscosity of the base fluid and the concentration of the particles, whereas the experimental studies show that the temperature, the particle diameter, and the kind of nanoparticle can also affect the effective viscosity of a nanofluid. A good understanding of the rheological properties and flow behavior of nanofluids is necessary before nanofluids can be commercialized in the heat transfer applications. These factors influencing the viscosity include concentration, size of nanoparticles, temperature of nanofluids, shear rate, etc. Thus, more thorough investigations should be carried out on the

Thermal Property Measurement of Al2O3-Water Nanofluids 339

In the measurement, the rotational rheometer, the piston-type rheometer, and the capillary viscometer are the most popular tools used to measure the viscosity of nanofluids. Rotational rheomters use the method that the torque required to turn an object in a fluid is a function of the viscosity (Chandrasekar et al., 2010). The relative rotation determines the shear stress under different rates. The advantage of this type of measurement is it is not affected by the flow rate of the fluids. The operation is simple and high repeatable. The piston type rheometer is based on the Couette flow inside a cylindrical chamber (Nguyen et al., 2007). It composes the magnetic coils installed inside a sensor body. These coils are used to generate a magnetically-induced force on a cylindrical piston that moves back and forth over a very small distance, imposing shear stress on the liquid. By powering the coils with a constant force alternatively, the elapsed time corresponding to a round trip of the piston can then be measured. Since the measurement of the piston motion is in two directions, variations due to gravity or flow forces are minimized. Because of the very small mass of the piston, the induced magnetic force would exceed any disturbances due to vibrations. However, the piston type viscometer is that the duration of the heating phase necessary to raise the fluid sample temperature is relative long, especially under the elevated temperature condition, some base fluids may be evaporated. The capillary viscometer is introduced in U-shaped arms (Li et al., 2007). The capillary viscometer is submerged in a glass water tank. A water tank is maintained at a prescribed constant temperature for the capillary viscometer by the water circulation. The vertical angle of the viscometer is accurately controlled with a special tripod. Li et al. (2007) pointed out that the capillary tube diameter may influence the apparent viscosity and result in inaccurate in the nanofluids at higher nanoparticle mass fractions, especially at a lower temperature. In addition, nanoparticles might stain at the inner wall of

due to the Brownian motion, and thermal interaction of dynamic nanoparticles with the base fluid molecules in their model, which considered the effects of concentration, temperature, and particle size. The predictions from this model agree with the experimental data of Lee et al. (1999) and Eastman et al. (2001). However, it may not be suitable in the high temperature since the Brownian motion effect was neglected. Prasher et al. (2005) proposed that the convection caused by the Brownian motion of nanoparticles is primarily responsible for the enhancement in the effective thermal conductivity of nanofluids. By introducing a general correlation for the heat transfer coefficient, they modified the Maxwell model by including the convection of the liquid near the particles due to the Brownian motion. The result showed that the model matched well with the experimental data under different fluid temperature in a certain range. A model for nanofluids, which takes account the effects of particle size, particle volume fraction and temperature dependence as well as properties of the base fluid and the particle subject to the Brownian motion, developed by Koo & Kleinstreuer (2004).

Although many models have been proposed, no theoretical models are available for predicting the thermal conductivity of nanofluids universally up to now. More experimental data are required. Such data should include more studies of the effects of size and shape of the nanoparticles, the interfacial contact resistance between nanoparticles and base fluids, the temperature dependence, the effect of the Brownian motion, or the effect of clustering of particles.

Experimental works have been reported on the thermal conductivity of nanofluids. The main techniques are the transient hot wire (THW) method (Kestin & Wakeham, 1978), the temperature oscillation technique (Wang et al., 1999), and the steady-state parallel-plate method (Das et al., 2003). Among them, the TWH method has been used most extensively. Since most nanofluids are electrically conductive, a modified hot-wire cell with an electrical system was proposed by Nagasaka & Nagashima (1981). The advantage of the method is its almost complete elimination of the effect of natural convection. The measuring principle of the THW technique is based on the calculation of the transient temperature field around a thin hot wire as a line source. A constant current is supplied to the wire to raise its temperature. The heat dissipated in the wire increases the temperature of the wire as well as that of the nanofluids. This temperature rise depends on the thermal conductivity of the nanofluids in which the hot wire is at the center. Therefore, the thermal conductivity value of the fluid can be determined. The oscillation method was proposed by Roetzel et al. (1990) and further developed by Czarnetzki & Roetzel (1995). In principle, the thermal diffusivity of a fluid can be measured very accurately by considering amplitude attenuating of thermal oscillation from the boundary to the center of the fluid. However, for direct measurement of thermal conductivity one has to consider the influence of the reference materials as well. Since the defects of the reference materials might bring out the uncertainty in the thermal conductivity measurement, a direct evaluation of the thermal conductivity of the fluid is less accurate. The apparatus for the steady-state parallel-plate method can be constructed on the basis of the design by Challoner & Powell (1956). The steady-state parallel-plate method needs to measure the temperature increase accurately in each thermocouple (Das et al., 2003). The difference in temperature readings needs to be minimized when the thermocouples are at the same temperature. In this method, it has to follow the assumption that there is no heat loss from the fluid to the surrounding. As a result, guard heaters would be applied to maintain a constant temperature in the fluid. However, it is challenging to control the conditions in which no heat radiated to the surrounding from the fluid. Thus, the TWH method was selected for this study.

#### **1.2 Viscosity of nanofluids**

4 Will-be-set-by-IN-TECH

due to the Brownian motion, and thermal interaction of dynamic nanoparticles with the base fluid molecules in their model, which considered the effects of concentration, temperature, and particle size. The predictions from this model agree with the experimental data of Lee et al. (1999) and Eastman et al. (2001). However, it may not be suitable in the high temperature since the Brownian motion effect was neglected. Prasher et al. (2005) proposed that the convection caused by the Brownian motion of nanoparticles is primarily responsible for the enhancement in the effective thermal conductivity of nanofluids. By introducing a general correlation for the heat transfer coefficient, they modified the Maxwell model by including the convection of the liquid near the particles due to the Brownian motion. The result showed that the model matched well with the experimental data under different fluid temperature in a certain range. A model for nanofluids, which takes account the effects of particle size, particle volume fraction and temperature dependence as well as properties of the base fluid and the particle subject to the Brownian motion, developed by Koo & Kleinstreuer (2004). Although many models have been proposed, no theoretical models are available for predicting the thermal conductivity of nanofluids universally up to now. More experimental data are required. Such data should include more studies of the effects of size and shape of the nanoparticles, the interfacial contact resistance between nanoparticles and base fluids, the temperature dependence, the effect of the Brownian motion, or the effect of clustering of

Experimental works have been reported on the thermal conductivity of nanofluids. The main techniques are the transient hot wire (THW) method (Kestin & Wakeham, 1978), the temperature oscillation technique (Wang et al., 1999), and the steady-state parallel-plate method (Das et al., 2003). Among them, the TWH method has been used most extensively. Since most nanofluids are electrically conductive, a modified hot-wire cell with an electrical system was proposed by Nagasaka & Nagashima (1981). The advantage of the method is its almost complete elimination of the effect of natural convection. The measuring principle of the THW technique is based on the calculation of the transient temperature field around a thin hot wire as a line source. A constant current is supplied to the wire to raise its temperature. The heat dissipated in the wire increases the temperature of the wire as well as that of the nanofluids. This temperature rise depends on the thermal conductivity of the nanofluids in which the hot wire is at the center. Therefore, the thermal conductivity value of the fluid can be determined. The oscillation method was proposed by Roetzel et al. (1990) and further developed by Czarnetzki & Roetzel (1995). In principle, the thermal diffusivity of a fluid can be measured very accurately by considering amplitude attenuating of thermal oscillation from the boundary to the center of the fluid. However, for direct measurement of thermal conductivity one has to consider the influence of the reference materials as well. Since the defects of the reference materials might bring out the uncertainty in the thermal conductivity measurement, a direct evaluation of the thermal conductivity of the fluid is less accurate. The apparatus for the steady-state parallel-plate method can be constructed on the basis of the design by Challoner & Powell (1956). The steady-state parallel-plate method needs to measure the temperature increase accurately in each thermocouple (Das et al., 2003). The difference in temperature readings needs to be minimized when the thermocouples are at the same temperature. In this method, it has to follow the assumption that there is no heat loss from the fluid to the surrounding. As a result, guard heaters would be applied to maintain a constant temperature in the fluid. However, it is challenging to control the conditions in which no heat radiated to the surrounding from the fluid. Thus, the TWH method was selected for

particles.

this study.

Viscosity of nanofluids is an important parameter in the fluid transporting. However, the data collected showed that no theoretical models (Batchelor, 1977; Brinkman, 1952; Einstein, 1906; Frankel & Acrivos, 1967; Graham, 1981; Lundgren, 1967) succeed in predicting the viscosity of nanofluids accurately until now. A few theoretical models were used to estimate particle suspension viscosities. Almost all the formulae were derived from the pioneering work of Einstein (1906), which is based on the assumption of a linearly viscous fluid containing the dilute, suspended, and spherical particles. The Einstein formula is found to be valid for relatively low particle volume fractions less than 0.01. Beyond this value, it underestimates the effective viscosity of the mixture. Later, many works have been devoted to the "correction" of his formula. Brinkman (1952) has extended the Einstein formula for use with moderate particle concentration. Lundgren (1967) proposed an equation under the form of a Taylor series. Batchelor (1977) considered the effect of the Brownian motion of particles on the bulk stress of an approximately isotropic suspension of rigid and spherical particles. Graham (1981) generalized the work of Frankel & Acrivos (1967), but the correlation was presented for low concentrations. Almost no model mentioned could predict the viscosity of nanofluids in a wide range of nanoparticle volume fraction so far. According to these correlations the effective viscosity depends only on the viscosity of the base fluid and the concentration of the particles, whereas the experimental studies show that the temperature, the particle diameter, and the kind of nanoparticle can also affect the effective viscosity of a nanofluid. A good understanding of the rheological properties and flow behavior of nanofluids is necessary before nanofluids can be commercialized in the heat transfer applications. These factors influencing the viscosity include concentration, size of nanoparticles, temperature of nanofluids, shear rate, etc. Thus, more thorough investigations should be carried out on the viscosity of nanofluids.

In the measurement, the rotational rheometer, the piston-type rheometer, and the capillary viscometer are the most popular tools used to measure the viscosity of nanofluids. Rotational rheomters use the method that the torque required to turn an object in a fluid is a function of the viscosity (Chandrasekar et al., 2010). The relative rotation determines the shear stress under different rates. The advantage of this type of measurement is it is not affected by the flow rate of the fluids. The operation is simple and high repeatable. The piston type rheometer is based on the Couette flow inside a cylindrical chamber (Nguyen et al., 2007). It composes the magnetic coils installed inside a sensor body. These coils are used to generate a magnetically-induced force on a cylindrical piston that moves back and forth over a very small distance, imposing shear stress on the liquid. By powering the coils with a constant force alternatively, the elapsed time corresponding to a round trip of the piston can then be measured. Since the measurement of the piston motion is in two directions, variations due to gravity or flow forces are minimized. Because of the very small mass of the piston, the induced magnetic force would exceed any disturbances due to vibrations. However, the piston type viscometer is that the duration of the heating phase necessary to raise the fluid sample temperature is relative long, especially under the elevated temperature condition, some base fluids may be evaporated. The capillary viscometer is introduced in U-shaped arms (Li et al., 2007). The capillary viscometer is submerged in a glass water tank. A water tank is maintained at a prescribed constant temperature for the capillary viscometer by the water circulation. The vertical angle of the viscometer is accurately controlled with a special tripod. Li et al. (2007) pointed out that the capillary tube diameter may influence the apparent viscosity and result in inaccurate in the nanofluids at higher nanoparticle mass fractions, especially at a lower temperature. In addition, nanoparticles might stain at the inner wall of

ml of the de-ionized water to prepare the different volume concentrations (1%, 2%, 3%, 4%, and 5%). Oxide-particle volume concentrations are normally below 5% in order to maintain moderate viscosity increases. To investigate the particle size effect on the thermal conductivity and viscosity, additional four sets of nanofluids each with a constant volume concentration of 5% but with different particle sizes (10 nm, 35 nm, 80 nm and 150 nm) were prepared. Sample preparation is carried out by using a sensitive mass balance with an accuracy of 0.1 mg. The volume fraction of the powder is calculated from the weight of dry powder using the density

Thermal Property Measurement of Al2O3-Water Nanofluids 341

vol% <sup>=</sup> *<sup>m</sup>*/*<sup>ρ</sup>*

The surfactant, CTAB with the density is 1.3115 g/cm3 at volume percentage of around 0.01-0.02 can stabilize the nanofluids (Sakamoto et al., 2002). The amount of 0.01 vol % CTAB was added into the Al2O3 water-based nanofluids to keep the nanoparticles well dispersed in

The nanofluid was then stirred by a magnetic stirrer for 8 hours before undergoing ultrasonicfication process (Fisher Scientific Model 500) for one and a half hours. This is to ensure uniform dispersion of nanoparticles and also to prevent the nanoparticles from the

In the study, we adopted the THW technique for measuring thermal conductivity, as shown in Fig. 1. The setup consists of a direct current (DC) power supply, a Wheatstone bridge

R2 (50Ω)

Vs

Wheatstone

bridge

R3 (2.7Ω)

R

Rw (2.37Ω)

Vg

DAQ

PC

Thermostat water bath

R1 (100Ω)

circuit, and a thin platinum wire surrounded by a circular nanofluid container, which is maintained by a thermostat bath. The DC power supply provides a constant voltage source to the Wheatstone bridge circuit at a constant rate to allow a uniform increment of temperature with respect to time. As the resistors used in this experiment have low values of resistance, V*s* is adjusted to a value of between 0 to 2.5V. A data acquisition unit (Yokogawa Electric Corporation, DaqMaster MW100) is applied to capture the readings, recorded in a computer. The voltage supplied by the stabilizer, the voltage supplied in the Wheatstone circuit, the

where *m* and *ρ* are the mass and density of the Al2O3 nanoparticles respectively.

<sup>100</sup>*ml*water <sup>+</sup> *<sup>m</sup>*/*<sup>ρ</sup>* (1)

provided by the supplier and the total volume of the suspension.

**2.2 Thermal conductivity measurement of Al**2**O**<sup>3</sup> **nanofluids**

R4 (5.62Ω)

Switch

rezlili bat S

Fig. 1. Schematics of the THW setup (Kwek et al., 2010).

the base fluid, water.

aggregation in the nanofluids.

DC Power

the bore. Because of the narrow diameter, cleaning is difficult if the nanoparticles are left. In our study, we adopted the rotational rheometer to measure the viscosity of nanofluids because of its simplicity and repeatability.

### **1.3 Surface tension of nanofluids**

Interfacial properties such as surface tension play an important role for the fluids having a free surface, however, the studies of the interfacial properties of nanofluids are limited. An understanding of nanofluid properties is essential so that we can optimize the usage of nanofluids and understand their limitations. The temperature dependence of surface tension of the liquid is crucial in the bubble or droplet formation. Wasan & Nikolov (2003) studied the spreading of nanofluids on solid surfaces and found that the existence of nanoparticles near the liquid/solid contact line can improve its spreading. Vafaei et al. (2009) investigated the effects of size and concentration of nanoparticles on the effective gas-liquid surface tension of the aqueous solutions of the bismuth telluride nanoparticles. Kumar & Milanova (2009) found that the single-walled carbon nanotube suspensions in a boiling environment can extend the saturated boiling regime and postpone catastrophic failure of the materials even further than that previously reported if the surface tension of the nanofluids is carefully controlled. The surface tension of a liquid strongly depends on the presence of contaminants or dispersion agents such as surfactants.

Pendant droplet analysis is a convenient way to measure surface tension of fluids. It is assumed that the droplet is symmetric and the drop is not in motion. The advantage of the technique is that the calibration is straightforward, only based on the optical magnification. This can lead to a high accuracy. Another advantage is that the cleanliness requirement is not high. Surface tension is determined by fitting the shape of the droplet to the Young-Laplace equation which relates surface tension to droplet shape. Pantzali et al. (2009) used the pendant droplet method to measure the surface tension of the CuO water-based nanofluids. The other common method to measure surface tension is the capillary method (Golubovic et al., 2009). The main component of the device is a capillary tube in which the liquids would show a significant rise with a meniscus due to the surface tension in order to balance the gravity force. The disadvantage of the capillary method is that cleaning is difficult if the nanoparticles are left in the small diameter capillary. Thus, the pendant drop technique was selected in this study.

In sum, the reported thermal property measurement are scattered, and lack of agreement with the models. It might be due to various factors such as the measuring technique, particle size, base fluid, volume fraction of nanoparticles in fluids, temperature, etc. The lack of reliable experimental data is one of the main reasons for no universal theoretical or empirical models. Therefore, we investigated the thermal properties of the Al2O3 water-based nanofluids. The thermal conductivity, viscosity, and surface tension were measured. The effects of particle volume fraction, temperature and particle size were discussed at the end of experiments.

## **2. Experimental procedure**

## **2.1 Preparation of Al**2**O**<sup>3</sup> **nanofluids**

As discussed by Kwek et al. (2010), different sizes of the Al2O3 nanoparticles and the surfactant, Cetyltrimethylammonium Bromide (CTAB), were purchased from Sigma Nanoamor and Aldrich respectively. During the experiments, we dispersed the Al2O3 nanoparticles with an average diameter of 25 nm and particle density of 3.7 g/cm<sup>3</sup> into 100 6 Will-be-set-by-IN-TECH

the bore. Because of the narrow diameter, cleaning is difficult if the nanoparticles are left. In our study, we adopted the rotational rheometer to measure the viscosity of nanofluids because

Interfacial properties such as surface tension play an important role for the fluids having a free surface, however, the studies of the interfacial properties of nanofluids are limited. An understanding of nanofluid properties is essential so that we can optimize the usage of nanofluids and understand their limitations. The temperature dependence of surface tension of the liquid is crucial in the bubble or droplet formation. Wasan & Nikolov (2003) studied the spreading of nanofluids on solid surfaces and found that the existence of nanoparticles near the liquid/solid contact line can improve its spreading. Vafaei et al. (2009) investigated the effects of size and concentration of nanoparticles on the effective gas-liquid surface tension of the aqueous solutions of the bismuth telluride nanoparticles. Kumar & Milanova (2009) found that the single-walled carbon nanotube suspensions in a boiling environment can extend the saturated boiling regime and postpone catastrophic failure of the materials even further than that previously reported if the surface tension of the nanofluids is carefully controlled. The surface tension of a liquid strongly depends on the presence of contaminants or dispersion

Pendant droplet analysis is a convenient way to measure surface tension of fluids. It is assumed that the droplet is symmetric and the drop is not in motion. The advantage of the technique is that the calibration is straightforward, only based on the optical magnification. This can lead to a high accuracy. Another advantage is that the cleanliness requirement is not high. Surface tension is determined by fitting the shape of the droplet to the Young-Laplace equation which relates surface tension to droplet shape. Pantzali et al. (2009) used the pendant droplet method to measure the surface tension of the CuO water-based nanofluids. The other common method to measure surface tension is the capillary method (Golubovic et al., 2009). The main component of the device is a capillary tube in which the liquids would show a significant rise with a meniscus due to the surface tension in order to balance the gravity force. The disadvantage of the capillary method is that cleaning is difficult if the nanoparticles are left in the small diameter capillary. Thus, the pendant drop technique was selected in this

In sum, the reported thermal property measurement are scattered, and lack of agreement with the models. It might be due to various factors such as the measuring technique, particle size, base fluid, volume fraction of nanoparticles in fluids, temperature, etc. The lack of reliable experimental data is one of the main reasons for no universal theoretical or empirical models. Therefore, we investigated the thermal properties of the Al2O3 water-based nanofluids. The thermal conductivity, viscosity, and surface tension were measured. The effects of particle volume fraction, temperature and particle size were discussed at the end of experiments.

As discussed by Kwek et al. (2010), different sizes of the Al2O3 nanoparticles and the surfactant, Cetyltrimethylammonium Bromide (CTAB), were purchased from Sigma Nanoamor and Aldrich respectively. During the experiments, we dispersed the Al2O3 nanoparticles with an average diameter of 25 nm and particle density of 3.7 g/cm<sup>3</sup> into 100

of its simplicity and repeatability.

**1.3 Surface tension of nanofluids**

agents such as surfactants.

**2. Experimental procedure**

**2.1 Preparation of Al**2**O**<sup>3</sup> **nanofluids**

study.

ml of the de-ionized water to prepare the different volume concentrations (1%, 2%, 3%, 4%, and 5%). Oxide-particle volume concentrations are normally below 5% in order to maintain moderate viscosity increases. To investigate the particle size effect on the thermal conductivity and viscosity, additional four sets of nanofluids each with a constant volume concentration of 5% but with different particle sizes (10 nm, 35 nm, 80 nm and 150 nm) were prepared. Sample preparation is carried out by using a sensitive mass balance with an accuracy of 0.1 mg. The volume fraction of the powder is calculated from the weight of dry powder using the density provided by the supplier and the total volume of the suspension.

$$\text{vo1}\,\text{\\$} = \frac{m/\rho}{100ml\,\text{water} + m/\rho} \tag{1}$$

where *m* and *ρ* are the mass and density of the Al2O3 nanoparticles respectively.

The surfactant, CTAB with the density is 1.3115 g/cm3 at volume percentage of around 0.01-0.02 can stabilize the nanofluids (Sakamoto et al., 2002). The amount of 0.01 vol % CTAB was added into the Al2O3 water-based nanofluids to keep the nanoparticles well dispersed in the base fluid, water.

The nanofluid was then stirred by a magnetic stirrer for 8 hours before undergoing ultrasonicfication process (Fisher Scientific Model 500) for one and a half hours. This is to ensure uniform dispersion of nanoparticles and also to prevent the nanoparticles from the aggregation in the nanofluids.

#### **2.2 Thermal conductivity measurement of Al**2**O**<sup>3</sup> **nanofluids**

In the study, we adopted the THW technique for measuring thermal conductivity, as shown in Fig. 1. The setup consists of a direct current (DC) power supply, a Wheatstone bridge

Fig. 1. Schematics of the THW setup (Kwek et al., 2010).

circuit, and a thin platinum wire surrounded by a circular nanofluid container, which is maintained by a thermostat bath. The DC power supply provides a constant voltage source to the Wheatstone bridge circuit at a constant rate to allow a uniform increment of temperature with respect to time. As the resistors used in this experiment have low values of resistance, V*s* is adjusted to a value of between 0 to 2.5V. A data acquisition unit (Yokogawa Electric Corporation, DaqMaster MW100) is applied to capture the readings, recorded in a computer. The voltage supplied by the stabilizer, the voltage supplied in the Wheatstone circuit, the

slope and intersect.

*Vg* <sup>=</sup> *<sup>R</sup>*<sup>3</sup>

conductivity to be determined, and *C* = exp(0.5772).

The average thermal conductivity was then determined.

conductivity values is in ±2% from the documental data.

Fig. 3. The image of the controlled shear rate rheometer (Contraves LS 40).

As shown in Fig. 3, the controlled shear rate rheometer (Contraves LS 40) was applied to measure the viscosity of the Al2O3 nanofluids. The rheometer has a cup and bob geometry. The bob is connected to the spindle drive while the cup is mounted onto the rheometer. As the cup is rotated, the viscous drag of the fluid against the spindle is measured by the deflection of the torsion wire. The cup and bob geometry requires a sample volume of around 5 ml, hence, the temperature equilibrium can be achieved quickly within 5 minutes. The spindle type and speed combination would produce satisfactory results when the applied torque is up to 100% of the maximum permissible torque. In the measurement, the cup was placed onto the rheometer while the bob was inserted into the top shaft. The nanofluids were then transferred to the cup in preventing any bubbles forming. Afterwards, the bob was lowered down until

**2.3 Viscosity measurement of Al**2**O**<sup>3</sup> **nanofluids**

(*R*<sup>3</sup> <sup>+</sup> *Rw*)<sup>2</sup> (*βRw*)

*Vsq* 4*πk*

where V*g* can be obtained directly from the Wheatstone bridge circuit, V*s* is the voltage supplied, R*<sup>w</sup>* is the known resistance of the Pt wire, R3 is the resistance along same branch of Wheatstone circuit, *q* is the heat rate per unit length, *α* is the thermal diffusivity of the surrounding medium, *β* is the resistance-temperature coefficient of the wire, *k* is the thermal

Thermal Property Measurement of Al2O3-Water Nanofluids 343

Figure 2 shows a sample of the unbalanced voltage (V*g*) as a function of the natural logarithm of time. The best fitting with R2 >0.993 was applied to determine the thermal conductivity.

Before the experiments of nanofluids, the THW setup was calibrated with the de-ionized water, the procedure was as same as the experimental process for measuring the thermal conductivity of nanofluids. The calibration showed that the accuracy of the measured thermal

(ln *<sup>t</sup>* <sup>+</sup> ln <sup>4</sup>*<sup>α</sup>*

*<sup>a</sup>*2*<sup>C</sup>* ) (2)

voltage for the platinum wire and the voltage across bridge (V*g*) can be monitored during the experiments. The main experimental cell is a part of the Wheatstone bridge circuit since the wire is used as one arm of the bridge circuit. Teflon spray is used for coating a platinum (Pt) wire to act as an electric insulation because the Al2O3 nanofluids are electrically conductive. The Pt wire has good resistance as a function of temperature over a wide temperature range. The resistance-temperature coefficient of the Pt wire is 0.0039092 ◦C (Bentley, 1984). The Pt wire of 100 *μ*m in diameter and 180 mm in length was used in the hot-wire cell whose electric resistance was measured. The dimensions of the nanofluid container are chosen to be sufficiently large to be considered as infinite in comparison with the diameter of the Pt wire. The volume and diameter of the nanofluid container are 100 ml and 30 mm respectively.

Fig. 2. V*g* as a function of (ln t) with the linear fitting curve.

To investigate the effect of temperature from 15 to 55 ◦C on the thermal conductivities of the nanofluids, the nanofluid container was enclosed with an acrylic container connected to a thermostat bath. Different temperatures of nanofluids can be reached during the measurement process. The nanofluid temperature was monitored with a thermocouple. In the measurement of the thermal conductivity of the Al2O3 nanofluids, the cylindrical shaped nanofluid container was filled with 100 ml of the Al2O3 water-based nanofluid. The required temperature was set at the thermostat to maintain a uniform temperature in the nanofluid. Then the DC power source was switched on with the input voltage (V*s*) being adjusted to 0.5 V while the switch in the circuit remained on the stabilizer resistor (R4 in Fig. 1) circuit. Thereafter, the switch was turned to the Wheatstone bridge circuit and V*g* (Fig. 1) was balanced by adjusting manually the variable resistor in circuit. Once there was no voltage change, the circuit was considered as being balanced. Again, it was switched back to the stabilizer resistor circuit and input voltage V*s* was then set to the desired value of 2.0 V before the switch was set back to the Wheatstone bridge circuit. The unbalanced voltage change (V*g*) occurring in the hot wire was recorded for 10 seconds in the computer via a data acquisition unit. The input voltage to the circuit was also recorded for each run. This measured unbalanced voltage over the natural logarithm of time was plotted in Fig. 2 by using Equation (2) (Kwek et al., 2010). The thermal conductivity is then calculated from the

slope and intersect.

8 Will-be-set-by-IN-TECH

voltage for the platinum wire and the voltage across bridge (V*g*) can be monitored during the experiments. The main experimental cell is a part of the Wheatstone bridge circuit since the wire is used as one arm of the bridge circuit. Teflon spray is used for coating a platinum (Pt) wire to act as an electric insulation because the Al2O3 nanofluids are electrically conductive. The Pt wire has good resistance as a function of temperature over a wide temperature range. The resistance-temperature coefficient of the Pt wire is 0.0039092 ◦C (Bentley, 1984). The Pt wire of 100 *μ*m in diameter and 180 mm in length was used in the hot-wire cell whose electric resistance was measured. The dimensions of the nanofluid container are chosen to be sufficiently large to be considered as infinite in comparison with the diameter of the Pt wire. The volume and diameter of the nanofluid container are 100 ml and 30 mm respectively.

All experimental data

Selected data to satisfy R2>0.993

Vg = 0.5749 ln t + 2.6014

R² = 0.9966


ln t

To investigate the effect of temperature from 15 to 55 ◦C on the thermal conductivities of the nanofluids, the nanofluid container was enclosed with an acrylic container connected to a thermostat bath. Different temperatures of nanofluids can be reached during the measurement process. The nanofluid temperature was monitored with a thermocouple. In the measurement of the thermal conductivity of the Al2O3 nanofluids, the cylindrical shaped nanofluid container was filled with 100 ml of the Al2O3 water-based nanofluid. The required temperature was set at the thermostat to maintain a uniform temperature in the nanofluid. Then the DC power source was switched on with the input voltage (V*s*) being adjusted to 0.5 V while the switch in the circuit remained on the stabilizer resistor (R4 in Fig. 1) circuit. Thereafter, the switch was turned to the Wheatstone bridge circuit and V*g* (Fig. 1) was balanced by adjusting manually the variable resistor in circuit. Once there was no voltage change, the circuit was considered as being balanced. Again, it was switched back to the stabilizer resistor circuit and input voltage V*s* was then set to the desired value of 2.0 V before the switch was set back to the Wheatstone bridge circuit. The unbalanced voltage change (V*g*) occurring in the hot wire was recorded for 10 seconds in the computer via a data acquisition unit. The input voltage to the circuit was also recorded for each run. This measured unbalanced voltage over the natural logarithm of time was plotted in Fig. 2 by using Equation (2) (Kwek et al., 2010). The thermal conductivity is then calculated from the

1.0

Fig. 2. V*g* as a function of (ln t) with the linear fitting curve.

1.5

2.0

2.5

3.0

Voltage change, Vg (mV)

3.5

4.0

4.5

5.0

$$V\_{\mathcal{S}} = \frac{R\_3}{(R\_3 + R\_w)^2} (\beta R\_w) \frac{V\_s q}{4\pi k} (\ln t + \ln \frac{4\alpha}{a^2 \mathcal{C}}) \tag{2}$$

where V*g* can be obtained directly from the Wheatstone bridge circuit, V*s* is the voltage supplied, R*<sup>w</sup>* is the known resistance of the Pt wire, R3 is the resistance along same branch of Wheatstone circuit, *q* is the heat rate per unit length, *α* is the thermal diffusivity of the surrounding medium, *β* is the resistance-temperature coefficient of the wire, *k* is the thermal conductivity to be determined, and *C* = exp(0.5772).

Figure 2 shows a sample of the unbalanced voltage (V*g*) as a function of the natural logarithm of time. The best fitting with R2 >0.993 was applied to determine the thermal conductivity. The average thermal conductivity was then determined.

Before the experiments of nanofluids, the THW setup was calibrated with the de-ionized water, the procedure was as same as the experimental process for measuring the thermal conductivity of nanofluids. The calibration showed that the accuracy of the measured thermal conductivity values is in ±2% from the documental data.

## **2.3 Viscosity measurement of Al**2**O**<sup>3</sup> **nanofluids**

Fig. 3. The image of the controlled shear rate rheometer (Contraves LS 40).

As shown in Fig. 3, the controlled shear rate rheometer (Contraves LS 40) was applied to measure the viscosity of the Al2O3 nanofluids. The rheometer has a cup and bob geometry. The bob is connected to the spindle drive while the cup is mounted onto the rheometer. As the cup is rotated, the viscous drag of the fluid against the spindle is measured by the deflection of the torsion wire. The cup and bob geometry requires a sample volume of around 5 ml, hence, the temperature equilibrium can be achieved quickly within 5 minutes. The spindle type and speed combination would produce satisfactory results when the applied torque is up to 100% of the maximum permissible torque. In the measurement, the cup was placed onto the rheometer while the bob was inserted into the top shaft. The nanofluids were then transferred to the cup in preventing any bubbles forming. Afterwards, the bob was lowered down until

In the experiments, the Al2O3 nanofluids with a certain volume concentration were filled into the syringe, which was held at the loading platform as shown in Fig. 4a. Once a pendant nanofluid droplet was formed, the image of droplet was taken. The surface tension, the

Thermal Property Measurement of Al2O3-Water Nanofluids 345

The calibration was conducted with the de-ionized water before the surface tension of nanofluid was measured. It was found that the surface tension of pure water was 72.93 ± 1.01 mN/m at room temperature. The value is very close to the standard value at 71.97 mN/m

> Hamilton-Crosser Model Bruggeman Model Yu & Choi Model This study Eastman et al. 1997 Das et al. 2003 Li &Peterson 2006

0 0.02 0.04 0.06

Fig. 5. Thermal conductivity enhancement as a function of volume concentrations of Al2O3

Each of the experimental data represents the average of six measurements at a specific concentration under room temperature. As shown in Fig. 5, the effective thermal conductivity ratio (k*eff*/k*f*) of the nanofluids is plotted as a function of nanoparticle volume fraction for a series of the Al2O3 nanofluids prepared from 25 nm Al2O3 powders and measured at 25 ◦C. k*eff* is the measured thermal conductivity of the nanofluids and k*<sup>f</sup>* is the thermal conductivity of pure water. Figure 5 also illustrates the data reported by Eastman et al. (1997) (33 nm), Das et al. (2003) (38.4 nm), Li & Peterson (2006) (36 nm), and the prediction from the Hamilton-Crosser model (Hamilton & Crosser, 1962), Bruggeman model (Bruggeman, 1935), and the modified model by Yu & Choi (2003). Direct quantitative comparisons are not possible in this case as the particle size used by the other researchers differs from this experimental results (25 nm). It can be noted that the previous experimental results, the predicted thermal conductivity, and the measured values in the study increase with an

**Par�cle volume frac�on**

droplet volume, and the surface area were then computed.

**3.1.1 Effect of volume concentration on thermal conductivity**

(Vargaftik et al., 1983).

**3. Results and discussion**

**3.1 Thermal conductivity of Al**2**O**<sup>3</sup> **nanofluids**

1.00

1.05

1.10

1.15

**keff/kf**

water-based nanofluids at 25 ◦C.

1.20

1.25

1.30

it was completely inserted into the cup and immersed in the nanofluids. The lever knob was then adjusted until the bob and cup were concentric. After the measuring settings such as the minimum and maximum shear rates were set, the experiment was run. The viscosity as a function of the shear rate was plotted.

For the temperature effect, the rheological property of the nanofluids was measured by the viscometer with the thermostat, which controls temperature in Fig. 3. The viscosity measurement was started at 15 ◦C, and temperature was gradually increased to 55 ◦C at an interval of 10 ◦C. The nanofluid temperature was also measured by using a thermocouple. All the viscosity measurements were recorded at steady state conditions.

Before the measurement of nanofluids, the viscometer was calibrated with the de-ionized water, having an error within ± 1%.

## **2.4 Surface tension measurement of Al**2**O**<sup>3</sup> **nanofluids**

Fig. 4. Surface tension measurement for Al2O3 water-based nanofluids, (a) FTA 200 system; (b) a pendant droplet of the fluid for measurement.

The surface tension of the Al2O3 water-based nanofluids under different volume concentrations was measured with First Ten Angstroms (FTA) 200, illustrated in Fig. 4a. The precision syringe pumps (KD Scientific Inc., USA) was used to drive the Al2O3 water-based nanofluids to form a pendant droplet as shown in Fig. 4b. An epi-fluorescent inverted microscope with a filter set (Nikon B-2A, excitation filter for 450 - 490 nm, dichroic mirror for 505 nm and emission filter for 520 nm) was used to monitor the hanging droplet . A sensitive interline transfer CCD camera (HiSense MKII, Dantec Dynamics, Denmark) was employed for recording the droplet shape.

In the experiments, the Al2O3 nanofluids with a certain volume concentration were filled into the syringe, which was held at the loading platform as shown in Fig. 4a. Once a pendant nanofluid droplet was formed, the image of droplet was taken. The surface tension, the droplet volume, and the surface area were then computed.

The calibration was conducted with the de-ionized water before the surface tension of nanofluid was measured. It was found that the surface tension of pure water was 72.93 ± 1.01 mN/m at room temperature. The value is very close to the standard value at 71.97 mN/m (Vargaftik et al., 1983).

### **3. Results and discussion**

10 Will-be-set-by-IN-TECH

it was completely inserted into the cup and immersed in the nanofluids. The lever knob was then adjusted until the bob and cup were concentric. After the measuring settings such as the minimum and maximum shear rates were set, the experiment was run. The viscosity as a

For the temperature effect, the rheological property of the nanofluids was measured by the viscometer with the thermostat, which controls temperature in Fig. 3. The viscosity measurement was started at 15 ◦C, and temperature was gradually increased to 55 ◦C at an interval of 10 ◦C. The nanofluid temperature was also measured by using a thermocouple. All

Before the measurement of nanofluids, the viscometer was calibrated with the de-ionized

Fig. 4. Surface tension measurement for Al2O3 water-based nanofluids, (a) FTA 200 system;

The surface tension of the Al2O3 water-based nanofluids under different volume concentrations was measured with First Ten Angstroms (FTA) 200, illustrated in Fig. 4a. The precision syringe pumps (KD Scientific Inc., USA) was used to drive the Al2O3 water-based nanofluids to form a pendant droplet as shown in Fig. 4b. An epi-fluorescent inverted microscope with a filter set (Nikon B-2A, excitation filter for 450 - 490 nm, dichroic mirror for 505 nm and emission filter for 520 nm) was used to monitor the hanging droplet . A sensitive interline transfer CCD camera (HiSense MKII, Dantec Dynamics, Denmark) was employed

the viscosity measurements were recorded at steady state conditions.

**(b)**

**2.4 Surface tension measurement of Al**2**O**<sup>3</sup> **nanofluids**

function of the shear rate was plotted.

water, having an error within ± 1%.

**(a)**

for recording the droplet shape.

(b) a pendant droplet of the fluid for measurement.

## **3.1 Thermal conductivity of Al**2**O**<sup>3</sup> **nanofluids**

#### **3.1.1 Effect of volume concentration on thermal conductivity**

Fig. 5. Thermal conductivity enhancement as a function of volume concentrations of Al2O3 water-based nanofluids at 25 ◦C.

Each of the experimental data represents the average of six measurements at a specific concentration under room temperature. As shown in Fig. 5, the effective thermal conductivity ratio (k*eff*/k*f*) of the nanofluids is plotted as a function of nanoparticle volume fraction for a series of the Al2O3 nanofluids prepared from 25 nm Al2O3 powders and measured at 25 ◦C. k*eff* is the measured thermal conductivity of the nanofluids and k*<sup>f</sup>* is the thermal conductivity of pure water. Figure 5 also illustrates the data reported by Eastman et al. (1997) (33 nm), Das et al. (2003) (38.4 nm), Li & Peterson (2006) (36 nm), and the prediction from the Hamilton-Crosser model (Hamilton & Crosser, 1962), Bruggeman model (Bruggeman, 1935), and the modified model by Yu & Choi (2003). Direct quantitative comparisons are not possible in this case as the particle size used by the other researchers differs from this experimental results (25 nm). It can be noted that the previous experimental results, the predicted thermal conductivity, and the measured values in the study increase with an

the nanofluids of 1 vol %, 3 vol %, and 5 vol %. With 1 vol % particles at about 15 ◦C, the enhancement is only about 1.7 %, but about 16 % at 55 ◦C. The present measurement shows that a higher enhancement can be achieved in the nanofluid having small volume ratio of nanoparticles in the fluids at a higher temperature. The measurement of 3 vol % and 5 vol % nanofluids shown in Fig. 6 demonstrates the enhancement goes from 6 % to 24 % and 15 % to 34 % respectively as a function of temperature from 15 to 55 ◦C. The average rate of enhancement in these cases is higher compared with that of 1 vol % nanofluids. The increasing slope of the fitted line of the 1 vol %, 3 vol %, or 5 vol % nanofluids has a gradient of 0.003575, 0.0045 or 0.00475 respectively. Thus it can be said that the enhancement of thermal conductivity with increases of temperature depends on the concentration of nanoparticles. The above trends are also explained by the experimental results of Das et al. (2003) (38.4 nm) and Chon et al. (2005) (47 nm) in Fig. 6. From the data of Das et al., the increasing rates are 0.002 and 0.005 for 1 vol % and 4 vol %, whereas the results of Chon et al. show the increasing rates of 0.001 and 0.003 for the nanofluids at 1 vol % and 4 vol %. The increasing trends

Thermal Property Measurement of Al2O3-Water Nanofluids 347

0 0.01 0.02 0.03 0.04 0.05 0.06

**Par�cle Volume Frac�on**

Fig. 7. Enhancement of thermal conductivity of the Al2O3 water-based nanofluids against

Figure 7 shows that there is a close agreement between the measured thermal conductivity and the Hamilton-Crosser and the Bruggeman models at 15 ◦C. However, this agreement is only at the low temperature. At higher temperature, the experiments of the Al2O3 water-based nanofluids disagree with the models. It is suggested that the present models cannot reflect on the effective conductivity with temperature. Das et al. (2003) stated that the main mechanism of the thermal conductivity enhancement in nanofluids can be thought as the stochastic motion of nanoparticles, and that the Brownian motion would depend on the fluid temperature. This enhancement in our experiments can be supported by the results of Das et al. (2003) and Chon et al. (2005). Their data have the maximum enhancements of 25 % and 19 % for 4 vol % at 55 ◦C whereas the Hamilton-Crosser model (Hamilton & Crosser, 1962) and the Bruggeman model (Bruggeman, 1935) predict only 12 % and 13 %, regardless of the temperature effect. At the low temperature, the Brownian motion was less significant. Thus the present results indicate that it is possible to have a threshold temperature at which the effective thermal conductivity of nanofluids starts deviating from that of the usual suspension and the enhancement through the stochastic motion of the particles starts

observed are quite similar.

1.00

particles concentration and comparison with models.

1.05

1.10

1.15

1.20

**keff/kf**

1.25

1.30

1.35

This study 15 °C

This study 25 °C This study 35 °C This study 45 °C This study 55 °C

Hamilton-Crosser model Bruggeman model

increase of nanoparticle concentration in a distinct linear fashion. However, the slopes are not same. From our experimental results, it is found that a small volume percentage at 1 - 5% addition of the Al2O3 nanoparticles in the water significantly increases the effective thermal conductivity of the Al2O3 water-based nanofluids by 6 to 20% respectively. If we disregard the minor differences in the particles size, clear discrepancies were found between the previous experimental data and ours on the amount of enhancement in Fig. 5. This difference may be caused by the various factors such as the different particle preparation, the particle source, or even the measurement technique. Up to now, there are no standard guidelines on the preparation of nanofluids such as the amount and type of surfactant added, the time duration for ultrasonification process, the measurement method and procedures, and the size and shape of nanoparticles in use. All these might add up to account for the difference in the experimental data.

By comparing the percentage difference in the effective thermal conductivity ratio with the measured values, our data are more consistent with the predicted values of the Yu & Choi correlation than those of the other correlations, especially at a high volume concentration where the percentage difference at 0.04 and 0.05 volume fraction is around 0.4 % and 1 % respectively. Thus, the conventional models underestimate the thermal conductivity enhancement when compared against the measured values. The reason may be that the present proposed models did not take into account the additional mechanisms such as the interfacial layer, the Brownian motion, the size and the shape of nanoparticles, and the nanoparticle aggregation. At this stage, most of these aforementioned mechanisms are neither well established nor well understood. Therefore, more experimental works are required before the concrete conclusions can be inferred from the thermal behavior of nanofluids.

#### **3.1.2 Effect of temperature on thermal conductivity**

Fig. 6. Temperature dependence of thermal conductivity enhancement for the Al2O3 water-based nanofluids.

The effective thermal conductivity ratio (k*eff*/k*f*) is expressed with a reference of the measured value of water at the related temperatures. The measurement was made for the Al2O3 water-based nanofluids with the given particle concentrations at different temperatures. Figure 6 shows the enhancement of thermal conductivity of Al2O3 nanofluids with temperature. There is a considerable increase in the enhancement from 15 to 55 ◦C in 12 Will-be-set-by-IN-TECH

increase of nanoparticle concentration in a distinct linear fashion. However, the slopes are not same. From our experimental results, it is found that a small volume percentage at 1 - 5% addition of the Al2O3 nanoparticles in the water significantly increases the effective thermal conductivity of the Al2O3 water-based nanofluids by 6 to 20% respectively. If we disregard the minor differences in the particles size, clear discrepancies were found between the previous experimental data and ours on the amount of enhancement in Fig. 5. This difference may be caused by the various factors such as the different particle preparation, the particle source, or even the measurement technique. Up to now, there are no standard guidelines on the preparation of nanofluids such as the amount and type of surfactant added, the time duration for ultrasonification process, the measurement method and procedures, and the size and shape of nanoparticles in use. All these might add up to account for the difference in the

By comparing the percentage difference in the effective thermal conductivity ratio with the measured values, our data are more consistent with the predicted values of the Yu & Choi correlation than those of the other correlations, especially at a high volume concentration where the percentage difference at 0.04 and 0.05 volume fraction is around 0.4 % and 1 % respectively. Thus, the conventional models underestimate the thermal conductivity enhancement when compared against the measured values. The reason may be that the present proposed models did not take into account the additional mechanisms such as the interfacial layer, the Brownian motion, the size and the shape of nanoparticles, and the nanoparticle aggregation. At this stage, most of these aforementioned mechanisms are neither well established nor well understood. Therefore, more experimental works are required before the concrete conclusions can be inferred from the thermal behavior of nanofluids.

0 20 40 60

The effective thermal conductivity ratio (k*eff*/k*f*) is expressed with a reference of the measured value of water at the related temperatures. The measurement was made for the Al2O3 water-based nanofluids with the given particle concentrations at different temperatures. Figure 6 shows the enhancement of thermal conductivity of Al2O3 nanofluids with temperature. There is a considerable increase in the enhancement from 15 to 55 ◦C in

Fig. 6. Temperature dependence of thermal conductivity enhancement for the Al2O3

**Temperature (oC)**

Das et al. (4 vol %) Chon et al. (1 vol %) Chon et al. (4 Vol %)

experimental data.

**3.1.2 Effect of temperature on thermal conductivity**

This study (1 vol %) This study (3 vol %) This study (5 vol %) Das et al. (1 vol %)

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35

**keff/kf**

water-based nanofluids.

the nanofluids of 1 vol %, 3 vol %, and 5 vol %. With 1 vol % particles at about 15 ◦C, the enhancement is only about 1.7 %, but about 16 % at 55 ◦C. The present measurement shows that a higher enhancement can be achieved in the nanofluid having small volume ratio of nanoparticles in the fluids at a higher temperature. The measurement of 3 vol % and 5 vol % nanofluids shown in Fig. 6 demonstrates the enhancement goes from 6 % to 24 % and 15 % to 34 % respectively as a function of temperature from 15 to 55 ◦C. The average rate of enhancement in these cases is higher compared with that of 1 vol % nanofluids. The increasing slope of the fitted line of the 1 vol %, 3 vol %, or 5 vol % nanofluids has a gradient of 0.003575, 0.0045 or 0.00475 respectively. Thus it can be said that the enhancement of thermal conductivity with increases of temperature depends on the concentration of nanoparticles. The above trends are also explained by the experimental results of Das et al. (2003) (38.4 nm) and Chon et al. (2005) (47 nm) in Fig. 6. From the data of Das et al., the increasing rates are 0.002 and 0.005 for 1 vol % and 4 vol %, whereas the results of Chon et al. show the increasing rates of 0.001 and 0.003 for the nanofluids at 1 vol % and 4 vol %. The increasing trends observed are quite similar.

Fig. 7. Enhancement of thermal conductivity of the Al2O3 water-based nanofluids against particles concentration and comparison with models.

Figure 7 shows that there is a close agreement between the measured thermal conductivity and the Hamilton-Crosser and the Bruggeman models at 15 ◦C. However, this agreement is only at the low temperature. At higher temperature, the experiments of the Al2O3 water-based nanofluids disagree with the models. It is suggested that the present models cannot reflect on the effective conductivity with temperature. Das et al. (2003) stated that the main mechanism of the thermal conductivity enhancement in nanofluids can be thought as the stochastic motion of nanoparticles, and that the Brownian motion would depend on the fluid temperature. This enhancement in our experiments can be supported by the results of Das et al. (2003) and Chon et al. (2005). Their data have the maximum enhancements of 25 % and 19 % for 4 vol % at 55 ◦C whereas the Hamilton-Crosser model (Hamilton & Crosser, 1962) and the Bruggeman model (Bruggeman, 1935) predict only 12 % and 13 %, regardless of the temperature effect. At the low temperature, the Brownian motion was less significant. Thus the present results indicate that it is possible to have a threshold temperature at which the effective thermal conductivity of nanofluids starts deviating from that of the usual suspension and the enhancement through the stochastic motion of the particles starts

transport equation. The solution approaches the prediction of the Fourier law when the particle radius is much larger than the heat-carrier mean free path of the host medium, which implies that the diffusive heat transport is dominant. The model shows a trend of the thermal conductivity enhancement as the particle size increases. In sum, there may be a threshold in particle size where either the Brownian motion or the diffusive heat transport is more

Thermal Property Measurement of Al2O3-Water Nanofluids 349

0 20 40 60 80 100 120

1 vol % 2 vol % 3 vol % 4 vol % 5 vol %

**Shear rate (1/s)**

0 0.02 0.04 0.06

**Par�cle Volume Frac�on**

Fig. 10. Relative viscosity of the Al2O3 nanofluids as a function of volume concentration.

Fig. 9. Viscosity as a function of shear rate for the Al2O3 nanofluids at different volume

This study Masoumi et al. Nguyen et al. Einstein Model Brinkman Model Batchelor Model Graham Model

The viscosity is illustrated in Fig. 9 as a function of the shear rate. The viscosity of the well-mixed Al2O3-water nanofluid is independent from the shear rate. The naofluids exhibit a Newtonian behavior. Figure 10 shows that the effective viscosity ratio increases as the volume concentrations increase. The results of Masoumi et al. (2009) (28 nm) and Nguyen et al. (2007)

dominant.

concentrations.

**3.2 Viscosity of Al**2**O**<sup>3</sup> **nanofluids**

**Viscosity (Pa.S)**

**3.2.1 Effect of volume concentrations on viscosity**

0.0007 0.0008 0.0009 0.0010 0.0011 0.0012 0.0013 0.0014 0.0015 0.0016

> 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

**ηeff/ηf**

dominating. The measurement of the thermal conductivity with the given concentrations at the different temperatures in Fig. 7 indicates the necessity for a better theoretical model for the entire range of temperature.

#### **3.1.3 Effects of particle size on thermal conductivity**

Fig. 8. Effect of diameter of nanoparticle on effective thermal conductivity of the Al2O3 water-based nanofluids.

As shown in Fig. 8, the experimental data in the study are compared with the predictions from the thermal conductivity model by Jang & Choi (2004), and a good agreement was found for 10 nm, 25 nm and 35 nm Al2O3 water-based nanofluids. Our experimental data indicate that the effective thermal conductivity decreases quickly with the decreasing size of nanoparticles from 10 nm to 35 nm, however as the nanoparticle size increases, the thermal conductivity deviates from the Jang & Choi model. As the nanoparticle diameter is reduced, the effective thermal conductivity of nanofluids becomes larger. Jang & Choi (2004) explained that this phenomenon is based on the Brownian motion, and that the smaller nanoparticles in average might produce a higher velocity of the Brownian motion in the fluid. As a result, the heat transfer by the convection would be enhanced, the effective thermal conductivity of nanofluids increases. However, if the particles approach to the micrometer size, they might not remain well suspended in the base fluid. Thus, large microparticles do not have the Brownian motion any more, and there would be no enhancement of the effective thermal conductivity. Our experimental results for the nanofluids with the 80 nm and 150 nm Al2O3 nanoparticles did not show a similar trend as described in the model of Jang & Choi (2004). Instead our experimental data shows that the thermal conductivity of the Al2O3 nanofluids increases as the particle size increases above 35 nm, similar to the data of Beck et al. (2009) above 50 nm. When the particles become larger, it can be better explained by the model of Chen (1996),

$$k\_p = k\_{bulk} \frac{0.75 d\_p / l\_p}{0.75 d\_p / l\_p + 1} \tag{3}$$

where k*p*, d*p*, l*<sup>p</sup>* and k*bulk* are the thermal conductivity of nanoparticle, the characteristic length of nanoparticles, the mean free path of nanoparticle, and the thermal conductivity of bulk materials respectively. The correlation of Chen (1996) is built on solving the Boltzmann transport equation. The solution approaches the prediction of the Fourier law when the particle radius is much larger than the heat-carrier mean free path of the host medium, which implies that the diffusive heat transport is dominant. The model shows a trend of the thermal conductivity enhancement as the particle size increases. In sum, there may be a threshold in particle size where either the Brownian motion or the diffusive heat transport is more dominant.

#### **3.2 Viscosity of Al**2**O**<sup>3</sup> **nanofluids**

14 Will-be-set-by-IN-TECH

dominating. The measurement of the thermal conductivity with the given concentrations at the different temperatures in Fig. 7 indicates the necessity for a better theoretical model for

This results (5 vol

Beck et al. (4 vol %)

Jang & Choi model (3

Chen et al. model (3 vol %)

%)

vol %)

0 100 200 300

**Par�cle size (nm)**

As shown in Fig. 8, the experimental data in the study are compared with the predictions from the thermal conductivity model by Jang & Choi (2004), and a good agreement was found for 10 nm, 25 nm and 35 nm Al2O3 water-based nanofluids. Our experimental data indicate that the effective thermal conductivity decreases quickly with the decreasing size of nanoparticles from 10 nm to 35 nm, however as the nanoparticle size increases, the thermal conductivity deviates from the Jang & Choi model. As the nanoparticle diameter is reduced, the effective thermal conductivity of nanofluids becomes larger. Jang & Choi (2004) explained that this phenomenon is based on the Brownian motion, and that the smaller nanoparticles in average might produce a higher velocity of the Brownian motion in the fluid. As a result, the heat transfer by the convection would be enhanced, the effective thermal conductivity of nanofluids increases. However, if the particles approach to the micrometer size, they might not remain well suspended in the base fluid. Thus, large microparticles do not have the Brownian motion any more, and there would be no enhancement of the effective thermal conductivity. Our experimental results for the nanofluids with the 80 nm and 150 nm Al2O3 nanoparticles did not show a similar trend as described in the model of Jang & Choi (2004). Instead our experimental data shows that the thermal conductivity of the Al2O3 nanofluids increases as the particle size increases above 35 nm, similar to the data of Beck et al. (2009) above 50 nm. When the particles become larger, it can be better explained by the model of

Fig. 8. Effect of diameter of nanoparticle on effective thermal conductivity of the Al2O3

*kp* = *kbulk*

0.75*dp*/*lp*

where k*p*, d*p*, l*<sup>p</sup>* and k*bulk* are the thermal conductivity of nanoparticle, the characteristic length of nanoparticles, the mean free path of nanoparticle, and the thermal conductivity of bulk materials respectively. The correlation of Chen (1996) is built on solving the Boltzmann

0.75*dp*/*lp* <sup>+</sup> <sup>1</sup> (3)

the entire range of temperature.

**3.1.3 Effects of particle size on thermal conductivity**

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45

**keff/kf**

water-based nanofluids.

Chen (1996),

#### **3.2.1 Effect of volume concentrations on viscosity**

Fig. 9. Viscosity as a function of shear rate for the Al2O3 nanofluids at different volume concentrations.

The viscosity is illustrated in Fig. 9 as a function of the shear rate. The viscosity of the well-mixed Al2O3-water nanofluid is independent from the shear rate. The naofluids exhibit a Newtonian behavior. Figure 10 shows that the effective viscosity ratio increases as the volume concentrations increase. The results of Masoumi et al. (2009) (28 nm) and Nguyen et al. (2007)

Fig. 10. Relative viscosity of the Al2O3 nanofluids as a function of volume concentration.

different for high particle fractions and for low ones. With an increase of temperature, the measured viscosity data have shown a gentle decrease with an increase of temperature. In our experiments, we have attempted to measure viscosity at the temperature higher than 55 ◦C, but a critical temperature has been observed, above the temperature, an 'erratic' increase of nanofluid viscosity was observed. The phenomenon may be resulted from the fast evaporation of nanofluids in the related small volume at a relative high temperature. Another possibility is that beyond the critical temperature, the surfactant might be broken down and accordingly the performance was considerably reduced or even destroyed, affecting the suspension capabilities. Thus, the particles have a tendency to form aggregation, resulting in

Thermal Property Measurement of Al2O3-Water Nanofluids 351

10 20 30 40 50 60

This study (1 vol %) This study (2 Vol %) This study (3 vol %) Nguyen et al. (1 vol%) Nguyen et al. (4.5 vol%) Masoumi et al. (4.5 vol%)

)−2.5*φ<sup>m</sup>* (4)

**Temperature (°C)**

Fig. 12. Relative viscosity as a function of temperature for various concentrations of the

As known, the water viscosity decreases with an increase of temperature. The viscosity values of the different concentration nanofluids measured from 15 to 55 ◦C are compared with a reference of the viscosity of water at these temperatures. As seen from Fig. 12, the effective viscosity under the different volume concentrations shows similar trends. For a given nanofluid and a particle fraction, the effective viscosity decreases at first and starts to increase at a certain temperature. This value implies that there should be an optimum temperature whereby when temperature increases, the decrease in viscosity is not effective. This observation can be substantiated by Nguyen et al. (2007) and Masoumi et al. (2009).

From Fig. 13, our experimental results show that as the particle sizes increase, the effective viscosity decreases significantly and reaches an almost constant value at the end. This trend is similar to the results of other researchers shown in Fig. 13 except for particle size greater than 100 nm. Timofeeva et al. (2007) suggested the small particle size can form larger aggregates. The Krieger model (Krieger & Dougherty, 1959) can be used to estimate the relative viscosity

> = (<sup>1</sup> <sup>−</sup> *<sup>φ</sup><sup>a</sup> φm*

*ηn f ηf*

the observed unpredictable increase of the nanofluid viscosity.

1.1

**3.2.3 Effect of particle size on viscosity**

between a nanofluid (*n f*) and its base fluid (*f*),

1.2

1.3

**ηeff/ηf**

Al2O3-water nanofluids.

1.4

1.5

1.6

(36 nm) show a similar trend. From our experiments, the measured viscosity of the Al2O3 nanofluids is significantly higher than the base fluid by about 20% and 61% at 1 vol % and 5 vol % respectively. The results of Masoumi, Nguyen and ours are much higher than those of predicted values using the Einstein, Brinkman, Batchelor and Graham equations, as shown in Fig. 10. It is suggested that these equations have underestimated the nanofluid viscosities. The Einstein formula, and the others originating from it, were obtained based on the theoretical assumption of a linear fluid surrounded by the isolated particles. Such a model may worked under the situation of a liquid that contains a small number of dispersed particles. However, for higher particle concentrations the departure of these formulae from our experimental data is considerable, indicating that the linear fluid theory may be no longer appropriate to represent the nanofluids. Even the Batchelor formula, considering the Brownian effect, also performs poorly. A possible explanation is mentioned by Chandrasekar et al. (2010), the large difference may be a result of the hydrodynamic interactions between particles which become important at higher volume concentrations. Hence the conventional models cannot explain the high viscosity ratio. Noted that there are also discrepancies between our experimental results and the previous studies in Fig. 10. Although the nanofluids prepared have slight differences in the size of particles, it is inappropriate to account for such a large difference in the viscosity ratio. It is difficult to draw any conclusive remarks for such results, unless this intriguing behavior may be attributed to the various factors such as nanofluid preparation methods and how the experiment is conducted.

#### **3.2.2 Effect of temperature on viscosity**

Fig. 11. Viscosity as a function of temperature for Al2O3 nanofluids.

The viscosities were measured for the nanofluids as a function of temperature. The viscosity under the particle volume fraction ranging at 1% , 2%, and 3% from 15 to 55 ◦C is shown in Fig. 11, the nanofluid viscosity decreases with an increase in temperature. The increasing temperature would weaken the inter-particle and inter-molecular adhesion forces. For all the nanofluids measured, the temperature gradient of viscosity is generally steeper at the temperature from 15 to 30 ◦C. Such the viscosity gradient is particularly more pronounced as the particle volume concentration increases. This observation is supported by Nguyen et al. (2007) results if we compare the gradient from 15 to 30 ◦C at 1 vol % and 4.5 vol %. The results suggest that the temperature effect on the particle suspension properties may be 16 Will-be-set-by-IN-TECH

(36 nm) show a similar trend. From our experiments, the measured viscosity of the Al2O3 nanofluids is significantly higher than the base fluid by about 20% and 61% at 1 vol % and 5 vol % respectively. The results of Masoumi, Nguyen and ours are much higher than those of predicted values using the Einstein, Brinkman, Batchelor and Graham equations, as shown in Fig. 10. It is suggested that these equations have underestimated the nanofluid viscosities. The Einstein formula, and the others originating from it, were obtained based on the theoretical assumption of a linear fluid surrounded by the isolated particles. Such a model may worked under the situation of a liquid that contains a small number of dispersed particles. However, for higher particle concentrations the departure of these formulae from our experimental data is considerable, indicating that the linear fluid theory may be no longer appropriate to represent the nanofluids. Even the Batchelor formula, considering the Brownian effect, also performs poorly. A possible explanation is mentioned by Chandrasekar et al. (2010), the large difference may be a result of the hydrodynamic interactions between particles which become important at higher volume concentrations. Hence the conventional models cannot explain the high viscosity ratio. Noted that there are also discrepancies between our experimental results and the previous studies in Fig. 10. Although the nanofluids prepared have slight differences in the size of particles, it is inappropriate to account for such a large difference in the viscosity ratio. It is difficult to draw any conclusive remarks for such results, unless this intriguing behavior may be attributed to the various factors such as nanofluid preparation

0 20 40 60 80

The viscosities were measured for the nanofluids as a function of temperature. The viscosity under the particle volume fraction ranging at 1% , 2%, and 3% from 15 to 55 ◦C is shown in Fig. 11, the nanofluid viscosity decreases with an increase in temperature. The increasing temperature would weaken the inter-particle and inter-molecular adhesion forces. For all the nanofluids measured, the temperature gradient of viscosity is generally steeper at the temperature from 15 to 30 ◦C. Such the viscosity gradient is particularly more pronounced as the particle volume concentration increases. This observation is supported by Nguyen et al. (2007) results if we compare the gradient from 15 to 30 ◦C at 1 vol % and 4.5 vol %. The results suggest that the temperature effect on the particle suspension properties may be

**Temperature (°C)**

This study (0 vol %) This study 1 vol % This study 2 vol % This study 3 Vol % Nguyen et al. (1 vol %) Nguyen et al. (4.5 vol %)

methods and how the experiment is conducted.

0.0004

Fig. 11. Viscosity as a function of temperature for Al2O3 nanofluids.

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

**3.2.2 Effect of temperature on viscosity**

**Viscosity (Pa.s)**

different for high particle fractions and for low ones. With an increase of temperature, the measured viscosity data have shown a gentle decrease with an increase of temperature. In our experiments, we have attempted to measure viscosity at the temperature higher than 55 ◦C, but a critical temperature has been observed, above the temperature, an 'erratic' increase of nanofluid viscosity was observed. The phenomenon may be resulted from the fast evaporation of nanofluids in the related small volume at a relative high temperature. Another possibility is that beyond the critical temperature, the surfactant might be broken down and accordingly the performance was considerably reduced or even destroyed, affecting the suspension capabilities. Thus, the particles have a tendency to form aggregation, resulting in the observed unpredictable increase of the nanofluid viscosity.

Fig. 12. Relative viscosity as a function of temperature for various concentrations of the Al2O3-water nanofluids.

As known, the water viscosity decreases with an increase of temperature. The viscosity values of the different concentration nanofluids measured from 15 to 55 ◦C are compared with a reference of the viscosity of water at these temperatures. As seen from Fig. 12, the effective viscosity under the different volume concentrations shows similar trends. For a given nanofluid and a particle fraction, the effective viscosity decreases at first and starts to increase at a certain temperature. This value implies that there should be an optimum temperature whereby when temperature increases, the decrease in viscosity is not effective. This observation can be substantiated by Nguyen et al. (2007) and Masoumi et al. (2009).

#### **3.2.3 Effect of particle size on viscosity**

From Fig. 13, our experimental results show that as the particle sizes increase, the effective viscosity decreases significantly and reaches an almost constant value at the end. This trend is similar to the results of other researchers shown in Fig. 13 except for particle size greater than 100 nm. Timofeeva et al. (2007) suggested the small particle size can form larger aggregates. The Krieger model (Krieger & Dougherty, 1959) can be used to estimate the relative viscosity between a nanofluid (*n f*) and its base fluid (*f*),

$$\frac{\eta\_{nf}}{\eta\_f} = (1 - \frac{\phi\_a}{\phi\_m})^{-2.5\phi\_m} \tag{4}$$

a well-dispersed suspension. The addition of a small amount of surfactant into the liquid

Thermal Property Measurement of Al2O3-Water Nanofluids 353

0 0.01 0.02 0.03 0.04 0.05 0.06

**Par�cle Volume Frac�on**

Fig. 14. Surface tension measurement of the Al2O3 nanofluids as a function of the volume

The thermal conductivity, viscosity, and surface tension of the Al2O3 water-based nanofluids were measured. It is found the thermal conductivity increases significantly with the nanoparticle volume fraction. With an increase of temperature, the thermal conductivity increases for a certain volume concentration of nanofluids, but the viscosity decreases. The size of nanoparticle also influences the thermal conductivity of nanofluids. It is indicated that existing classical models cannot explain the observed enhanced thermal conductivity in the nanofluids. Similarly, the viscosity increases as the concentration increases at room temperature. At the volume concentrations of 5%, the viscosity has an increment of 60%. The effect of particle sizes on the viscosity is limited. The addition of surfactant is believed to be the reason behind the decrease in surface tension in comparison with the base fluid. The significant deviation between the experimental results and the existing theoretical models is still unaccounted for. More comprehensive models therefore need to be developed. Particles sizes, particle dispersions, clustering, and temperature should be taken into account in the model development for nanofluids. Hence, to reach universal models for the thermal properties, more complete experiments involving a wide range of nanoparticle sizes would

The research mainly depends on the experimental work of Mr. D. Kwok under the support of NTU-SUG and AcRF Tier 1 funding. The author would like to thank Profs. Kai Choong Leong and Charles Yang for their generosity in sharing their HWT and surface tension equipment. The author would also like thank to Dr. Liwen Jin for sharing his knowledge on the thermal

Batchelor, G.K. (1977). The effect of Brownian motion on the bulk stress in the suspension of

spherical particles. *J. Fluid Mech.*, 83, 97-117.

reduced the surface tension (Binks, 2002; Bresme & Faraudo, 2007).

**Surface tension (mN/m)**

concentration.

**4. Conclusion**

be conducted in future.

**5. Acknowledgments**

conductivity measurement.

**6. References**

Fig. 13. Relative viscosity as a function of diameter of the Al2O3 nanoparticles in the base fluids.

where 2.5 is the intrinsic viscosity of spherical particles, *φa* is the volume fraction of aggregates, *φm* is the volume fraction of densely packed spheres and the volume fraction of aggregates is expressed as *φ<sup>a</sup>* = *φ*( *da <sup>d</sup>* )3−*df* , in which *da* is the diameter of aggregates, *<sup>d</sup>* is the nominal diameter of particle, *d <sup>f</sup>* is the fractal dimension of the aggregates, *φ* is the volume fraction of the well-dispersed individual particles. For well-dispersed individual particles, *φa* is equal to *φ*, and the Krieger model reduces to the Einstein model. This is a very ideal case where there is zero aggregation. However, none of the researches is able to obey fully the Einstein model until now. The reason may be that it is unlikely to eliminate the aggregation completely (Duan et al., 2011). When nanoparticle size increases, the magnitude of *da d* decreases, thus the volume fraction of the aggregates decreases and relative viscosity ratio decreases. In addition, due to aggregation, the shape of the aggregate is no longer spherical. Theoretically, Einstein obtained the intrinsic viscosity at 2.5 for spherical particles, however the intrinsic viscosity would be greater than 2.5 for the other shapes (Rubio-hernandez et al., 2006) as the aggregate shape becomes disordered. This can also account for the increase of viscosity ratio as the particle diameter decreases.

Slight aggregation is likely to remain in our nanofluids measured just after preparation since the measurements are made for different particle sizes at a constant 5 % volume concentration, which is considered high. Based on Equation (4), the viscosity ratio would be higher after aggregation.

#### **3.3 Surface tension measurements of nanofluid**

Figure 14 shows the surface tension as a function of the volume concentration. The results demonstrate that the surface tensions of the Al2O3 water-based nanofluids are significantly lower than those of the base fluid, pure water. At each point, the error bars are too small to be observed. However, as the volume concentration increases, the surface tension remains almost unchanged in the Al2O3 nanofluids. Hence we can deduce that particle volume concentration does not have a major effect on the surface tension of the nanofluids. The experimental results of Golubovic et al. (2009) and Kim et al. (2007) have shown that the surface tensions of the Al2O3 nanofluids without surfactant is independent on concentration and has the same values as that of pure water. In our prepared nanofluids, the surfactant, CTAB was added to obtain a well-dispersed suspension. The addition of a small amount of surfactant into the liquid reduced the surface tension (Binks, 2002; Bresme & Faraudo, 2007).

Fig. 14. Surface tension measurement of the Al2O3 nanofluids as a function of the volume concentration.

#### **4. Conclusion**

18 Will-be-set-by-IN-TECH

This study (5 vol %) Lu et al. (5 vol%) Masoumi et al.(2.85%) Prasher et al. (3 vol%)

*<sup>d</sup>* )3−*df* , in which *da* is the diameter of aggregates, *<sup>d</sup>* is the

*d*

0 50 100 150

**Par�cle size (nm)**

Fig. 13. Relative viscosity as a function of diameter of the Al2O3 nanoparticles in the base

where 2.5 is the intrinsic viscosity of spherical particles, *φa* is the volume fraction of aggregates, *φm* is the volume fraction of densely packed spheres and the volume fraction of

nominal diameter of particle, *d <sup>f</sup>* is the fractal dimension of the aggregates, *φ* is the volume fraction of the well-dispersed individual particles. For well-dispersed individual particles, *φa* is equal to *φ*, and the Krieger model reduces to the Einstein model. This is a very ideal case where there is zero aggregation. However, none of the researches is able to obey fully the Einstein model until now. The reason may be that it is unlikely to eliminate the aggregation completely (Duan et al., 2011). When nanoparticle size increases, the magnitude of *da*

decreases, thus the volume fraction of the aggregates decreases and relative viscosity ratio decreases. In addition, due to aggregation, the shape of the aggregate is no longer spherical. Theoretically, Einstein obtained the intrinsic viscosity at 2.5 for spherical particles, however the intrinsic viscosity would be greater than 2.5 for the other shapes (Rubio-hernandez et al., 2006) as the aggregate shape becomes disordered. This can also account for the increase of

Slight aggregation is likely to remain in our nanofluids measured just after preparation since the measurements are made for different particle sizes at a constant 5 % volume concentration, which is considered high. Based on Equation (4), the viscosity ratio would be higher after

Figure 14 shows the surface tension as a function of the volume concentration. The results demonstrate that the surface tensions of the Al2O3 water-based nanofluids are significantly lower than those of the base fluid, pure water. At each point, the error bars are too small to be observed. However, as the volume concentration increases, the surface tension remains almost unchanged in the Al2O3 nanofluids. Hence we can deduce that particle volume concentration does not have a major effect on the surface tension of the nanofluids. The experimental results of Golubovic et al. (2009) and Kim et al. (2007) have shown that the surface tensions of the Al2O3 nanofluids without surfactant is independent on concentration and has the same values as that of pure water. In our prepared nanofluids, the surfactant, CTAB was added to obtain

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

viscosity ratio as the particle diameter decreases.

**3.3 Surface tension measurements of nanofluid**

**ηeff/ηf**

aggregates is expressed as *φ<sup>a</sup>* = *φ*( *da*

fluids.

aggregation.

The thermal conductivity, viscosity, and surface tension of the Al2O3 water-based nanofluids were measured. It is found the thermal conductivity increases significantly with the nanoparticle volume fraction. With an increase of temperature, the thermal conductivity increases for a certain volume concentration of nanofluids, but the viscosity decreases. The size of nanoparticle also influences the thermal conductivity of nanofluids. It is indicated that existing classical models cannot explain the observed enhanced thermal conductivity in the nanofluids. Similarly, the viscosity increases as the concentration increases at room temperature. At the volume concentrations of 5%, the viscosity has an increment of 60%. The effect of particle sizes on the viscosity is limited. The addition of surfactant is believed to be the reason behind the decrease in surface tension in comparison with the base fluid. The significant deviation between the experimental results and the existing theoretical models is still unaccounted for. More comprehensive models therefore need to be developed. Particles sizes, particle dispersions, clustering, and temperature should be taken into account in the model development for nanofluids. Hence, to reach universal models for the thermal properties, more complete experiments involving a wide range of nanoparticle sizes would be conducted in future.

#### **5. Acknowledgments**

The research mainly depends on the experimental work of Mr. D. Kwok under the support of NTU-SUG and AcRF Tier 1 funding. The author would like to thank Profs. Kai Choong Leong and Charles Yang for their generosity in sharing their HWT and surface tension equipment. The author would also like thank to Dr. Liwen Jin for sharing his knowledge on the thermal conductivity measurement.

#### **6. References**

Batchelor, G.K. (1977). The effect of Brownian motion on the bulk stress in the suspension of spherical particles. *J. Fluid Mech.*, 83, 97-117.

Hamilton, R.L. & Crosser, O.K. (1962). Thermal conductivity of heterogeneous two component

Thermal Property Measurement of Al2O3-Water Nanofluids 355

Jang, S.P. & Choi, S.U.S. (2004). Role of Brownian motion in the enhanced thermal conductivity

Keblinski, P.; Eastman, J.A. & Cahill, D.G. (2005). Nanofluids for thermal transport. *Mater*

Keblinski, P.; Phillpot, S.R.; Choi, S.U.S. & Eastman, J.A. (2002). Mechanisms of heat flow

Kestin, J. & Wakeham W.A. (1978). A contribution to the theory of the transient hot-wire technique for thermal conductivity measurements. *Physica A*, 92, 102-116. Kim, J.; Kang, Y.T. & Choi, C.K. (2004). Analysis of convective instability and heat transfer

Kim, S.J.; Bang, I.C.; Buongiorno, J. & Hu, L.W. (2007). Surface wettability change during pool

Koo, J. & Kleinstreuer, C. (2004). A newthermal conductivity model for nanofluids. *J. Nanopart.*

Krieger, I.M. & Dougherty, T.J. (1959). A mechanism for non-newtonian flow in suspensions

Kumar, D.H. Patel, H.E.; Kumar, V.R.R.; Sundararajan, T.; Pradeep, T. & Das, S.K. (2004).

Kumar, R. & Milanova, D.(2009). Effect of surface tension on nanotube nanofluids. *Appl. Phys.*

Kwek, D.; Crivoi, A. & Duan, F. (2010). Effects of temperature and particle size on the thermal

Lee, S.; Choi, S.U.S.; Li, S. & Eastman, J.A. (1999). Measuring thermal conductivity of fluids

Li, C.H. & Peterson G.P.(2006). Experimental investigation of temperature and volume

Li, X.; Zhu, D. & Wang X. (2007). Evaluation on dispersion behaviour of the aqueous copper

Li, Y.; Zhou J.; Tung, S.; Schneider, E. & Xi, S. (2009). A review on development of nanofluid

Lundgren, T.S. (1972). Slow flow through stationary random beds and suspensions of spheres.

Maxwell, J.C. (1892). *A Treatise on Electricity and Magnetism, 3rd ed.*, Oxford University Press,

Nagasaka, Y. & Nagashima A. (1981). Absolute measurement of the thermal conductivity

Nguyen, C.T.; Desgranges, F.; Roy, G.; Galanis, N.; Mare, T.; Boucher, S. & Angue Mintsa,

nanofluids - hysteresis phenomenon. *Int. J. Heat Fluid Flow*, 28, 1492-1506.

of electrically conducting liquids by the transient hot-wire method. *J. Phys. E*, 14,

H. (2007). Temperature and particle-size dependent viscosity data for water-based

Mandelbrot; B.B. (1982). *The Fractal Geometry of Nature*, W.H. Freeman Press, San Francisco. Masoumi, N.; Sohrabi, N. & Behzadmehr, A. (2009). A new model for calculating the effective

property measurements of Al2O3-water nanofluids. *J. Chem. Eng. Data*, 55, 5690-5695.

fraction variations on the effective thermal conductivity of nanoparticle suspensions

Model for heat conduction in nanofluids. *Phys. Rev. Lett.*, 93, 1-4.

containing oxide nanoparticles. *J. Heat Transfer*, 121, 280-289.

preparation and characterization. *Powder Technol.*, 196, 89-101.

viscosity of nanofluids. *J. Phys. D: Appl. Phys.*, 42, 055501.

nano-suspensions. *J. Colloid Interface Sci.*, 310, 456-463.

in suspensions of nano-sized particles (nanofluids). *Int. J. Heat Mass Transfer*, 45,

boiling of nanofluids and its effect on critical heat flux. *Int. J. Heat Mass Transfer*, 50

systems. *Ind. Eng. Chem. Fundam.*, 1, 187-191.

of nanofluids. *Appl. Phys. Lett.*, 84, 4316-4318.

characteristics of nanofluids. *Phys. Fluids*, 16, 2395-2401.

of rigid spheres. *Trans. Soc. Rheology*, 3, 137-152.

(nanofluids). *J. Appl. Phys.*, 99, 1-8.

*J. Fluid Mech.*, 51, 273-299.

London.

1435-1440.

*Today*, 8, 36-44.

(2007) 4105-4116.

*Res.*, 6, 577-588.

*Lett.*, 94, 073107.

855-863.


20 Will-be-set-by-IN-TECH

Beck, M.P.; Yuan, Y.; Warrier, P. & Teja, A.S. (2009). The effect of particle size on the thermal

Bruggeman, D.A.G. (1935). Calculation of various physics constants in heterogenous

Bentley, J.P. (1984). Temperature sensor characteristics and measurement system design. *J.*

Bhattacharya, P.; Saha, S.K.; Yadav, A.; Phelan, P.E. & Prasher, R.S. (2004). Brownian dynamics

Binks, B. (2002). Particles as surfactants - similarities and differences. *Curr. Opin. Colloid*

Bresme, F. & Faraudo, J. (2007). Particles as surfactants - similarities and differences. *J. Phys.:*

Brinkman, H.C. (1952). The viscosity of concentrated suspensions and solution. *J. Chem. Phys.*,

Chandrasekar, M.; Suresh, S. & Chandra Bose, A. (2010). Experimental investigations and

Challoner, A.R. & Powell. R.W. (1956). Thermal conductivity of liquids: new determinations for seven liquids and appraisal of existing values. *Proc. R. Soc. Lond.*, 238, 90-106. Chen, G. (1996). Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles.

Choi, S.U.S. (1995). Enhancing thermal conductivity of fluids with nanoparticles, In:

Chon, C.H.; Kihm, K.D.; Lee, S.P. & Choi, S.U.S. (2005). Empirical correlation finding the

Czarnetzki, W. & Roetzel W. (1995). Temperature oscillation techniques for simultaneous

Das, S.K.; Putta, N.; Thiesen, P. & Roetzel W. (2003). Temperature dependence of thermal conductivity enhancement for nanofluids. *J. Heat Transfer*, 125, 567-574. Duan, F; Kwek D & Crivoi A. (2011). Viscosity affected by nanoparticle aggregation in

Eastman, J.A.; Choi, S.U.S.; Li, S.; Thompson, L.J. & Lee, S. (1997). Enhanced thermal

Eastman, J.A.; Choi, S.U.S.; Li, S.; Yu, W. & Thompson, L.J. (2001). Anomalously increased

Einstein, A. (1906). A new determination of the molecular dimensions. *Ann. Phys.*, 19, 289-306. Frankel, N.A. & Acrivos, A. (1967). On the viscosity of a concentrated suspension of solid

Golubovic, M.N.; Madhawa Hettiarachchi, H.D.; Worek, W.M. & Minkowycz, W.J. (2009).

Graham, A.L. (1981). On the viscosity of suspension of solid spheres. *Appl. Sci. Res.*, 37,

substances. I. Dielectricity constants and conductivity of mixed bodies from isotropic

simulation to determine the effective thermal conductivity of nanofluids. *J. Appl.*

theoretical determination of thermal conductivity and viscosity of Al2O3/water

*Developments and Applications of Non-Newtonian Flows*, Sinfiner, D.A. & Wang, H.P.,

role of temperature and particle size for nanofluid (Al2O3) thermal conductivity

measurement of thermal diffusivity and conductivity. *Int. J. Thermophys.*, 16, 413-422.

conductivity through the development of nanofluids. *Mater. Res. Soc. Symp. Proc.*,

effective thermal conductivities of ethylene glycol-based nanofluids containing

Nanofluids and critical heat flux, experimental and analytical study. *Appl. Therm.*

conductivity of alumina nanofluids. *J. Nanopart. Res.*, 11, 1129-1136.

substances. *Ann. Phys. (Paris)*, 24, 636-664.

nanofluid. *Exp. Therm. Fluid Sci.*, 34, 210-216.

PP 99-105, ASME, FED-vol.231 MD-vol.66, USA.

Al2O3-water nanofluids. *Nanoscale Res. Lett.*, 6, 248.

copper nanoparticles. *Appl. Phys. Lett.*, 78, 718-720.

spheres. *Chem. Eng. Sci.*, 22, 847-853.

*ASME J. Heat Transfer*, 118, 539-545.

enhancement. *Appl. Phys. Lett.*, 87, 1-3.

*Phys. E*, 17, 430-439.

*Phys.*, 95, 6492-6494.

*Interface Sci.*, 7, 21-41.

20, 571.

457, 3-11.

275-286.

*Eng.*, 29, 1281-1288.

*Condens. Matter*, 19, 375110.


**16** 

*Taiwan* 

**Magnetic Nanoparticles: Its Effect on** 

Hon-Man Liu1 and Jong-Kai Hsiao2

*2Tzu-Chi University, Department of Radiology* 

*1National Taiwan University, Department of Radiology* 

**Cellular Behaviour and Potential Applications** 

With the advancement of nanotechnology and the development of molecular medicine, molecular and imaging becomes one of the most popular researches in the latest medicine. Molecular imaging can be defined as the imaging of targeted molecules non-invasively and repetitively in living organisms and cellular imaging can be defined similarly as the imaging of cells or cellular process non-invasively and repetitively in living organisms. At present, the common imaging tools for clinical study include ultrasound, computed tomography (CT), and magnetic resonance imaging (MRI). However, MRI is superior to CT for its better in soft tissue contrast, more sensitive in pathology detection, and lack of ionization

In clinical practice, gadolinium-contained compound is the commonest contrast medium used in MRI study. Molecular imaging differs from traditional imaging in that contrast agents are typically used to help identify particular biomarkers or pathways with high sensitivity and selectivity (Achilefu, 2010). However, gadolinium (Gd) is not proper for the molecular imaging and cellular imaging due to its low relaxivity, that further decrease upon cellular internalization; not biocompatible and potential toxicity following cellular dechelation over time. Iron oxide (IO) nanoparticle contrast medium is another contrast medium used in clinical study. They provide the most significant signal change per unit of metal atom, especially on T2\* MR imaging. Iron oxide nanoparticle are made of thousands of iron atoms in Fe3O4 or γ-Fe2O3 form so that they can increase the contrast-to-noise ratio and make its sensitivity superior to Gd contrast agent on MR examination. Their main component, oxidized iron, can be metabolized in liver and recycled as important component of red blood cells. Iron oxide nanoparticle have a relatively long circulation time and low toxicity (Bradbury and Hricak 2005; Funovics et al., 2004; Harisinghani et al., 2003; Jain et al., 2005; Montet et al., 2006). Their surfaces coating may strategically contain chemical linkage of functional groups and ligands for multimodal imaging purpose (Rogers & Basu, 2005). They can be easily detected by light and electron microscopy. Iron oxide nanoparticle posses some novel properties not seen with the other macromolecules. They can be manipulated by conjugating both targeting ligands or peptide and therapeutic components such as photosensitizer to help in diagnosis and treatment. Iron oxide nanoparticles can be used to monitor cellular migration, molecular events, and signal pathway associated with different

**1. Introduction** 

irradiation.


## **Magnetic Nanoparticles: Its Effect on Cellular Behaviour and Potential Applications**

Hon-Man Liu1 and Jong-Kai Hsiao2 *1National Taiwan University, Department of Radiology 2Tzu-Chi University, Department of Radiology Taiwan* 

## **1. Introduction**

22 Will-be-set-by-IN-TECH

356 Smart Nanoparticles Technology

Pantzali, M.N.; Kanaris, A.G.; Antoniadis, K.D.; Mouza, A.A. & Paras, S.V. (2009). Effect of

Prasher, R.; Bhattacharya, P.; Phelan, P.E. & Das, S.K. (2005). Thermal conductivity of nanoscale colloidal solutions (nanofluids). *Phys. Rev. Lett.*, 94, 025901. Roetzel, W.; Prinzen, S. & Xuan Y. (1990). Measurement of thermal diffusivity using

Rubio-hernandez, F.J.; Ayucar-Rubio, M.F.; Velazquez-Navarro J.F. & Galindo-Rosales, F.J.

Sakamoto, M.; Kanda, Y.; Miyahara, M. & Higashitani, K. (2002). Origin of long-range

Schwartz, L.; Garboczi, E. & Bentz, D. (1995). Interfacial transport in porous media: application to dc electrical conductivity of mortars. *J. Appl. Phys.*, 78, 5898-5908. Timofeeva, E.V.; Gavrilov, A.N.; McCloskey, J.M. & Tolmachev, Y.V. (2007). Thermal

Vafaei, S.; Purkayastha, A.; Jain, A.; Ramanath, G. & Borca-Tasciuc, T. (2009). The effect of

Vargaftik, N.B.; Volkov, B.N. & Voljak, L.D. (1983). International tables of the surface tension

Wang, B.X. Zhou, L.P. & Peng, X.F. (2003). A fractal model for predicting the eeffective thermal

Wang, X.; Xu, X. & Choi, S.U.S. (1999). Thermal conductivity of nanoparticle - fluid mixture. *J.*

Wasan, D.T. & Nikolov, A.D. (2003). Spreading of nanofluids on solids. *Nature*, 423, 156-159. Xie, H.; Fujii, M. & Zhang, X. (2005). Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticle-fluid mixture. *Int. J. Heat Mass Transfer*, 48, 2926-2932. Xuan Y. & Li, Q. (2000). Heat transfer enhancement of nanofluids. *Int. J. Heat Fluid Flow*, 21,

Xuan, Y.; Li, Q. & Hu, W. (2003). Aggregation structure and thermal conductivity of

Xue, Q. (2003). Model for effective thermal conductivity of nanofluids. *Phys. Lett. A*, 307,

Xue, Q. & Xu, W.-M. (2005). A model of thermal conductivity of nanofluids with interfacial

Yang, B. & Han, Z.H. (2006). Temperature-dependent thermal conductivity of nanorod based

Yu, W. & Choi, S.U.S. (2003). The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model. *J. Nanopart. Res.*, 5, 167-171. Yu, W. & Choi, S.U.S. (2004). The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Hamilton-Crosser model. *J. Nanopart. Res.*, 6, 355-361.

surface. *Int. J. Heat Fluid Flow*, 30, 691-699.

H.A., Ed., 201-207, Plenum Press, New York.

*Interface Sci.*, 298, 967-972.

theory. *Phys. Rev. E*, 76, 061203.

of water. *Phys. Chem. Ref. Data*, 12, 817.

*Thermophys. Heat Tr.*, 13, 474-480.

nanofluids. *AICHE J.*, 49, 1038-1043.

shells. *Mater. Chem. Phys.*, 90, 298-301.

nanofluids. *Appl. Phys. Lett.*, 89, 1-3.

18, 5713-5719.

20, 185702.

2665-2672.

58-64.

313-317.

nanofluids on the performance of a miniature plate heat exchanger with modulated

temperature oscillations, In: *Measurement of conductivity 21*, Cremers C.J. & Fine,

(2006). Intrinsic viscosity of SiO2, Al2O3 and TiO2 aqueous suspensions. *J. Colloid*

attractive force between surfaces hydrophobized by surfactant adsorption. *Langmuir*,

conductivity and particle agglomeration in alumina nanofluids: Experiment and

nanoparticles on the liquid-gas surface tension of Bi2Te3 nanofluids. *Nanotechnology*,

conductivity of liquid with suspension of nnanoparticles. *Int. J. Heat Mass Transfer*, 46,

With the advancement of nanotechnology and the development of molecular medicine, molecular and imaging becomes one of the most popular researches in the latest medicine. Molecular imaging can be defined as the imaging of targeted molecules non-invasively and repetitively in living organisms and cellular imaging can be defined similarly as the imaging of cells or cellular process non-invasively and repetitively in living organisms. At present, the common imaging tools for clinical study include ultrasound, computed tomography (CT), and magnetic resonance imaging (MRI). However, MRI is superior to CT for its better in soft tissue contrast, more sensitive in pathology detection, and lack of ionization irradiation.

In clinical practice, gadolinium-contained compound is the commonest contrast medium used in MRI study. Molecular imaging differs from traditional imaging in that contrast agents are typically used to help identify particular biomarkers or pathways with high sensitivity and selectivity (Achilefu, 2010). However, gadolinium (Gd) is not proper for the molecular imaging and cellular imaging due to its low relaxivity, that further decrease upon cellular internalization; not biocompatible and potential toxicity following cellular dechelation over time. Iron oxide (IO) nanoparticle contrast medium is another contrast medium used in clinical study. They provide the most significant signal change per unit of metal atom, especially on T2\* MR imaging. Iron oxide nanoparticle are made of thousands of iron atoms in Fe3O4 or γ-Fe2O3 form so that they can increase the contrast-to-noise ratio and make its sensitivity superior to Gd contrast agent on MR examination. Their main component, oxidized iron, can be metabolized in liver and recycled as important component of red blood cells. Iron oxide nanoparticle have a relatively long circulation time and low toxicity (Bradbury and Hricak 2005; Funovics et al., 2004; Harisinghani et al., 2003; Jain et al., 2005; Montet et al., 2006). Their surfaces coating may strategically contain chemical linkage of functional groups and ligands for multimodal imaging purpose (Rogers & Basu, 2005). They can be easily detected by light and electron microscopy. Iron oxide nanoparticle posses some novel properties not seen with the other macromolecules. They can be manipulated by conjugating both targeting ligands or peptide and therapeutic components such as photosensitizer to help in diagnosis and treatment. Iron oxide nanoparticles can be used to monitor cellular migration, molecular events, and signal pathway associated with different

Magnetic Nanoparticles: Its Effect on Cellular Behaviour and Potential Applications 359

Positive contrast media appear brighter on MR images owing to a reduction in T1 relaxation time. They include those containing Gd, manganese or iron ions. Negative contrast agents appear dark on MR imaging due to shortening T1, T2, and T2\* relaxation times. Iron oxide is

As mentioned before, gadolinium agent is not suitable for molecular or cellular imaging. In the last 10 years, most research of molecular imaging using MRI is focused on the

Compared to larger particles of the same chemical composition, nanoparticles can pass some biological barriers such as capillaries. Human albumin, a circulatory macromolecule, is similar to nanoparticles with a diameter of 5-10 nm (Wiwanitkit, 2006). Enzymes and receptors are also ranged in the similar size (Rawat, 2006). A nanoparticle of such size can have in excess of 1500 potential sites for chemical modification (Debbage et al., 2008; Harris et al., 2003) without loss of biological functionality. It is 150 times more than an antibody has. The high capacity for nanoparticle modification has led to their use as amplifiers for in vivo imaging. Both the surface properties and size of nanoparticles are important for their interaction with biological systems and therefore for their distribution in the circulation.

In considering the use in *in vivo* imaging, the ideal IO nanoparticles is with small size (5–150 nm) (table 1), high mass magnetization value, and great surface functionality. If the diameter of the MNPs is larger than 200 nm, they are usually taken up by the liver, spleen, and reticuloendothelial system and resulting in decreased blood circulation times. If their diameters are less than 5 nm, they are rapidly removed through the kidney (Gupta & Gupta, 2005). Different sizes of IO nanoparticles including SPIO (superparamagnetic IO, 60–150 nm), USPIO (ultrasmall SPIO, 10–50 nm), and MION (monocrystalline IO, 5–10 nm) can lead to different magnetic properties and function differently in various applications (Choi et al.,

The magnetism of MNP and its effect on MR imaging can depend significantly on their morphology, crystal structure, size and uniformity. The crystal structure of SPIO nanoparticle has the general formula of Fe3+O3M2+O, where M2+represents a divalent metal ion (i.e., iron, manganese, nickel, cobalt or magnesium) (Kateb et al., 2011). The ferric iron (Fe3+) makes the complex magnetic (Daldrup-Link et al., 2003; Wang et al., 2001) and large, unpaired, thermodynamically independent spines (single domain particles) makes the complex superparamagnetic. Single domain particles or magnetic domains have a net magnetic dipole. External magnetic fields can cause the magnetic domain to re-orient. The signal intensity of these MNP is related to the size of the particle, its position, its concentration within a given voxel, data acquisition parameters, the magnetic field, and dosage of the SPIO (Wang et al., 2001). In order to achieve higher relaxivity, types of MNPs have also been designed and included those doped with alternative metals such as CoFe2O4, NiFe2O4, MnFe2O4, Gd2O3 and gold-coated cobalt nanoparticles (Bouchard, et al., 2009; Bridot et al., 2007; Lee et al., 2007). Magnetism in MNPs is highly sensitive to its size because it arises from the collective interaction of atomic magnetic dipoles. At a critical size, MNPs will change from a state that has multiple magnetic domains to only a single domain. Below this critical size, the thermal energy becomes comparable to what is needed for spins to flip, and the magnetic dipoles are in status of rapid randomization. Such MNPs do not have

2006; Corot et al., 2006; de Vries et al., 2005; Thorek et al., 2006; Wang et al. 2001;).

the most common negative contrast medium used clinically.

application of IO nanoparticle.

pathological status. Owing to its magnetic character, iron oxide nanoparticle can be manipulated magnetically and altered their magnetic character according to size of core and the condition of the coating. In this assay, we are going to review the characteristic and types of magnetic nanoparticles (MNP), especially the IO nanoparticles, the mechanism of internalization of MNP into the cell, the impact to cellular and other behaviour of macrophage and stem cell after labelling with MNP, and the future of application of MNP in nanomedicine.

## **2. Magnetic resonance imaging and magnetic nanoparticles**

When we put a body into a strong magnetic field and then apply an external radiofrequency (RF) for a period. The RF may causes disturbance of the thermal equilibrium in the body system. After the RF stopped, MR imaging detects the different signals due to the different proton relaxation times (T) of hydrogen atom of the tissue in different body part. This makes MR offers great contrast between different soft tissues in the body. There are two types of MR imaging mechanisms: T1-weighted and T2-weighted.

T1, the ''longitudinal'' (spin-lattice) relaxation time is defined as the time required for a substance to regain the 63% of its original longitudinal magnetization after an RF pulse. It represents the correlation of frequency between molecular motions and the Larmor frequency. The frequencies of small molecule (e.g. water) and large molecule (e.g. protein) are significantly different from the Larmor frequency and thereby have long T1 and present as low signal intensity (dark) on T1-weighted images. The motion frequency of medium-sized molecule such as cholesterol close to those used for MR imaging, thereby it has a short T1 relaxation time and thus appear high signal intensity (bright) on T1 weighted images. T1 relaxation time can be shortened from the interaction between the unpaired electrons in the paramagnetic iron such as Gd ions in contrast medium and the protons in water. This makes those pathology with pooling of Gd contrast agent appear bright on T1-weighted images.

T2 is the ''transverse'' (spin-spin) relaxation time. Following a 90 degree RF pulse, the protons lose their coherence and transverse magnetization. The tissue inhomogeneity causes fluctuations of the magnetic field randomly, leading to variations in the precession frequency of different spins on x-y plane. Consequently, the net x-y magnetization is lost since the initial phase coherence is lost. This results in T2 relaxation. Thus T2 relaxation is a measure of how long the resonating protons of a substance can be changed from coherent to de-coherent and then back to coherent stage following 90 degree RF pulse in x-y plane. T2 relaxation time is defined as the time needed for the transverse magnetization decreases to 37% of its original magnitude after a 90 degree RF pulse. Generally, T2 relaxation is much less dependent on the magnetic field strength than T1 relaxation time. However, the magnetic field is not homogenous, and the process is depending on the exact location of the molecules in the magnet. In such circumstances, a special transverse relaxation time constant is defined as T2\*, which is usually much smaller than T2 and highly sensitive to magnetic field strength.

The MR contrast medium can be divided into positive and negative contrast media according to their characteristic appearance on T1- weighted or T2-weighted images.

pathological status. Owing to its magnetic character, iron oxide nanoparticle can be manipulated magnetically and altered their magnetic character according to size of core and the condition of the coating. In this assay, we are going to review the characteristic and types of magnetic nanoparticles (MNP), especially the IO nanoparticles, the mechanism of internalization of MNP into the cell, the impact to cellular and other behaviour of macrophage and stem cell after labelling with MNP, and the future of application of MNP in

When we put a body into a strong magnetic field and then apply an external radiofrequency (RF) for a period. The RF may causes disturbance of the thermal equilibrium in the body system. After the RF stopped, MR imaging detects the different signals due to the different proton relaxation times (T) of hydrogen atom of the tissue in different body part. This makes MR offers great contrast between different soft tissues in the body. There are two types of

T1, the ''longitudinal'' (spin-lattice) relaxation time is defined as the time required for a substance to regain the 63% of its original longitudinal magnetization after an RF pulse. It represents the correlation of frequency between molecular motions and the Larmor frequency. The frequencies of small molecule (e.g. water) and large molecule (e.g. protein) are significantly different from the Larmor frequency and thereby have long T1 and present as low signal intensity (dark) on T1-weighted images. The motion frequency of medium-sized molecule such as cholesterol close to those used for MR imaging, thereby it has a short T1 relaxation time and thus appear high signal intensity (bright) on T1 weighted images. T1 relaxation time can be shortened from the interaction between the unpaired electrons in the paramagnetic iron such as Gd ions in contrast medium and the protons in water. This makes those pathology with pooling of Gd contrast agent appear

T2 is the ''transverse'' (spin-spin) relaxation time. Following a 90 degree RF pulse, the protons lose their coherence and transverse magnetization. The tissue inhomogeneity causes fluctuations of the magnetic field randomly, leading to variations in the precession frequency of different spins on x-y plane. Consequently, the net x-y magnetization is lost since the initial phase coherence is lost. This results in T2 relaxation. Thus T2 relaxation is a measure of how long the resonating protons of a substance can be changed from coherent to de-coherent and then back to coherent stage following 90 degree RF pulse in x-y plane. T2 relaxation time is defined as the time needed for the transverse magnetization decreases to 37% of its original magnitude after a 90 degree RF pulse. Generally, T2 relaxation is much less dependent on the magnetic field strength than T1 relaxation time. However, the magnetic field is not homogenous, and the process is depending on the exact location of the molecules in the magnet. In such circumstances, a special transverse relaxation time constant is defined as T2\*, which is usually much smaller than T2 and highly sensitive to

The MR contrast medium can be divided into positive and negative contrast media

according to their characteristic appearance on T1- weighted or T2-weighted images.

**2. Magnetic resonance imaging and magnetic nanoparticles** 

MR imaging mechanisms: T1-weighted and T2-weighted.

bright on T1-weighted images.

magnetic field strength.

nanomedicine.

Positive contrast media appear brighter on MR images owing to a reduction in T1 relaxation time. They include those containing Gd, manganese or iron ions. Negative contrast agents appear dark on MR imaging due to shortening T1, T2, and T2\* relaxation times. Iron oxide is the most common negative contrast medium used clinically.

As mentioned before, gadolinium agent is not suitable for molecular or cellular imaging. In the last 10 years, most research of molecular imaging using MRI is focused on the application of IO nanoparticle.

Compared to larger particles of the same chemical composition, nanoparticles can pass some biological barriers such as capillaries. Human albumin, a circulatory macromolecule, is similar to nanoparticles with a diameter of 5-10 nm (Wiwanitkit, 2006). Enzymes and receptors are also ranged in the similar size (Rawat, 2006). A nanoparticle of such size can have in excess of 1500 potential sites for chemical modification (Debbage et al., 2008; Harris et al., 2003) without loss of biological functionality. It is 150 times more than an antibody has. The high capacity for nanoparticle modification has led to their use as amplifiers for in vivo imaging. Both the surface properties and size of nanoparticles are important for their interaction with biological systems and therefore for their distribution in the circulation.

In considering the use in *in vivo* imaging, the ideal IO nanoparticles is with small size (5–150 nm) (table 1), high mass magnetization value, and great surface functionality. If the diameter of the MNPs is larger than 200 nm, they are usually taken up by the liver, spleen, and reticuloendothelial system and resulting in decreased blood circulation times. If their diameters are less than 5 nm, they are rapidly removed through the kidney (Gupta & Gupta, 2005). Different sizes of IO nanoparticles including SPIO (superparamagnetic IO, 60–150 nm), USPIO (ultrasmall SPIO, 10–50 nm), and MION (monocrystalline IO, 5–10 nm) can lead to different magnetic properties and function differently in various applications (Choi et al., 2006; Corot et al., 2006; de Vries et al., 2005; Thorek et al., 2006; Wang et al. 2001;).

The magnetism of MNP and its effect on MR imaging can depend significantly on their morphology, crystal structure, size and uniformity. The crystal structure of SPIO nanoparticle has the general formula of Fe3+O3M2+O, where M2+represents a divalent metal ion (i.e., iron, manganese, nickel, cobalt or magnesium) (Kateb et al., 2011). The ferric iron (Fe3+) makes the complex magnetic (Daldrup-Link et al., 2003; Wang et al., 2001) and large, unpaired, thermodynamically independent spines (single domain particles) makes the complex superparamagnetic. Single domain particles or magnetic domains have a net magnetic dipole. External magnetic fields can cause the magnetic domain to re-orient. The signal intensity of these MNP is related to the size of the particle, its position, its concentration within a given voxel, data acquisition parameters, the magnetic field, and dosage of the SPIO (Wang et al., 2001). In order to achieve higher relaxivity, types of MNPs have also been designed and included those doped with alternative metals such as CoFe2O4, NiFe2O4, MnFe2O4, Gd2O3 and gold-coated cobalt nanoparticles (Bouchard, et al., 2009; Bridot et al., 2007; Lee et al., 2007). Magnetism in MNPs is highly sensitive to its size because it arises from the collective interaction of atomic magnetic dipoles. At a critical size, MNPs will change from a state that has multiple magnetic domains to only a single domain. Below this critical size, the thermal energy becomes comparable to what is needed for spins to flip, and the magnetic dipoles are in status of rapid randomization. Such MNPs do not have

Magnetic Nanoparticles: Its Effect on Cellular Behaviour and Potential Applications 361

solutions, well biocompatibility, and also with prolonged blood circulation time when they are delivered intravenously. The PEG can be modified for bioconjugation of various moieties such as antibody, oligonucleotides, and peptides and may allow for molecular specific intracellular targeting of specific proteins and nucleic acid (Gupta & Gupta, 2005; Kohler et al., 2004; Kumagai et al., 2007; Lee et al., 2006, 2007a; Mikhaylova et al., 2004; Nitin et al., 2004; Veiseh et al., 2005). PEG-coated MNP has the disadvantage such as limited binding sites available for further ligand binding (Gupta & Gupta, 2005), and the coating thickness can significantly affect their relaxivity (Laconte et al., 2007). In addition to PEG coating, other materials such as antibiofouling poly(TMSMA-r-PEGMA) (Lee et al., 2006), hyaluronic acid layers (Kumar et al., 2007) and carboxylfunctionalized poly(amidoamine) dendrimers of generation 3 (Shi et al., 2007) have also been used to coat the surface of IO nanoparticles for either increasing circulation time in the blood or delivering peptides at

For most of the clinical imaging application on magnetic nanoparticles, the delivery route is intravenous injection. The human immune system, mostly reticuloendothelial system, recognizes these magnetic nanoparticles and ingests them. The size and surface charge of the magnetic nanoparticles determine which kind of cells that interact with magnetic nanoparticles (Moghimi & Bonnemain 1999) For particles larger than 20 nm, macrophage and Kuppfer cell is the corresponding cells that deal with MNP (Moghimi & Hunter 2001, 2005). If the MNPs are less than 20 nm, these MNPs have greater opportunity to reside in lymph nodes, after they extravasate into interstitial spaces (Moghimi & Bonnemain 1999). Currently clinical approved iron oxide nanoparticles for MR images ranged mostly from 50- 100 nm, in which macrophages play important roles in ingestion of these MNPs. Macrophages are cells that prevent invading bacteria, viruses by phagocytosis of these microbes. It initiates inflammatory change by secreting cytokines such as tumor necrosis factor-alpha and interleukin 2-beta which recruits more circulating cells for repairing damaged tissue. Recent studies reveal macrophages also play important roles in tumor invasion. Consequently, alteration of macrophage behaviour has potential influence on human immunity, inflammatory process and cancer invasion. Understanding of impacts of

macrophages toward ingested magnetic nanoparticles is herein clinically important.

Two different MNPs are now under clinical use. Ferucarbotran is composed of both Fe3O4 (magnetite) and g-Fe2O3 (maghemite) and coated with carboxydextran that is negatively charged. Ferumoxides is also composed of iron oxide that coated with dextran. Protamine sulfate is usually added in cell culture for more efficient ferumoxides labelling (Arbab et al.,

Studies on clinically used MNPs, ferucarbotran, toward murine macrophage cell line revealed MNPs ingestion stimulates TNF-alpha and IL-2 Beta secretion. The migratory ability of MNPs laden macrophage increased but the phagocytotic activity of macrophages decreased (Hsiao et al., 2008) However, these findings are based on 100 ug Fe/mL MNP concentration that is 11 times higher than plasma concentration (Metz et al., 2004). Similar findings could be observed on murine peritoneal macrophage cultured with 100 ug Fe/mL MNPs. The secretion of TNF-alpha, IL-2 Beta and Nitric oxide, a bactericidal chemical, are

**3. Impact of magnetic nanoparticles in immunologic cell** 

high efficiency.

2006).


permanent magnetic moments in the absence of an external field but can quickly respond to an external magnetic field and are referred to as superparamagnetic.

Table 1. Examples of available SPIO and USPIO agents. Modified from Corot et al., 2006.

MION has a magnetically labeled cell probe MR imaging agent with size about 5-10nm. It has monocrystallinity and can be used for receptor-directed MR imaging. Its small size make MION can easily pass through capillary endothelium without changing its supermagnetism. It has been stated that it is possible to be detected by MR imaging at concentration as low as 1 ug Fe/g tissue. Though it is still in the experimental state, the preliminary targeted MR imaging with MION prove to be a powerful tool for cellular and molecular MR imaging in the future.

Many different chemical methods can be used for synthesizing magnetic nanoparticles. The most commonly used are precipitation-based approaches, either by co-precipitation or reverse micelle synthesis (Nitin et al., 2004; Shen et al., 1993). MNP without any surface coating are not stable in aqueous media, readily aggregate, and precipitate. For *in vivo* applications via intravenous route, these particles aggregates in blood frequently and are recognized and phagocytosed by macrophages (Lee et al., 2006). Therefore, the surface of MNP should be coated with a variety of different moieties that can eliminate or minimize their aggregation under physiological conditions. Usually, two main approaches are used for coating MNP, including in situ coatings and post-synthesis coatings (Berry et al., 2004; Horak et al., 2007; Jodin et al., 2006). With in situ coating, the MNP are coated during the synthesis process. This coating approach involves a co-precipitation process in the presence of the polysaccharide dextran and a cross linked chemically to increase its stability. This particular coating approach has been very successful in producing dextran SPIOs which are biocompatible and water – soluble. Other coatings in this class include carboxydextran coating, starch-based coating, and dendrimer-based coatings. The post-synthesis coatings can be used for coating MNP with a variety of materials, including, monolayer ligands, polymers, combinations of polymers and biomolecules such as phospholipids and carbohydrates, and silica.

Multiple MNP can also be encapsulated in liposomes to create magnetoliposomes (De Cuyper & Joniau, 1988). Polyethylene glycol (PEG)-modified, phospholipid micelles coating is favourable since this can results in satisfactory solubility and stability in aqueous

permanent magnetic moments in the absence of an external field but can quickly respond to

(nm)

Dextran T10 120-128 10.1 120

Carboxydextran 60 9.7 189

Pegylated starch 20 n.a. n.a.

Relaxivity (mM-1sec -1) r1

15-30 9.9 65

Relaxivity (mM-1sec -1) r2

an external magnetic field and are referred to as superparamagnetic.

Dextran T10, T1

Supravist SHU- 555 C Carboxydextran 21 10.7 38

Table 1. Examples of available SPIO and USPIO agents. Modified from Corot et al., 2006.

MION has a magnetically labeled cell probe MR imaging agent with size about 5-10nm. It has monocrystallinity and can be used for receptor-directed MR imaging. Its small size make MION can easily pass through capillary endothelium without changing its supermagnetism. It has been stated that it is possible to be detected by MR imaging at concentration as low as 1 ug Fe/g tissue. Though it is still in the experimental state, the preliminary targeted MR imaging with MION prove to be a powerful tool for cellular and

Many different chemical methods can be used for synthesizing magnetic nanoparticles. The most commonly used are precipitation-based approaches, either by co-precipitation or reverse micelle synthesis (Nitin et al., 2004; Shen et al., 1993). MNP without any surface coating are not stable in aqueous media, readily aggregate, and precipitate. For *in vivo* applications via intravenous route, these particles aggregates in blood frequently and are recognized and phagocytosed by macrophages (Lee et al., 2006). Therefore, the surface of MNP should be coated with a variety of different moieties that can eliminate or minimize their aggregation under physiological conditions. Usually, two main approaches are used for coating MNP, including in situ coatings and post-synthesis coatings (Berry et al., 2004; Horak et al., 2007; Jodin et al., 2006). With in situ coating, the MNP are coated during the synthesis process. This coating approach involves a co-precipitation process in the presence of the polysaccharide dextran and a cross linked chemically to increase its stability. This particular coating approach has been very successful in producing dextran SPIOs which are biocompatible and water – soluble. Other coatings in this class include carboxydextran coating, starch-based coating, and dendrimer-based coatings. The post-synthesis coatings can be used for coating MNP with a variety of materials, including, monolayer ligands, polymers, combinations of polymers and biomolecules such as phospholipids and

Multiple MNP can also be encapsulated in liposomes to create magnetoliposomes (De Cuyper & Joniau, 1988). Polyethylene glycol (PEG)-modified, phospholipid micelles coating is favourable since this can results in satisfactory solubility and stability in aqueous

Name Coating Size

Feridex/Endorem, Ferumoxides AMI-25

SHU-555 A

NC-100150

Resovist, Ferucarbotran

Combidex/ Sinerem Ferumoxtran-10 AMI-227

Clariscan, Feruglose

molecular MR imaging in the future.

carbohydrates, and silica.

solutions, well biocompatibility, and also with prolonged blood circulation time when they are delivered intravenously. The PEG can be modified for bioconjugation of various moieties such as antibody, oligonucleotides, and peptides and may allow for molecular specific intracellular targeting of specific proteins and nucleic acid (Gupta & Gupta, 2005; Kohler et al., 2004; Kumagai et al., 2007; Lee et al., 2006, 2007a; Mikhaylova et al., 2004; Nitin et al., 2004; Veiseh et al., 2005). PEG-coated MNP has the disadvantage such as limited binding sites available for further ligand binding (Gupta & Gupta, 2005), and the coating thickness can significantly affect their relaxivity (Laconte et al., 2007). In addition to PEG coating, other materials such as antibiofouling poly(TMSMA-r-PEGMA) (Lee et al., 2006), hyaluronic acid layers (Kumar et al., 2007) and carboxylfunctionalized poly(amidoamine) dendrimers of generation 3 (Shi et al., 2007) have also been used to coat the surface of IO nanoparticles for either increasing circulation time in the blood or delivering peptides at high efficiency.

## **3. Impact of magnetic nanoparticles in immunologic cell**

For most of the clinical imaging application on magnetic nanoparticles, the delivery route is intravenous injection. The human immune system, mostly reticuloendothelial system, recognizes these magnetic nanoparticles and ingests them. The size and surface charge of the magnetic nanoparticles determine which kind of cells that interact with magnetic nanoparticles (Moghimi & Bonnemain 1999) For particles larger than 20 nm, macrophage and Kuppfer cell is the corresponding cells that deal with MNP (Moghimi & Hunter 2001, 2005). If the MNPs are less than 20 nm, these MNPs have greater opportunity to reside in lymph nodes, after they extravasate into interstitial spaces (Moghimi & Bonnemain 1999). Currently clinical approved iron oxide nanoparticles for MR images ranged mostly from 50- 100 nm, in which macrophages play important roles in ingestion of these MNPs. Macrophages are cells that prevent invading bacteria, viruses by phagocytosis of these microbes. It initiates inflammatory change by secreting cytokines such as tumor necrosis factor-alpha and interleukin 2-beta which recruits more circulating cells for repairing damaged tissue. Recent studies reveal macrophages also play important roles in tumor invasion. Consequently, alteration of macrophage behaviour has potential influence on human immunity, inflammatory process and cancer invasion. Understanding of impacts of macrophages toward ingested magnetic nanoparticles is herein clinically important.

Two different MNPs are now under clinical use. Ferucarbotran is composed of both Fe3O4 (magnetite) and g-Fe2O3 (maghemite) and coated with carboxydextran that is negatively charged. Ferumoxides is also composed of iron oxide that coated with dextran. Protamine sulfate is usually added in cell culture for more efficient ferumoxides labelling (Arbab et al., 2006).

Studies on clinically used MNPs, ferucarbotran, toward murine macrophage cell line revealed MNPs ingestion stimulates TNF-alpha and IL-2 Beta secretion. The migratory ability of MNPs laden macrophage increased but the phagocytotic activity of macrophages decreased (Hsiao et al., 2008) However, these findings are based on 100 ug Fe/mL MNP concentration that is 11 times higher than plasma concentration (Metz et al., 2004). Similar findings could be observed on murine peritoneal macrophage cultured with 100 ug Fe/mL MNPs. The secretion of TNF-alpha, IL-2 Beta and Nitric oxide, a bactericidal chemical, are

Magnetic Nanoparticles: Its Effect on Cellular Behaviour and Potential Applications 363

Stem cells play promising roles in tissue regeneration and engineering. They could be used for tissue transplantation and it is now understand that stem cells also interact with cancer cells. Some of the stem cell promotes the growth of cancer cells whereas some animal model

There are different types of stem cells. Embryonic stem cells are pluripotent, which means the cells could differentiate into almost all cells. However, the ethics concern and current stem cell technology progress makes it less interesting for cell labelling. Mesenchymal stem cells are multi-potent cells that could differentiate into different kinds of cells of medical

Bone marrow derived mesenchymal stem cells are capable of differentiating into many tissue that is essential for tissue repair. However, when these cells delivered into damaged tissue, it is hard to differentiate where these cells are. Labelling cells with MNPs are then important to monitor the location, migration in vivo. It has been proved that MNPs labelled mesenchymal stem cells can be visualized for implantation into damaged cardiac tissue in porcine model (Kraitchman et al., 2002). In the study, ferumoxides incorporated with poly-L-lysine were incubated with swine mesenchymal stem cells and injected into myocardiocytes under X-ray guidance. Post-mortem histology shows injected cells resides in designated myocardial tissue. The labelled mesenchymal stem cells are also applied for monitoring the repair of lipopolysaccarides induced damaged brain tissue in rat model by using MNPs-tat peptide conjugate. The result shows cell migratory behaviour into the damaged brain (Jackson et al., 2010). For understanding of interaction between mesenchymal stem cells and tumor, labelled mesenchymal stem cells is also monitored for its interaction with glioma in mouse model by using ferucarbontran in conjunction with protamine sulfate and proved that mesenchymal stem cells reduce glioma growth and mesenchymal stem cells is capable of migration into glioma tissue (Chien et al., 2010).

The mechanism of MNPs uptake by different kinds of stem cells are not fully investigated but recent study shows endocytosis by clathrin receptor is one of the mechanisms (Huang et al., 2005; Lu et al., 2007). These study shows inhibitor of clathrin receptor, phenylarsine oxide, can block the ingestion of mesoporous iron oxide nanoparticles into human mesenchymal stem cells. Macropinocytosis also play significant role once if protamine sulfate is used. It is also proved that tat peptide linked MNPs enter cell by macropinocytosis

Most of stem cell labelling for MR imaging is based on T2 weighted contrast. However, some efforts aiming on T1 contrast agent such as gadolinium based chelates conjugating into mesoporous silica nanoparticles has been proved for its imaging capability in animals injected with human mesenchymal stem cells. The viability and differentiating capacity of these mesenchymal stem cells are preserved (Hsiao et al., 2008; Tsai et al., 2008). The mesoporous nanoparticles has also been labelled with fluorescent dyes that monitoring the

In addition to cell viability, labelled mesenchymal stem cells has been verified for its mitochondrial potential and reactive oxygen species, both of which represents intracellular stress. Neither mitochondrial potential nor reactive oxygen species change under

cells with fluorescent imaging modality is also possible.

**4. Impact of magnetic nanoparticles in stem cell** 

shows stem cell suppresses the tumor growth.

interest such as bone tissue and cartilage.

(Arbab et al., 2006).

all increased in conjunction with the promotion of macrophage migration ability (Yeh et al., 2010).

Long term exposure to MNPs has significant influence on macrophages. Research on human macrophages treated with ferucarbotran show increased apoptosis after 120 hours of incubation even at the concentration of 1 ug Fe/mL. Human macrophage also shows apoptotic change when facing smaller MNPs, supravist, a smaller particle of 20.8 nm in diameter, for 120 hours at the concentration of 0.1 ug Fe/mL (Lunov et al., 2010a). The apoptotic event is inducted by N-terminal kinase (JNK) pathway that is activated by reactive oxygen species (Lunov et al., 2010a; 2010b). There is evidence that elevated TNF-alpha induce human macrophage apoptosis after these macrophages expose to ferucarbotran for 3- 5 days. However, there is no evidence that support ferucarbotran stimulate TNF-alpha secretion on human macrophage. All of studies performed above are in vitro experiments that intravenous injection of MNPs and collecting of circulating macrophage are still pending. Moreover, under intravenous injection condition, all of clinical MNPs are eliminated by reticuloendothelial system within 30 minutes in which no toxic event are observed.

Human monocyte cell line, THP-1, is a precursor of macrophage and it has been evaluated for its interaction with ferumoxides. The ferumoxides has been mixed with 1mg/mL of protamine sulfate for higher labeling efficiency. Under incubation concentration of 4.5 ug Fe/mL of ferumoxides-protamine complex for 2 hours, there is no significant TNF-alpha secretion level change upon lipopolysaccharide stimulation (Janic et al., 2008). The CD-54 and CD-83 is not upregulated in response to lipopolysaccharide.

Lymphocytes are important immune cells that regulate both cellular and humoral immunity against invading organism and cancer cells. Although lymphocytes are not easily labeled with MNPs, it is still possible by modifying surface of MNPs with tat peptide, a HIV membrane translocating peptide that is specific to CD4+ lymphocytes (Garden et al., 2006). The synthesized Tat linked MNPs are 31.3± 8.5nm which is slightly larger than original MNPs that is 25.7± 6.1 nm. Under TEM, these particles located at both cytoplasm and nucleus, which is different from other MNPs that only located at lysosomes. There is neither proliferation ability nor IL-2 secretion capability change of CD4+ CD25+ lymphocytes after labelling with tat-linked MNPs (Garden et al., 2006). Dendritic cells are antigen presenting cells that express antigens to other immune cells, mostly lymphocytes, to continue immune response. Labelling of dendritic cells allows monitoring migration of these cells in vivo (Tavaré et al., 2011; Noh et al., 2011) The mouse dendritic cells were labelled with endorem, a clinically proved MNPs in Europe with corresponding product named ferumoxide in USA. There is no drastic effect of labelled dendritic cells such as T lymphocyte proliferation, in vivo growth rate of lymph nodes after labelled or unlabeled dendritic cells labelling. Under B16 melanoma lung metastatic model, both labelled and unlabeled dendritic cells show protective effect upon pulmonary metastasis (Tavaré et al., 2011).

In conclusion, the effects of MNPs toward immune cells are diverse, the cell type, particle size, charge and labelling amount all contribute to cell behaviour change. Although some reports show immunological response change after MNPs labelling, most of the MNPs exceeds the daily clinical practice. However, systemically analysis of MNPs and immune cells interaction is important and this study may have potential impact on immune therapy.

## **4. Impact of magnetic nanoparticles in stem cell**

362 Smart Nanoparticles Technology

all increased in conjunction with the promotion of macrophage migration ability (Yeh et al.,

Long term exposure to MNPs has significant influence on macrophages. Research on human macrophages treated with ferucarbotran show increased apoptosis after 120 hours of incubation even at the concentration of 1 ug Fe/mL. Human macrophage also shows apoptotic change when facing smaller MNPs, supravist, a smaller particle of 20.8 nm in diameter, for 120 hours at the concentration of 0.1 ug Fe/mL (Lunov et al., 2010a). The apoptotic event is inducted by N-terminal kinase (JNK) pathway that is activated by reactive oxygen species (Lunov et al., 2010a; 2010b). There is evidence that elevated TNF-alpha induce human macrophage apoptosis after these macrophages expose to ferucarbotran for 3- 5 days. However, there is no evidence that support ferucarbotran stimulate TNF-alpha secretion on human macrophage. All of studies performed above are in vitro experiments that intravenous injection of MNPs and collecting of circulating macrophage are still pending. Moreover, under intravenous injection condition, all of clinical MNPs are eliminated by reticuloendothelial system within 30 minutes in which no toxic event are

Human monocyte cell line, THP-1, is a precursor of macrophage and it has been evaluated for its interaction with ferumoxides. The ferumoxides has been mixed with 1mg/mL of protamine sulfate for higher labeling efficiency. Under incubation concentration of 4.5 ug Fe/mL of ferumoxides-protamine complex for 2 hours, there is no significant TNF-alpha secretion level change upon lipopolysaccharide stimulation (Janic et al., 2008). The CD-54

Lymphocytes are important immune cells that regulate both cellular and humoral immunity against invading organism and cancer cells. Although lymphocytes are not easily labeled with MNPs, it is still possible by modifying surface of MNPs with tat peptide, a HIV membrane translocating peptide that is specific to CD4+ lymphocytes (Garden et al., 2006). The synthesized Tat linked MNPs are 31.3± 8.5nm which is slightly larger than original MNPs that is 25.7± 6.1 nm. Under TEM, these particles located at both cytoplasm and nucleus, which is different from other MNPs that only located at lysosomes. There is neither proliferation ability nor IL-2 secretion capability change of CD4+ CD25+ lymphocytes after labelling with tat-linked MNPs (Garden et al., 2006). Dendritic cells are antigen presenting cells that express antigens to other immune cells, mostly lymphocytes, to continue immune response. Labelling of dendritic cells allows monitoring migration of these cells in vivo (Tavaré et al., 2011; Noh et al., 2011) The mouse dendritic cells were labelled with endorem, a clinically proved MNPs in Europe with corresponding product named ferumoxide in USA. There is no drastic effect of labelled dendritic cells such as T lymphocyte proliferation, in vivo growth rate of lymph nodes after labelled or unlabeled dendritic cells labelling. Under B16 melanoma lung metastatic model, both labelled and unlabeled dendritic cells

In conclusion, the effects of MNPs toward immune cells are diverse, the cell type, particle size, charge and labelling amount all contribute to cell behaviour change. Although some reports show immunological response change after MNPs labelling, most of the MNPs exceeds the daily clinical practice. However, systemically analysis of MNPs and immune cells interaction is important and this study may have potential impact on immune therapy.

and CD-83 is not upregulated in response to lipopolysaccharide.

show protective effect upon pulmonary metastasis (Tavaré et al., 2011).

2010).

observed.

Stem cells play promising roles in tissue regeneration and engineering. They could be used for tissue transplantation and it is now understand that stem cells also interact with cancer cells. Some of the stem cell promotes the growth of cancer cells whereas some animal model shows stem cell suppresses the tumor growth.

There are different types of stem cells. Embryonic stem cells are pluripotent, which means the cells could differentiate into almost all cells. However, the ethics concern and current stem cell technology progress makes it less interesting for cell labelling. Mesenchymal stem cells are multi-potent cells that could differentiate into different kinds of cells of medical interest such as bone tissue and cartilage.

Bone marrow derived mesenchymal stem cells are capable of differentiating into many tissue that is essential for tissue repair. However, when these cells delivered into damaged tissue, it is hard to differentiate where these cells are. Labelling cells with MNPs are then important to monitor the location, migration in vivo. It has been proved that MNPs labelled mesenchymal stem cells can be visualized for implantation into damaged cardiac tissue in porcine model (Kraitchman et al., 2002). In the study, ferumoxides incorporated with poly-L-lysine were incubated with swine mesenchymal stem cells and injected into myocardiocytes under X-ray guidance. Post-mortem histology shows injected cells resides in designated myocardial tissue. The labelled mesenchymal stem cells are also applied for monitoring the repair of lipopolysaccarides induced damaged brain tissue in rat model by using MNPs-tat peptide conjugate. The result shows cell migratory behaviour into the damaged brain (Jackson et al., 2010). For understanding of interaction between mesenchymal stem cells and tumor, labelled mesenchymal stem cells is also monitored for its interaction with glioma in mouse model by using ferucarbontran in conjunction with protamine sulfate and proved that mesenchymal stem cells reduce glioma growth and mesenchymal stem cells is capable of migration into glioma tissue (Chien et al., 2010).

The mechanism of MNPs uptake by different kinds of stem cells are not fully investigated but recent study shows endocytosis by clathrin receptor is one of the mechanisms (Huang et al., 2005; Lu et al., 2007). These study shows inhibitor of clathrin receptor, phenylarsine oxide, can block the ingestion of mesoporous iron oxide nanoparticles into human mesenchymal stem cells. Macropinocytosis also play significant role once if protamine sulfate is used. It is also proved that tat peptide linked MNPs enter cell by macropinocytosis (Arbab et al., 2006).

Most of stem cell labelling for MR imaging is based on T2 weighted contrast. However, some efforts aiming on T1 contrast agent such as gadolinium based chelates conjugating into mesoporous silica nanoparticles has been proved for its imaging capability in animals injected with human mesenchymal stem cells. The viability and differentiating capacity of these mesenchymal stem cells are preserved (Hsiao et al., 2008; Tsai et al., 2008). The mesoporous nanoparticles has also been labelled with fluorescent dyes that monitoring the cells with fluorescent imaging modality is also possible.

In addition to cell viability, labelled mesenchymal stem cells has been verified for its mitochondrial potential and reactive oxygen species, both of which represents intracellular stress. Neither mitochondrial potential nor reactive oxygen species change under

Magnetic Nanoparticles: Its Effect on Cellular Behaviour and Potential Applications 365

can traverse vasculature barrier and go into intercellular space or even cell surface once if

Hyperthermia with MNPs is based on the fact that tumor cells are more liable toward temperature change. It have been investigated that temperature between 41°C and 42°C can induce tumor cell death by destruction of cell membrane (Sellins & Cohen, 1991). The enzymatic system is also influenced. The hyperthermia is achieved by alternating current magnetic field system around the frequency of 100 KHz at the magnetic field intensity in 30.6 kA/m (Silva et al., 2011). Limited clinical trial was done and showed controversial effect (Maier-Hauff et al., 2007; 2011). In one study, 66 patients of glioblastoma, a high grade brain tumor, were enrolled and MNPs were injected into tumor of these patient. Hyperthermia associated with radiotherapy was done and there is statistical difference between hyperthermia group and traditional radiotherapy group. The survival after first diagnosis is 8.6 months longer in hyperthermia group compared with conventional treatment group. In addition, the adverse effect of hyperthermia is not significant according

Photodynamic therapy is one of the cancer treatment methods that have also been used for theragnostic purpose. The mechanism of photodynamic therapy is based on synthesis of singlet oxygen at the expense of photon activation of photosensitizer. The produced singlet oxygen is capable of destruct adjacent cells by oxidation. Some of the photosensitizers are clinically available. Efforts trying to conjugate MNPs with photosensitizers have potential benefits such as understanding the location of drugs accumulation and MNPs can also be guided by magnetic fields. The model of multi-functional MNPs has been proved possible in vitro. Hela cells can be imaged and killed by iridium complexes conjugated iron oxide nanoparticles (Lai et al., 2008). The iridium complexes have been also conjugated to MnO based mesoporous silicate nanoparticles that exhibit T1 weighted contrast enhancement. The photodynamic therapy effect is proved efficacious at in vitro HeLa cell model (Peng et al.,

Gene therapy is at the edge of new strategy for cancer therapy. MNPs is capable of serving gene delivery carrier and also used for magnetic guidance. Studies focused on cancer related gene such as E1A has been successfully delivered into HeLa cells after E1A gene incoporated with iron oxide nanoparticles. Intratumoral injection of the plasmid-MNPs complex results in tumor size reduction compared with control group, whereas only

In conclusion, multifunctional MNPs are at the initial stage of development. The benefits of biodistribution and magnetic character make theragnostic strategy different from other treatment. However, more efforts upon toxicity and therapeutic range should be done

Cellular Imaging can be an application of MNP as cellular marker for imaging of macrophage activity and as cellular marker for imaging of cell migration and cell trafficking. With the advancement of modern molecule design, we can also have the capability of design

recognizing molecules has been conjugated at the MNPs surface.

to the observation of the study (Maier-Hauff et al., 2011).

radiation therapy was done (Shen et al., 2010).

before it has been used widely in the clinical medical fields.

a MNP with the role of both diagnostic and treatment.

2011).

**6. Future** 

ferucarbotran incubation at the concentration of 100 ug Fe/mL for 24 hours (Hsiao et al., 2007). Long term incubation up to 72 hours has also been investigated and shows no adverse effect upon mesenchymal stem cells (Yang et al., 2011). Similar results are found on ferumoxide-polylysine and ferumoxides-protamine sulfate complex toward mesenchymal stem cells (Arbab et al., 2003; Pawelczyk et al., 2006).

Stem cells are valuable for its differentiation capacity. Concerns for preserving its differentiating capacity are essential. For clinical used MNPs such as ferucarbotran for directly labelling, it has been showed that labelled mesenchymal stem cells is still capable of differentiating to adipose tissue, and bone tissue at the labelling period of 24 hours (Hsiao et al., 2007). The long term effect has also been evaluated for its cartilage differentiation capacity (Yang et al., 2011). The activity of chondrogenesis of ferucarbontran labelled mesenchymal stem cells decreased as iron content increases (Hinning et al., 2009). Similar finding upon osteogenesis is also found. Dose dependent osteogenesis inhibition is observed on human mesenchymal stem cells (Chen et al., 2010). The labelling dose is consequently very important.

Labelling of mesenchymal stem cells with ferumoxides in conjunction with transfection agent is also popular. The differentiation capacity has also been studied. The adipogenesis and osteogenesis capacity is preserved but there is debate upon chondrogenesis (Kostura et al., 2004; Arbab et al., 2005). The model of ferumoxides-polylysine shows inhibition of chondrogenesis whereas ferumoxide-protamine sulfate shows no inhibitory effect. Although there is no study comparing these two labelling method, the ferumoxide-protamine sulfate and ferumoxide-polylysine complex, labelling mesenchymal stem cells with ferumoxideprotamine sulfate might be better for further investigation. Besides, labelling dose of MNPs should be suitable for preserving imaging capability and differentiating capacity.

In conclusion, labelling of stem cells for imaging is medically important that could be used for cell trafficking and potentially tumor inhibition. Although imaging capability of these labelled mesenchymal stem cells is concerned, the differentiation capacity of these cells should be preserved. Meanwhile, no satisfactory methods or consensus about labelling stem cell with MNP established though direct labelling using ferucarbotran or labelling ferumoxides with protamine sulfate are popular. Efforts on designing novel MNPs for cell labelling is still demanding.

## **5. Bifunctional, multi-functional, and theragnostic magnetic nanoparticles**

Nanoparticles have advantages for their multi-conjugating capability that makes it possible to exhibit imaging and therapeutic character in one particle. The capability of imaging is mostly rely on the core that is magnetic. Either the shell or the core itself exhibit therapeutic effect. The therapeutic effects include gene delivery, hyperthermia, chemotherapy and photodynamic therapy. The benefits of theragnostic design are based on the following advantages. First, the magnetic core plays both imaging and magnetic guidance character. Targeting to specific organ or tissue is theoretically possible once if a guiding magnetic is applied. Secondly, the location where MNPs resides and acts as therapeutic agent can be visualized. Unlike most drugs that are small molecules, MNPs has different, specific organ and cell distribution that makes it possible for different treatment strategy. Lastly, MNPs can traverse vasculature barrier and go into intercellular space or even cell surface once if recognizing molecules has been conjugated at the MNPs surface.

Hyperthermia with MNPs is based on the fact that tumor cells are more liable toward temperature change. It have been investigated that temperature between 41°C and 42°C can induce tumor cell death by destruction of cell membrane (Sellins & Cohen, 1991). The enzymatic system is also influenced. The hyperthermia is achieved by alternating current magnetic field system around the frequency of 100 KHz at the magnetic field intensity in 30.6 kA/m (Silva et al., 2011). Limited clinical trial was done and showed controversial effect (Maier-Hauff et al., 2007; 2011). In one study, 66 patients of glioblastoma, a high grade brain tumor, were enrolled and MNPs were injected into tumor of these patient. Hyperthermia associated with radiotherapy was done and there is statistical difference between hyperthermia group and traditional radiotherapy group. The survival after first diagnosis is 8.6 months longer in hyperthermia group compared with conventional treatment group. In addition, the adverse effect of hyperthermia is not significant according to the observation of the study (Maier-Hauff et al., 2011).

Photodynamic therapy is one of the cancer treatment methods that have also been used for theragnostic purpose. The mechanism of photodynamic therapy is based on synthesis of singlet oxygen at the expense of photon activation of photosensitizer. The produced singlet oxygen is capable of destruct adjacent cells by oxidation. Some of the photosensitizers are clinically available. Efforts trying to conjugate MNPs with photosensitizers have potential benefits such as understanding the location of drugs accumulation and MNPs can also be guided by magnetic fields. The model of multi-functional MNPs has been proved possible in vitro. Hela cells can be imaged and killed by iridium complexes conjugated iron oxide nanoparticles (Lai et al., 2008). The iridium complexes have been also conjugated to MnO based mesoporous silicate nanoparticles that exhibit T1 weighted contrast enhancement. The photodynamic therapy effect is proved efficacious at in vitro HeLa cell model (Peng et al., 2011).

Gene therapy is at the edge of new strategy for cancer therapy. MNPs is capable of serving gene delivery carrier and also used for magnetic guidance. Studies focused on cancer related gene such as E1A has been successfully delivered into HeLa cells after E1A gene incoporated with iron oxide nanoparticles. Intratumoral injection of the plasmid-MNPs complex results in tumor size reduction compared with control group, whereas only radiation therapy was done (Shen et al., 2010).

In conclusion, multifunctional MNPs are at the initial stage of development. The benefits of biodistribution and magnetic character make theragnostic strategy different from other treatment. However, more efforts upon toxicity and therapeutic range should be done before it has been used widely in the clinical medical fields.

## **6. Future**

364 Smart Nanoparticles Technology

ferucarbotran incubation at the concentration of 100 ug Fe/mL for 24 hours (Hsiao et al., 2007). Long term incubation up to 72 hours has also been investigated and shows no adverse effect upon mesenchymal stem cells (Yang et al., 2011). Similar results are found on ferumoxide-polylysine and ferumoxides-protamine sulfate complex toward mesenchymal

Stem cells are valuable for its differentiation capacity. Concerns for preserving its differentiating capacity are essential. For clinical used MNPs such as ferucarbotran for directly labelling, it has been showed that labelled mesenchymal stem cells is still capable of differentiating to adipose tissue, and bone tissue at the labelling period of 24 hours (Hsiao et al., 2007). The long term effect has also been evaluated for its cartilage differentiation capacity (Yang et al., 2011). The activity of chondrogenesis of ferucarbontran labelled mesenchymal stem cells decreased as iron content increases (Hinning et al., 2009). Similar finding upon osteogenesis is also found. Dose dependent osteogenesis inhibition is observed on human mesenchymal stem cells (Chen et al., 2010). The labelling dose is consequently

Labelling of mesenchymal stem cells with ferumoxides in conjunction with transfection agent is also popular. The differentiation capacity has also been studied. The adipogenesis and osteogenesis capacity is preserved but there is debate upon chondrogenesis (Kostura et al., 2004; Arbab et al., 2005). The model of ferumoxides-polylysine shows inhibition of chondrogenesis whereas ferumoxide-protamine sulfate shows no inhibitory effect. Although there is no study comparing these two labelling method, the ferumoxide-protamine sulfate and ferumoxide-polylysine complex, labelling mesenchymal stem cells with ferumoxideprotamine sulfate might be better for further investigation. Besides, labelling dose of MNPs

In conclusion, labelling of stem cells for imaging is medically important that could be used for cell trafficking and potentially tumor inhibition. Although imaging capability of these labelled mesenchymal stem cells is concerned, the differentiation capacity of these cells should be preserved. Meanwhile, no satisfactory methods or consensus about labelling stem cell with MNP established though direct labelling using ferucarbotran or labelling ferumoxides with protamine sulfate are popular. Efforts on designing novel MNPs for cell

**5. Bifunctional, multi-functional, and theragnostic magnetic nanoparticles** 

Nanoparticles have advantages for their multi-conjugating capability that makes it possible to exhibit imaging and therapeutic character in one particle. The capability of imaging is mostly rely on the core that is magnetic. Either the shell or the core itself exhibit therapeutic effect. The therapeutic effects include gene delivery, hyperthermia, chemotherapy and photodynamic therapy. The benefits of theragnostic design are based on the following advantages. First, the magnetic core plays both imaging and magnetic guidance character. Targeting to specific organ or tissue is theoretically possible once if a guiding magnetic is applied. Secondly, the location where MNPs resides and acts as therapeutic agent can be visualized. Unlike most drugs that are small molecules, MNPs has different, specific organ and cell distribution that makes it possible for different treatment strategy. Lastly, MNPs

should be suitable for preserving imaging capability and differentiating capacity.

stem cells (Arbab et al., 2003; Pawelczyk et al., 2006).

very important.

labelling is still demanding.

Cellular Imaging can be an application of MNP as cellular marker for imaging of macrophage activity and as cellular marker for imaging of cell migration and cell trafficking. With the advancement of modern molecule design, we can also have the capability of design a MNP with the role of both diagnostic and treatment.

Magnetic Nanoparticles: Its Effect on Cellular Behaviour and Potential Applications 367

Arbab, A.S., Yocum, G.T., Rad, A.M., Khakoo, A.Y., Fellowes, V., Read, E.J., & Frank J.A.

Arbab, A.S., Liu, W., & Frank, J.A. (2006).Cellular magnetic resonance imaging: current

Achilefu, S. (2010) Introduction to concept and strategies for molecular imaging. *Chem. Rev.* 

Berry, C.C., Wells, S., Charles, S., Aitchison, G., & Curtis, A.S. (2004). Cell response to

Bouchard, L.S., Anwar, M.S., Liu, G.L., Hann, B., Xie, Z.H., Gray, J.W., Wang, X., Pines, A., &

Bradbury, M. & Hricak, H. (2005). Molecular MR imaging in oncology. *Magn Reson Imaging* 

Bridot, J.L., Faure, A.C., Laurent, S., Rivière, C., Billotey, C., Hiba, B., Janier, M., Josserand,

Briley-Saebo, K., Bjørnerud, A., Grant, D., Ahlstrom, H., Berg, T., & Kindberg, G.M. (2004).

Chen, Y.C., Hsiao, J.K., Liu, H.M., Lai, I.Y., Yao, M., Hsu, S.C., Ko, B.S., Chen, Y.C., Yang,

Chien, L.Y., Hsiao, J.K., Hsu, S.C., Yao, M., Lu, C.W., Liu, H.M., Chen, Y.C., Yang, C.S., &

Choi, S.H., Han, M.H., Moon, W.K., Son, K.R., Won, J.K., Kim, J.H., Kwon, B.J., Na, D.G.,

Corot, C. Robert, P., Idée, J.M., & Port, M. (2006) Recent advances in iron oxide nanocrystal technology for medical imaging. Adv. Drug Deliv. Rev. 58, 1471–1504. Daldrup-Link, H.E., Rudelius, M., Oostendorp, R.A., Settles, M., Piontek, G., Metz, S.,

rabbit model of head and neck cancer. *Radiology*, 241 (3), 753–762.

status and future prospects. *Expert Rev Med Devices,* 3(4), 427-439.

nanoparticles. *Proc. Natl. Acad. Sci.* 106, 4085–4089

imaging. *J. Am. Chem. Soc.* 129, 5076–5084

glioma model. *Biomaterials,* 32(12), 3275-3284.

MR imaging. *Radiology*, 229(3),838-846.

cells. *NMR in Biomed,* 18(8), 553-559.

110, 2575–2578

*Clin N Am,* 13,225–240.

*Cell Tissue Res.* 316, 315–323.

245(2), 272-279.

*Radiology*, 228, 760–767.

5405–5413.

with superparamagnetic iron oxide nanoparticles and transfection agent for cellular

(2005). Labeling of cells with ferumoxides-protamine sulfate complexes does not inhibit function or differentiation capacity of hematopoietic or mesenchymal stem

dextranderivatised iron oxide nanoparticles post internalisation. *Biomaterials,* 25,

Chen, F.F. (2009). Picomolar sensitivity MRI and photoacoustic imaging of cobalt

V., Coll, J.L., Elst, L.V., Muller, R., Roux, S., Perriat, P., & Tillement, O. (2007). Hybrid gadolinium oxide nanoparticles: multimodal contrast agents for in vivo

Hepatic cellular distribution and degradation of iron oxide nanoparticles following single intravenous injection in rats: implications for magnetic resonance imaging.

C.S., & Huang, D.M. (2010). The inhibitory effect of superparamagnetic iron oxide nanoparticle (Ferucarbotran) on osteogenic differentiation and its signaling mechanism in human mesenchymal stem cells. *Toxicology and Applied Pharmacology,*

Huang, D.M. (2011). In vivo magnetic resonance imaging of cell tropism, trafficking mechanism, and therapeutic impact of human mesenchymal stem cells in a murine

Weinmann, H.J., & Chang, K.H. (2006). Cervical lymph node metastases: MR imaging of gadofluorine M and monocrystalline iron oxide nanoparticle-47 in a

Rosenbrock, H., Keller, U., Heinzmann, U., Rummeny, E.J., Schlegel, J., & Link, T.M., (2003). Targeting of hematopoietic progenitor cells with MR contrast agents.

A major limitation of IO MNP is the loss of signal on T2-weighted MRI and creating 'black holes' on images; that (1) prevent direct anatomical MR evaluation of the tissue in question (requiring comparison of pre- and post-contrast images), and (2) make it difficult to discriminate between targeted cells and image artefacts (i.e. as caused by susceptibility artifacts or imperfect pulse sequences).One such approach could be the use of a 'white marker' MR T1-weighted sequence, that creates positive MNP contrast. For cellular imaging, as labelling is not permanent and self-replicable like reporter genes, with dilution of label upon cell division, iron oxide detection may rapidly become impossible. Finally, careful iron oxide titration and cellular differentiation studies need to be performed. Short- and longterm toxicity studies are warranted. It needs a comprehensive study on the fate of the particles in vivo following biodegradation; quantify the number of iron oxide labelled molecules or cells per voxel and to increase the specificity of detection of iron oxides.

Perhaps the least studied limitation is the potential acute and chronic systemic toxicity of the particles themselves. Toxicity can result from the MNP themselves or the individual components of the MNP that can be released during degradation in vivo. Nanomaterials may influence a living organism through different biological pathways (Nel et al., 2006). From previous limited report IO MNP and gold colloids seem to be less of a concern in terms of toxicity and IO can be cleared from the body via various routes with minimal toxicity (Briley-Saebo et al., 2004; Corot et al., 2006; Jain et al., 2008). Different types of nanoparticles have been shown to be cytotoxic to human cells (Lewinski et al., 2008), induce oxidative stress (Long et al., 2006), or elicit an immune response (Dobrovolskaia et al., 2007). After administration, nanoparticles must traverse a complex and often hostile environments that have evolved to seek out and exclude foreign material (Minchin et al., 1999). The first few steps of this dangerous journey include the interacting with plasma proteins and accumulating in macrophages or the reticuloendothelial system of the liver, spleen, or lymph nodes. The types of proteins that absorb to the surface are affected by size, shape, and surface characteristics. Importantly, there is now strong evidence that the proteins that surround the nanoparticles play a critical role in determining their fate in vivo (Kreuter et al., 2002; Owens et al.; 2006, Lynch et al., 2006). Dextran is clinically approved for modifying IO MNP but liver accumulation is still evident. Silica nanoparticles have been evaluated for potential hepatoxicity because of their propensity to be taken up by the liver (Nishimori et al., 2009).Whereas large particles (>300nm) showed little adverse effects, particles less than 100 nm induced acute liver damage and cytokine release.

## **7. Conclusion**

The nanotechnology offer great opportunities for molecular imaging and future medicine. However, they are difficulty in designing and administration. The possible acute or chronic toxicity associated with the nanoparticle is still under investigated. The implementation of nanotechnology in medicine will depend on more understand and depth knowledge about them.

## **8. References**

Arbab, A.S., Bashaw, L.A., Miller, B.R., Jordan, E.K., Lewis, B.K., Kalish, H., & Frank, J.A. (2003). Characterization of biophysical and metabolic properties of cells labeled

A major limitation of IO MNP is the loss of signal on T2-weighted MRI and creating 'black holes' on images; that (1) prevent direct anatomical MR evaluation of the tissue in question (requiring comparison of pre- and post-contrast images), and (2) make it difficult to discriminate between targeted cells and image artefacts (i.e. as caused by susceptibility artifacts or imperfect pulse sequences).One such approach could be the use of a 'white marker' MR T1-weighted sequence, that creates positive MNP contrast. For cellular imaging, as labelling is not permanent and self-replicable like reporter genes, with dilution of label upon cell division, iron oxide detection may rapidly become impossible. Finally, careful iron oxide titration and cellular differentiation studies need to be performed. Short- and longterm toxicity studies are warranted. It needs a comprehensive study on the fate of the particles in vivo following biodegradation; quantify the number of iron oxide labelled

molecules or cells per voxel and to increase the specificity of detection of iron oxides.

100 nm induced acute liver damage and cytokine release.

**7. Conclusion** 

**8. References** 

them.

Perhaps the least studied limitation is the potential acute and chronic systemic toxicity of the particles themselves. Toxicity can result from the MNP themselves or the individual components of the MNP that can be released during degradation in vivo. Nanomaterials may influence a living organism through different biological pathways (Nel et al., 2006). From previous limited report IO MNP and gold colloids seem to be less of a concern in terms of toxicity and IO can be cleared from the body via various routes with minimal toxicity (Briley-Saebo et al., 2004; Corot et al., 2006; Jain et al., 2008). Different types of nanoparticles have been shown to be cytotoxic to human cells (Lewinski et al., 2008), induce oxidative stress (Long et al., 2006), or elicit an immune response (Dobrovolskaia et al., 2007). After administration, nanoparticles must traverse a complex and often hostile environments that have evolved to seek out and exclude foreign material (Minchin et al., 1999). The first few steps of this dangerous journey include the interacting with plasma proteins and accumulating in macrophages or the reticuloendothelial system of the liver, spleen, or lymph nodes. The types of proteins that absorb to the surface are affected by size, shape, and surface characteristics. Importantly, there is now strong evidence that the proteins that surround the nanoparticles play a critical role in determining their fate in vivo (Kreuter et al., 2002; Owens et al.; 2006, Lynch et al., 2006). Dextran is clinically approved for modifying IO MNP but liver accumulation is still evident. Silica nanoparticles have been evaluated for potential hepatoxicity because of their propensity to be taken up by the liver (Nishimori et al., 2009).Whereas large particles (>300nm) showed little adverse effects, particles less than

The nanotechnology offer great opportunities for molecular imaging and future medicine. However, they are difficulty in designing and administration. The possible acute or chronic toxicity associated with the nanoparticle is still under investigated. The implementation of nanotechnology in medicine will depend on more understand and depth knowledge about

Arbab, A.S., Bashaw, L.A., Miller, B.R., Jordan, E.K., Lewis, B.K., Kalish, H., & Frank, J.A.

(2003). Characterization of biophysical and metabolic properties of cells labeled

with superparamagnetic iron oxide nanoparticles and transfection agent for cellular MR imaging. *Radiology*, 229(3),838-846.


Magnetic Nanoparticles: Its Effect on Cellular Behaviour and Potential Applications 369

Jackson, J.S., Golding , J.P., Chapon, C., Jones, W.A., & Bhakoo, K.K. (2010) Homing of stem

Jain, T.K. Reddy, M.K., Morales, M.A., Leslie-Pelecky, D.L., & Labhasetwar, V. (2008).

Janic, B., Iskander,,A.S., Rad, A.M., Soltanian-Zadeh, H., & Arbab, A.S. (2008). Effects of

Jodin, L., Dupuis, A.C., Rouviere, E., & Reiss, P. (2006). Infl uence of the catalyst type on the

Kateb, B., Chiu, K., Black, K.L., Yamamoto, V., Khalsa, B., Ljubimova, J.Y., Ding, H. , Patil,

Kostura, L., Kraitchman, D.L., Mackay, A.M., Pittenger, M.F., & Bulte, J.W. (2004). Feridex

Kraitchman, D.L., Heldman, A,W,, Atalar, E,, Amado, L.C., Martin, B.J., Pittenger, M.F.,

Kumagai, M., Imai, Y., Nakamura, T., Yamasaki, Y., Sekino, M., Ueno, S., Hanaoka, K.,

Kumar, A., Sahoo, B., Montpetit, A., Behera, S., Lockey, R.F., & Mohapatra, S.S. (2007).

Laconte, L.E., Nitin, N., Zurkiya, O., Caruntu, D., O'Connor, C.J., Hu, X., & Bao, G. (2007).

Lai, C.W., Wang, Y.H., Lai, CH., Yang, M.J., Chen, C.Y., Chou, P.T., Chan, C.S., Chi, Y.,

drugs across the blood-brain barrier. *J Drug Target,* 10,317–325.

drug delivery: What should be the policy? *NeuroImage*, 54, S106–S124 Kohler, N., Fryxell, G.E., & Zhang, M. (2004). A bifunctional poly(ethylene glycol) silane

administration: a longitudinal imaging study. *Stem Cell Res Ther.* 1(2),17. Jain, K.K. (2005). Role of nanobiotechnology in developing personalized medicine for cancer.

implication for stem cell tracking. *FASEB J.,* 19(14),2014-2016.

*Technol Cancer Res Treat,* 4,645–650.

110,7328–7333.

nanoparticles in rats. *Mol. Pharm.,* 5, 316–327.

targeting agents. *J Am Chem Soc,* 126,7206–7211.

osteogenesis. *NMR in Biomed,* 17(7),513-517.

imaging. *Colloids Surf B Biointerfaces,* 56,174–81.

delivery of peptides. *Nanomedicine,* 3,132–137.

*Magn Reson Imaging,* 26,1634–41.

of Macrophage-like THP-1 Cells. *PLoS ONE,* 3(6), e2499.

labeling of mesoporous nanoparticles in human mesenchymal stem cells:

cells to sites of inflammatory brain injury after intracerebral and intravenous

Biodistribution, clearance, and biocompatibility of iron oxide magnetic

Ferumoxides – Protamine Sulfate Labeling on Immunomodulatory Characteristics

growth of carbon nanotubes via methane chemical vapor deposition. *J Phys Chem B,* 

R., Portilla-Arias, J.A. , Modo, M. , Moore, D.F., Farahani, K., Okun, M.S., Prakash, N., Neman, J., Ahdoot, D., Grundfest, W., Nikzad, S., & Heiss, J.D. (2011). Nanoplatforms for constructing new approaches to cancer treatment, imaging, and

immobilized on metallic oxide-based nanoparticles for conjugation with cell

labeling of mesenchymal stem cells inhibits chondrogenesis but not adipogenesis or

Hare, J.M.,& Bulte, J.W. (2003). In Vivo Magnetic Resonance Imaging of Mesenchymal Stem Cells in Myocardial Infarction. *Circulation,* 107(18), 2290-2293. Kreuter, J., Shamenkov, D., Petrov, V., Ramge, P., Cychutek, K., Koch-Brandt, C., &

Alyautdin, R. (2002). Apolipoprotein-mediated transport of nanoparticle-bound

Kikuchi, K., Nagano, T., Kaneko, E., Shimokado, K., & Kataoka, K. (2007). Iron hydroxide nanoparticles coated with poly(ethylene glycol)-poly(aspartic acid) block copolymer as novel magnetic resonance contrast agents for in vivo cancer

Development of hyaluronic acid-Fe2O3 hybrid magnetic nanoparticles for targeted

Coating thickness of magnetic iron oxide nanoparticles affects R(2) relaxivity. *J* 

Chen, Y.C., & Hsiao, J.K. (2008). Iridium-complex-functionalized Fe3O4/SiO2


Debbage, P., & Jaschke,W. (2008). Molecular imaging with nanoparticles: giant roles for

De Cuyper, M., & Joniau, M. (1988). Magnetoliposomes. Formation and structural

de Vries, I.J., Lesterhuis, W.J., Barentsz, J.O., Verdijk, P., van Krieken, J.H., Boerman, O.C.,

Dobrovolskaia, M.A., & McNeil, S.E. (2007). Immunological properties of engineered

Funovics, M.A., Kapeller, B., Hoeller, C., Su, H.S., Kunstfeld, R., Puig, S., & Macfelda, K.

Garden, O.A., Reynolds, P.R., Yates, J., Larkman, D.J., Marelli-Berg, F.M., Haskard, D.O.,

Gupta, A.K., & Gupta, M. (2005). Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications. *Biomaterials,* 26, 3995–4021. Harisinghani, M.G., Barentsz, J., Hahn, P.F., Deserno, W.M., Tabatabaei, S., van de Kaa,

Henning, T.D., Sutton, E.J., Kim, A., Golovko, D., Horvai, A., Ackerman, L., Sennino, B.,

Horak, D., Babic, M., Jendelova, P., Herynek, V., Trchová, M., Pientka, Z., Pollert, E., Hájek,

Hsiao, J.K., Tai, M.F., Chu, H.H., Chen, S.T., Li, H., Lai, D.M., Hsieh, S.T., Wang, J.L., & Liu,

magnetic resonance at the single cell level. *Magn Reson Med,* 58(4),717-724. Hsiao, J.K., Chu, H.H., Wang, Y.H., Lai, C.W., Chou, P.T., Hsieh, S.T., Wang, J.L., & Liu,

Hsiao, J.K., Tsai, C.P., Chung, T.H., Hung, Y., Yao, M., Liu, H.M., Mou, C.Y., Yang, C.S.,

immunospecific contrast agents. *Magn Reson Imaging,* 22,843–850.

Oyen, W.J., Bonenkamp, J.J., Boezeman, J.B., Adema, G.J., Bulte, J.W., Scheenen, T.W., Punt, C.J., Heerschap, A., & Figdor, C.G., (2005). Magnetic resonance tracking of dendritic cells in melanoma patients for monitoring cellular therapy. *Nat.* 

(2004). MR imaging of the her2/neu and 9.2.27 tumor antigens using

Edwards, A.D., & George, A.J. (2006). A rapid method for labelling CD4+ T cells with ultrasmall paramagnetic iron oxide nanoparticles for magnetic resonance imaging that preserves proliferative, regulatory and migratory behaviour in vitro.

C.H., de la Rosette, J., & Weissleder, R. (2003). Noninvasive detection of clinically occult lymph-node metastases in prostate cancer. *N Engl J Med,* 348,2491–2499. Harris, L.A., Goff, J.D., Carmichael, A.Y., Riffle, J.S., Harburn, J.J., St. Pierre, T.G., &

Saunders, M. (2003) Magnetite nanoparticle dispersions stabilized with triblock

McDonald, D., Lotz, J., & Daldrup-Link, H.E. (2009). The influence of ferucarbotran on the chondrogenesis of human mesenchymal stem cells. *Contrast media &* 

M., & Syková, E. (2007). D-mannose-modified iron oxide nanoparticles for stem cell

H.M. (2007). Magnetic nanoparticle labeling of mesenchymal stem cells without transfection agent: cellular behavior and capability of detection with clinical 1.5 T

H.M. (2008). Macrophage physiological function after superparamagnetic iron

Chen, Y.C., & Huang, D.M. (2008). Mesoporous silica nanoparticles as a delivery system of gadolinium for effective human stem cell tracking. *Small,* 4(9),1445-1452. Huang, D.M., Hung, Y., Ko, B.S., Hsu, S.C., Chen, W.H., Chien, C.L., Tsai, C.P., Kuo, C.T.,

Kang, J.C., Yang, C.S., Mou, C.Y., & Chen, Y.C. (2005). Highly efficient cellular

dwarf actors. *Histochem Cell Biol,* 130,845–875.

characterization. *Eur Biophys J,* 15,311–319.

nanomaterials. *Nat Nanotechnol*, 2,469–478.

*Journal of Immunological Methods,* 314(1-2), 123-133.

copolymers. *Chem Mater*, 15,1367–1377.

*molecular imaging,* 4(4),165-173.

labeling. *Bioconjug Chem,* 18,635–644.

oxide labeling. *NMR Biomed,* 21(8),820-829.

*Biotechnol,* 23 (11), 1407–1413.

labeling of mesoporous nanoparticles in human mesenchymal stem cells: implication for stem cell tracking. *FASEB J.,* 19(14),2014-2016.


Magnetic Nanoparticles: Its Effect on Cellular Behaviour and Potential Applications 371

Mikhaylova, M., Kim, D.K., Bobrysheva, N., Osmolowsky, M., Semenov, V., Tsakalakos, T.,

Minchin, R.F., Orr, R.J., Cronin, A.S., & Puls, R.L. (1999) The pharmacology of gene therapy.

Moghimi, S.M. & Bonnemain, B. (1999). Subcutaneous and intravenous delivery of

indirect lymphography. *Advanced Drug Delivery Reviews,* 37(1-3), 295-312. Moghimi, S.M. & Hunter, A.C. (2001). Recognition by Macrophages and Liver Cells of

Moghimi, S.M., Hunter, A.C., & Murray, J.C. (2005). Nanomedicine: current status and

Montet, X., Montet-Abou, K., Reynolds, F., Weissleder, R., & Josephson, L. (2006). Nanoparticle imaging of integrins on tumor cells. *Neoplasia,* 8,214–222. Nel, A., Xia, T., Mädler, L., & Li, N. (2006). Toxic potential of materials at the nanolevel.

Nishimori, H., Kondoh, M., Isoda, K., Tsunoda, S., Tsutsumi, Y., Yagi, K. (2009) Silica nanoparticles as hepatotoxicants. *Eur J Pharmaceut Biopharmaceut,* 72,496–501. Nitin, N., LaConte, L.E., Zurkiya, O., Hu, X., Bao, G. (2004). Functionalization and

Noh, Y.-W., Jang, Y.S., Ahn, K.J., Lim, Y.T., & Chung, B.H. (2011). Simultaneous in vivo

Owens, 3rd D.E., & Peppas, N.A. (2006). Opsonization, biodistribution, and pharmacokinetics of polymeric nanoparticles. *Int J Pharmaceut,* 307,93–102. Pawelczyk, E., Arbab, A.S., Pandit, S., Hu, E., & Frank, J.A. (2006). Expression of transferrin

Peng, Y.K., Lai, C.W., Liu, C.L., Chen, H.C., Hsiao, Y.H., Liu, W.L., Tang, K.C., Chi, Y.,

Rawat, M., Singh, D., Saraf, S., & Saraf, S. (2006). Nanocarriers: promising vehicle for

Rogers, W.J. & Basu, P. (2005). Factors regulating macrophage endocytosis of nanoparticles:

Sellins, K.S. & Cohen, J.J. (1991). Hyperthermia induces apoptosis in thymocytes. *Radiation* 

Shen, L.-F., Chen, J., Zeng, S., Zhou, R.R., Zhu, H., Zhong, M.Z., Yao, R.J., & Shen, H. (2010).

peptidebased delivery of magnetic nanoparticles as an intracellular MRI contrast

tracking of dendritic cells and priming of an antigen-specific immune response.

receptor and ferritin following ferumoxides-protamine sulfate labeling of cells: implications for cellular magnetic resonance imaging. *NMR in Biomed,* 19(5), 581-

Hsiao, J.K., Lim, K.E., Liao, H.E., Shyue, J.J., & Chou, P.T. (2011). A new and facile method to prepare uniform hollow MnO/functionalized mSiO core/shell

implications for targeted magnetic resonance plaque imaging. *Atherosclerosis,* 178,

The Superparamagnetic Nanoparticles Carrying the E1A Gene Enhance the Radiosensitivity of Human Cervical Carcinoma in Nude Mice. *Molecular Cancer* 

dependence on surface modification. *Langmuir,* 20,2472–2477.

*Croat Med J* 40,381–391.

*Research,* 18(1), 1-8.

Science 311, 622–627.

future prospects. *Faseb J.,* 19(3),311-330.

agent. *J Biol Inorg Chem,* 9,706–712.

nanocomposites. *ACS nano,* 5(5), 4177-4187.

bioactive drugs. *Biol. Pharm. Bull.*, 29, 1790–1798.

*Biomaterials,* 32(26), 6254-6263.

592.

67–73.

*Research,* 126(1), 88-95.

*Therapeutics,* 9(7), 2123-2130.

& Muhammed, M. (2004). Superparamagnetism of magnetite nanoparticles:

diagnostic agents to the lymphatic system: applications in lymphoscintigraphy and

Opsonized Phospholipid Vesicles and Phospholipid Headgroups. *Pharmaceutical* 

core/shell nanoparticles: a facile three-in-one system in magnetic resonance imaging, luminescence imaging, and photodynamic therapy. *Small,* 4(2), 218-224.


Lee, J.H., Huh, Y.M., Jun, Y.W., Seo, J.W., Jang, J.T., Song, H.T., Kim, S., Cho, E.J., Yoon,

Lee, H., Yu, M.K., Park, S., Moon, S., Min, J.J., Jeong, Y.Y., Kang, H.W., & Jon, S. (2007).

Lewinski, N., Colvin, V., & Drezek, R. (2008). Cytotoxicity of nanoparticles. *Small*, 4,26–49. Long, T.C., Saleh, N., Tilton, R.D., Lowry, G.V., & Veronesi, B. (2006). Titanium dioxide

Lunov, O., Syrovets, T., Büchele, B., Jiang, X., Röcker, C., Tron, K., Nienhaus, G.U., Walther,

Lunov, O., Syrovets, T., Röcker, C., Tron, K., Nienhaus, G.U., Rasche, V., Mailänder, V.,

Lynch, I., Dawson, K.A., & Linse, S. (2006). Detecting cryptic epitopes created by

Maier-Hauff, K., Rothe, R., Scholz, R., Gneveckow, U., Wust, P., Thiesen, B., Feussner, A.,

Maier-Hauff, K., Ulrich, F., Nestler, D., Niehoff, H., Wust, P., Thiesen, B., Orawa, H.,

Metz, S., Bonaterra, G., Rudelius, M., Settles, M., Rummeny, E.J., & Daldrup-Link, H.E.

professional phagocytes. *Biomaterials,* 31(34), 9015-9022.

multiforme. *Journal of Neuro-Oncology,* 81(1), 53-60.

contrast agents in vitro. *Eur Radiol,* 14(10), 1851-1858.

nanoparticles. *Sci STKE*, 2006, pe14

*Oncology,* 103(2), 317-24.

ultra-sensitive molecular imaging. *Nat. Med.* 13, 95–99.

7389.

12745.

*Lett,* 7(1), 149-154.

31(19),5063-5071.

core/shell nanoparticles: a facile three-in-one system in magnetic resonance imaging, luminescence imaging, and photodynamic therapy. *Small,* 4(2), 218-224. Lee, H., Lee, E., Kim, do K., Jang, N.K., Jeong, Y.Y., & Jon, S. (2006). Antibiofouling polymer-

coated superparamagnetic iron oxide nanoparticles as potential magnetic resonance contrast agents for in vivo cancer imaging. *J Am Chem Soc,* 128,7383–

H.G., Suh, J.S., & Cheon, J. (2007) Artificially engineered magnetic nanoparticles for

Thermally cross-linked superparamagnetic iron oxide nanoparticles: synthesis and application as a dual imaging probe for cancer in vivo. *J Am Chem Soc,* 129,12739–

(P25) produces reactive oxygen species in immortalized brain microglia (BV2): implications for nanoparticle neurotoxicity. *Environ Sci Technol,* 40,4346–4352. Lu, C.W., Hung, Y., Hsiao, J.K., Yao, M., Chung, T.H., Lin, Y.S., Wu, S.H., Hsu, S.C., Liu,

H.M., Mou, C.Y., Yang, C.S., Huang, D.M., & Chen, Y.C. (2007). Bifunctional magnetic silica nanoparticles for highly efficient human stem cell labeling. *Nano* 

P., Mailänder, V., Landfester, K., & Simmet, T. (2010a). The effect of carboxydextran-coated superparamagnetic iron oxide nanoparticles on c-Jun Nterminal kinase-mediated apoptosis in human macrophages. *Biomaterials,*

Landfester, K., & Simmet, T. (2010b). Lysosomal degradation of the carboxydextran shell of coated superparamagnetic iron oxide nanoparticles and the fate of

von Deimling, A., Waldoefner, N., Felix, R., & Jordan, A. (2007). Intracranial thermotherapy using magnetic nanoparticles combined with external beam radiotherapy: results of a feasibility study on patients with glioblastoma

Budach, V., & Jordan, A. (2011). Efficacy and safety of intratumoral thermotherapy using magnetic iron-oxide nanoparticles combined with external beam radiotherapy on patients with recurrent glioblastoma multiforme. *Journal of Neuro-*

(2004). Capacity of human monocytes to phagocytose approved iron oxide MR


**1. Introduction**

Smith & Wojciechowski (2008).

structural disorder (Dutta et al., 2004).

Magnetic nanopowders placed in the nonmagnetic polymer matrices become a new type of smart materials which combine mechanical properties of temperature responsive polymer matrix and magnetic response of nanoparticles. These properties are used in some biotechnological and medical applications like hyperthermia treatment, nanocolloids, magnetic nanocapsules for drug targeting, magnetic resonance imaging (MRI), intracellular manipulation etc. (e.g. (Gao & Xu, 2009; Liu et al., 2009)), in the processes of mechanical and electrical micropower generation, in nanoelectromechanical systems as MEMS/NEMS devices (e.g. (Zahn, 2001)), electromagnetic interference suppression (Wilson et al., 2004). Recently, the unusual polymer/magnetic nanoparticles systems with a negative Poisson's ratio (e.g. ferrogels Dudek & Wojciechowski (2008); Wood & Camp (2011)) have begun to be studied. They belong to the so-called auxetic materials Evans et al. (1991); Lakes (1987);

**Thermal Effects on the Ferromagnetic** 

**Magnetic Nanoparticles Fillers** 

*2Solid State Physics Section, Department of Physics,* 

*University of Athens, Panepistimiopolis* 

*1,3Poland 2Greece* 

**17**

*1Institute of Physics, University of Zielona Góra, Zielona Góra* 

**Resonance in Polymer Composites with** 

Mirosãaw R. Dudek1, Nikos Guskos2,3 and Marcin KoĤmider1

*3Institute of Physics,West Pomeranian University of Technology, Szczecin* 

Ferromagnetic resonance experiment (FMR) (Vleck, 1950) is one of the basic tools to study the magnetic properties of magnetic agglomerates in viscoelastic nonmagnetic polymer matrix. As a particular example, we consider the FMR experiment with the *γ*-Fe2O3 (maghemite) ferrimagnetic nanoparticles embedded in a multiblock poly(ether-ester) copolymer nonmagnetic matrix which has been studied both experimentally (Guskos et al., 2006; 2008) and theoretically (Dudek et al., 2010). However, the obtained results are general and applicable to other nanoparticles and other viscous materials. Note that in medical applications magnetic iron oxides are used due to their low toxicity to human. Their saturation magnetization is practically equal to the bulk value at high temperatures, with negligible coercivity and no exchange bias below the blocking temperature. These properties of the iron oxide magnetic nanoparticles suggest nearly perfect nanocrystals without significant


## **Thermal Effects on the Ferromagnetic Resonance in Polymer Composites with Magnetic Nanoparticles Fillers**

Mirosãaw R. Dudek1, Nikos Guskos2,3 and Marcin KoĤmider1 *1Institute of Physics, University of Zielona Góra, Zielona Góra 2Solid State Physics Section, Department of Physics, University of Athens, Panepistimiopolis 3Institute of Physics,West Pomeranian University of Technology, Szczecin 1,3Poland 2Greece* 

#### **1. Introduction**

372 Smart Nanoparticles Technology

Shen, T., Weissleder, R., Papisov, M., Bogdanov, A. Jr, & Brady, T.J. (1993). Monocrystalline

Shi, X., Thomas, T.P., Myc, L.A., Kotlyar, A., & Baker, J.R. Jr. (2007). Synthesis,

Silva, A.C., Oliveira, T.R., Mamani, J.B., Malheiros, S.M., Malavolta, L., Pavon, L.F., Sibov,

dendritic cells during anti-tumour vaccination. *PLoS ONE,* 6(5), e19662. Thorek, D.L., Chen, A.K., Czupryna, J., & Tsourkas, A. (2006). Superparamagnetic iron oxide nanoparticle probes for molecular imaging. *Ann Biomed Eng,* 34,23–38. Tsai, C.P., Hung, Y., Chou, Y.H., Huang, D.M., Hsiao, J.K., Chang, C., Chen, Y.C., & Mou,

Veiseh, O., Sun, C., Gunn, J., Kohler, N., Gabikian, P., Lee, D., Bhattarai, N., Ellenbogen, R.,

multifunctional nanoprobe for targeting gliomas. *Nano Lett,* 5,1003–1008. Wang, Y.X., Hussain, S.M., & Krestin, G.P. (2001). Superparamagnetic iron oxide contrast

Wiwanitkit, V. (2006). Glomerular pore size corresponding to albumin molecular size, an

Yang, C.Y., Hsiao, J.K., Tai, M.F., Chen, S.T., Cheng, H.Y., Wang, J.L., & Liu, H.M. (2011).

Yeh, C.-H., Hsiao, J.K., Wang, J.L., & Fuu Sheu, F. (2010). Immunological impact of magnetic

a multifunctional cell-imaging probe. *Small,* 4(2),186-191.

29,599–604.

*Phys,* 9, 5712–5720.

*Radiol.*, 11, 2319–2331.

*Biol.* 13(3), 443-451.

nanolevel. *Renal Fail,* 28,101.

*Nanoparticle Research,* 12(1), 151-160.

iron oxide nanocompounds (MION): physicochemical properties. *Magn Reson Med,* 

characterization, and intracellular uptake of carboxyl-terminated poly(amidoamine) dendrimer-stabilized iron oxide nanoparticles. *Phys Chem Chem* 

T.T., Amaro, E. Jr, Tannús, A., Vidoto, E.L., Martins, M.J., Santos, R.S., & Gamarra, L.F. (2011). Application of hyperthermia induced by superparamagnetic iron oxide nanoparticles in glioma treatment. *International journal of nanomedicine,* 6, 591-603. Tavaré, R., Sagoo, P., Varama, G., Tanriver, Y., Warely, A., Diebold, S.S., Southworth, R.,

Schaeffter, T., Lechler, R.I., Razavi, R., Lombardi, G., & Mullen, G.E. (2011). Monitoring of in vivo function of superparamagnetic iron oxide labelled murine

C.Y. (2008). High-contrast paramagnetic fluorescent mesoporous silica nanorods as

Sze, R., Hallahan, A., Olson, J., & Zhang, M. (2005). Optical and MRI

agents: physicochemical characteristics and applications in MR imaging. *Eur.* 

explanation for underlying structural pathology leading to albuminuria at

Direct labeling of hMSC with SPIO: the long-term influence on toxicity, chondrogenic differentiation capacity, and intracellular distribution. *Mol Imaging* 

nanoparticles (Ferucarbotran) on murine peritoneal macrophages. J*ournal of* 

Magnetic nanopowders placed in the nonmagnetic polymer matrices become a new type of smart materials which combine mechanical properties of temperature responsive polymer matrix and magnetic response of nanoparticles. These properties are used in some biotechnological and medical applications like hyperthermia treatment, nanocolloids, magnetic nanocapsules for drug targeting, magnetic resonance imaging (MRI), intracellular manipulation etc. (e.g. (Gao & Xu, 2009; Liu et al., 2009)), in the processes of mechanical and electrical micropower generation, in nanoelectromechanical systems as MEMS/NEMS devices (e.g. (Zahn, 2001)), electromagnetic interference suppression (Wilson et al., 2004). Recently, the unusual polymer/magnetic nanoparticles systems with a negative Poisson's ratio (e.g. ferrogels Dudek & Wojciechowski (2008); Wood & Camp (2011)) have begun to be studied. They belong to the so-called auxetic materials Evans et al. (1991); Lakes (1987); Smith & Wojciechowski (2008).

Ferromagnetic resonance experiment (FMR) (Vleck, 1950) is one of the basic tools to study the magnetic properties of magnetic agglomerates in viscoelastic nonmagnetic polymer matrix. As a particular example, we consider the FMR experiment with the *γ*-Fe2O3 (maghemite) ferrimagnetic nanoparticles embedded in a multiblock poly(ether-ester) copolymer nonmagnetic matrix which has been studied both experimentally (Guskos et al., 2006; 2008) and theoretically (Dudek et al., 2010). However, the obtained results are general and applicable to other nanoparticles and other viscous materials. Note that in medical applications magnetic iron oxides are used due to their low toxicity to human. Their saturation magnetization is practically equal to the bulk value at high temperatures, with negligible coercivity and no exchange bias below the blocking temperature. These properties of the iron oxide magnetic nanoparticles suggest nearly perfect nanocrystals without significant structural disorder (Dutta et al., 2004).

**2. Modeling ferromagnetic resonance experiment**

in Polymer Composites with Magnetic Nanoparticles Fillers

magnetic field −→*<sup>H</sup>* eff,i of the form (Füzi, 2006):

−→*<sup>H</sup>* eff,i <sup>=</sup> −→*<sup>H</sup>* dc <sup>+</sup> −→*<sup>H</sup>* ac <sup>+</sup>

external alternating current (ac) magnetic field of frequency *f* ,

−→*<sup>H</sup> <sup>i</sup>*,dipole <sup>=</sup> <sup>−</sup> <sup>1</sup>

represents the magnetic anisotropy field which is defined as

the components

Theoretical basis of ferromagnetic resonance can be found in the paper by van Vleck (Vleck, 1950) in which a magnetic resonance condition (Kittel's formula) for ferromagnetic materials has been derived with the help of a simple quantum model. It has been noted in the paper the importance of the effect of magnetic anisotropy on the resonance frequency. In our considerations we restrict to the case when an uniaxial anisotropy is the dominating magnetic anisotropy of the magnetic nanoparticles (Shliomis, 1975). Then, the term magnetic anisotropy axis is substituted for the easy axis of magnetization. The magnetization of magnetic nanoparticles changes after an external magnetic field is switched on and there are two mechanisms of this change: the reorientation process of magnetic nanoparticle as a whole (Brownian motion) and the Néel relaxation process of the magnetization itself. A magnetic nanoparticle, and by this the magnetic anisotropy axis, can rotate freely in a liquid carrier, but not in the case when the nanoparticle is part of a large agglomerate or its surrounding is a solid phase. The dominant interparticle interactions in the agglomerate are dipole interactions unless the nanoparticles do not form dense agglomerates where exchange interactions become important. So if we take into account the FMR experiment and we consider the agglomerate consisting of N single-domain magnetic nanoparticles, each of them experiences an effective

<sup>375</sup> Thermal Effects on the Ferromagnetic Resonance

*Ha*

 −→*Mj r*3 *ij* − 3 ( −→*Mj*· −→*r ji*) −→*r ji*

−→*Mi* denotes magnetization of the nanoparticle *<sup>i</sup>* (*<sup>M</sup>* <sup>=</sup> *MsV* for the nanoparticle of volume *V* and saturation magnetization *Ms*), *rij* is the distance between nanoparticles *i* and *j*, *Ha*

> *Ha* <sup>=</sup> <sup>2</sup>*Ka μ*0*Ms*

where *Ka* is magnetic anisotropy constant, and *μ*<sup>0</sup> is constant of permeability. The symbol −→*n <sup>i</sup>* in Eq. (1) is a unit vector along the magnetic anisotropy direction of the nanoparticle *i* with

and *ϕ<sup>i</sup>* and *θ<sup>i</sup>* are the angles vector −→*n <sup>i</sup>* makes with the *z*-axis and *x*-axis, respectively.

−→*Mi* · −→*<sup>n</sup> <sup>i</sup>*)

*r*5

*ji*

*nx*,*<sup>i</sup>* = sin(*ϕi*) cos(*θi*), (4) *ny*,*<sup>i</sup>* = sin(*ϕi*) sin(*θi*), (5) *nz*,*<sup>i</sup>* = cos(*ϕi*). (6)

−→*<sup>n</sup> <sup>i</sup>* <sup>+</sup> −→*<sup>H</sup> <sup>i</sup>*,dipole (1)

ac cos(2*π f t*) is the

, (2)

(3)

−→*<sup>H</sup> <sup>i</sup>*,dipole represents dipolar


where −→*<sup>H</sup>* dc is the external direct current (dc) magnetic field, −→*<sup>H</sup>* ac <sup>=</sup> −→*<sup>H</sup>* <sup>0</sup>

magnetic field produced by the magnetic nanoparticles of the agglomerate

*N* ∑ *j*=1,*j*�=*i*

4*π*

Fig. 1. SEM picture: an example of stucking a single magnetic nanoparticle in a pore - here, a carbon coated nickel nanoparticle in the porous sodium borosilicate glass.

The peculiar feature of the synthesized PEN-block-PTMO copolymer is that the magnetic fillers form agglomerates numbering from several to tens of nanoparticles. In the agglomerates the interparticle dipole - dipole magnetic interaction becomes important as well as the interaction of the magnetic nanoparticles with a non-magnetic matrix. Although the agglomerates are uniformly dispersed in the matrix their FMR spectra show additional peaks in low temperatures which originate from the orientational anisotropy of the frozen polymer blocks. The orientational dependence of the FMR spectra has been found earlier by Owens (Owens, 2003) for a colloidal suspension of *γ*-Fe2O3 nanoparticles which have been solidified in a static magnetic field (dc magnetic field). Similar observation has been found theoretically in a recent paper by Sukhov et al. (Sukhov et al., 2008). There is very instructive discussion on the shape of the ferromagnetic resonance spectra for the ensemble of the randomly distributed magnetic anisotropy axes as well as the discussion of the dependence of these spectra on temperature in terms of a stochastic model. The model is restricted to the case when the orientation of each anisotropy axis is frozen during computer simulation but it shares many features common with the experimental results, like the broadening of the FMR signal for the randomly distributed magnetic anisotropy axes as compared to the magnetic nanoparticles which all have the same orientation of the magnetic anisotropy. In paper (Dudek et al., 2008) it has been shown directly that blocking the rotational freedom of the magnetic nanoparticles, e.g. when the nanoparticles are stuck in the pores as it is suggested in Fig. 1, can produce additional resonance peaks in the FMR spectrum. In the latter case stochastic equations were used both for the magnetic nanoparticles magnetization and the rotational oscillations of the magnetic nanoparticles as a whole. The influence of the magnetic anisotropy orientation and temperature on the FMR spectra of magnetic agglomerates in polymer matrix was discussed in (Dudek et al., 2010). The most important property of the FMR spectrum depending on temperature will be discussed in the sections below.

2 Will-be-set-by-IN-TECH

Fig. 1. SEM picture: an example of stucking a single magnetic nanoparticle in a pore - here, a

The peculiar feature of the synthesized PEN-block-PTMO copolymer is that the magnetic fillers form agglomerates numbering from several to tens of nanoparticles. In the agglomerates the interparticle dipole - dipole magnetic interaction becomes important as well as the interaction of the magnetic nanoparticles with a non-magnetic matrix. Although the agglomerates are uniformly dispersed in the matrix their FMR spectra show additional peaks in low temperatures which originate from the orientational anisotropy of the frozen polymer blocks. The orientational dependence of the FMR spectra has been found earlier by Owens (Owens, 2003) for a colloidal suspension of *γ*-Fe2O3 nanoparticles which have been solidified in a static magnetic field (dc magnetic field). Similar observation has been found theoretically in a recent paper by Sukhov et al. (Sukhov et al., 2008). There is very instructive discussion on the shape of the ferromagnetic resonance spectra for the ensemble of the randomly distributed magnetic anisotropy axes as well as the discussion of the dependence of these spectra on temperature in terms of a stochastic model. The model is restricted to the case when the orientation of each anisotropy axis is frozen during computer simulation but it shares many features common with the experimental results, like the broadening of the FMR signal for the randomly distributed magnetic anisotropy axes as compared to the magnetic nanoparticles which all have the same orientation of the magnetic anisotropy. In paper (Dudek et al., 2008) it has been shown directly that blocking the rotational freedom of the magnetic nanoparticles, e.g. when the nanoparticles are stuck in the pores as it is suggested in Fig. 1, can produce additional resonance peaks in the FMR spectrum. In the latter case stochastic equations were used both for the magnetic nanoparticles magnetization and the rotational oscillations of the magnetic nanoparticles as a whole. The influence of the magnetic anisotropy orientation and temperature on the FMR spectra of magnetic agglomerates in polymer matrix was discussed in (Dudek et al., 2010). The most important property of the FMR spectrum depending on

carbon coated nickel nanoparticle in the porous sodium borosilicate glass.

temperature will be discussed in the sections below.

#### **2. Modeling ferromagnetic resonance experiment**

Theoretical basis of ferromagnetic resonance can be found in the paper by van Vleck (Vleck, 1950) in which a magnetic resonance condition (Kittel's formula) for ferromagnetic materials has been derived with the help of a simple quantum model. It has been noted in the paper the importance of the effect of magnetic anisotropy on the resonance frequency. In our considerations we restrict to the case when an uniaxial anisotropy is the dominating magnetic anisotropy of the magnetic nanoparticles (Shliomis, 1975). Then, the term magnetic anisotropy axis is substituted for the easy axis of magnetization. The magnetization of magnetic nanoparticles changes after an external magnetic field is switched on and there are two mechanisms of this change: the reorientation process of magnetic nanoparticle as a whole (Brownian motion) and the Néel relaxation process of the magnetization itself. A magnetic nanoparticle, and by this the magnetic anisotropy axis, can rotate freely in a liquid carrier, but not in the case when the nanoparticle is part of a large agglomerate or its surrounding is a solid phase. The dominant interparticle interactions in the agglomerate are dipole interactions unless the nanoparticles do not form dense agglomerates where exchange interactions become important. So if we take into account the FMR experiment and we consider the agglomerate consisting of N single-domain magnetic nanoparticles, each of them experiences an effective magnetic field −→*<sup>H</sup>* eff,i of the form (Füzi, 2006):

$$
\overrightarrow{H}\_{\text{eff,i}} = \overrightarrow{H}\_{\text{dc}} + \overrightarrow{H}\_{\text{ac}} + \frac{H\_{\text{a}}}{|\overrightarrow{M}\_{i}|} (\overrightarrow{M}\_{i} \cdot \overrightarrow{n}\_{i}^{\flat}) \overrightarrow{n}\_{i}^{\flat} + \overrightarrow{H}\_{i, \text{dipole}} \tag{1}
$$

where −→*<sup>H</sup>* dc is the external direct current (dc) magnetic field, −→*<sup>H</sup>* ac <sup>=</sup> −→*<sup>H</sup>* <sup>0</sup> ac cos(2*π f t*) is the external alternating current (ac) magnetic field of frequency *f* , −→*<sup>H</sup> <sup>i</sup>*,dipole represents dipolar magnetic field produced by the magnetic nanoparticles of the agglomerate

$$\overrightarrow{H}\_{i, \text{dipole}} = -\frac{1}{4\pi} \sum\_{j=1, j \neq i}^{N} \left( \frac{\overrightarrow{M}\_j}{r\_{ij}^3} - 3 \frac{(\overrightarrow{M}\_j \cdot \overrightarrow{r}\_{ji}^\flat) \, \overrightarrow{r}^\flat\_{ji}}{r\_{ji}^5} \right) \,. \tag{2}$$

−→*Mi* denotes magnetization of the nanoparticle *<sup>i</sup>* (*<sup>M</sup>* <sup>=</sup> *MsV* for the nanoparticle of volume *V* and saturation magnetization *Ms*), *rij* is the distance between nanoparticles *i* and *j*, *Ha* represents the magnetic anisotropy field which is defined as

$$H\_d = \frac{2K\_d}{\mu\_0 M\_s} \tag{3}$$

where *Ka* is magnetic anisotropy constant, and *μ*<sup>0</sup> is constant of permeability. The symbol −→*n <sup>i</sup>* in Eq. (1) is a unit vector along the magnetic anisotropy direction of the nanoparticle *i* with the components

$$n\_{\mathbf{x},i} = \sin(\varphi\_i)\cos(\theta\_i),\tag{4}$$

$$m\_{\mathcal{Y},\dot{l}} = \sin(\varphi\_{\dot{l}})\sin(\theta\_{\dot{l}}) \,\tag{5}$$

$$m\_{\mathbb{Z},i} = \cos(\varphi\_{\mathbb{I}}).\tag{6}$$

and *ϕ<sup>i</sup>* and *θ<sup>i</sup>* are the angles vector −→*n <sup>i</sup>* makes with the *z*-axis and *x*-axis, respectively.



dc

Fig. 3. The same as in Fig. 2 but the magnetic anisotropy axis orientation oscillates around

μ0

<sup>377</sup> Thermal Effects on the Ferromagnetic Resonance

*<sup>s</sup>* /4), *α* = 0.066, *R* = 2nm, *Ms* = 450*kA*/*m*, T=10K.

Fig. 2. Magnetic hysteresis loop of the *z*-component of the magnetic nanoparticle's magnetization in the case when the orientation of the magnetic anisotropy axis undergoes the small oscillations around the *z*-direction (parallel to the external dc magnetic field). Some parameters of the computer simulation: demagnetizing factor in shape anisotropy *D* = 0.15



the *x*-direction (transverse to the external dc magnetic field).


0

M (H )/M z

dc

s

0.5

1

(*Ka* <sup>=</sup> *<sup>μ</sup>*0(<sup>1</sup> <sup>−</sup> <sup>3</sup>*D*)*M*<sup>2</sup>


0

M (H)/M z

s

0.5

1

in Polymer Composites with Magnetic Nanoparticles Fillers

A rotating external magnetic field −→*<sup>H</sup>* ac is transverse to −→*<sup>H</sup>* dc. We assume that the external dc magnetic field is oriented in the *z*-direction and the external ac magnetic field in the *x*-direction (Jung et al., 2002). Then, for the effective magnetic field defined in Eq. (1) the ferromagnetic resonance condition can be expressed as follows:

$$f = \frac{\gamma}{2\pi} H\_{\text{eff}} \tag{7}$$

where *<sup>γ</sup>* <sup>=</sup> 2.21 <sup>×</sup> 105*s*−1(*A*/*m*)−<sup>1</sup> denotes the gyromagnetic ratio. In practice, the spectrometers EPR/FMR are built for one value of frequency *f* and then the dc magnetic field becomes a parameter to be changed to get the resonance condition. In our case the ac magnetic field frequency *f* = 9.37 GHz. Note that even in the case of a single magnetic nanoparticle (N=1) its resonance frequency strongly depends on the orientation of the magnetic anisotropy axis with respect to the dc magnetic field direction.

It turns out that the magnetic nanoparticle's magnetization dynamics can be modeled with the help of the classical spin model which represents stochastic version of the Landau-Lifshitz equation ((Gilbert, 1955; Landau & Lifshitz, 1953)) :

$$\frac{d\overrightarrow{M}\_{\rm i}}{dt} = -\gamma \overrightarrow{M}\_{\rm i} \times \left[\overrightarrow{H}\_{\rm eff,i} + \overrightarrow{B}\_{\rm i}\right] - \alpha \frac{\gamma}{M\_{\rm s}V} \overrightarrow{M}\_{\rm i} \times (\overrightarrow{M}\_{\rm i} \times \left[\overrightarrow{H}\_{\rm eff,i} + \overrightarrow{B}\_{\rm i}\right]),\tag{8}$$

where *<sup>i</sup>* <sup>=</sup> 1, 2, . . . , *<sup>N</sup>*, and *<sup>α</sup>* denotes the damping constant. The symbol −→*<sup>B</sup> <sup>i</sup>* represents the white-noise field fluctuations (e.g. (Jönsson, 2003), (Usadel, 2006)). Then the thermal averages of −→*<sup>B</sup> <sup>i</sup>* = (*Bx*,*i*, *By*,*i*, *Bz*,*i*) fulfill the relations:

$$
\langle B\_{q,i}(t) \rangle = 0, \ q = \mathfrak{x}, \mathfrak{y}, \mathfrak{z}, \tag{9}
$$

$$
\langle B\_{q,i}(t)B\_{p,i}(t')\rangle = \frac{2ak\_BT}{\gamma M\_sV} \delta\_{q,p} \delta(t-t'), \ \ p = x, y, z. \tag{10}
$$

The magnetic properties of the magnetic nanoparticles can be described with the help of the solutions −→*Mi*(*t*) of this set of equations.They strongly depend on the magnetic anisotropy axis orientation. In particular, the shape of the magnetic hysteresis loop can change from the almost square like to the case when it vanishes depending on the orientation of the external dc magnetic field with respect to the orientation of the magnetic anisotropy axis. This can be seen in Fig. 2 and Fig. 3 in which the magnetic hysteresis loops are presented for the *z*-component of the nanoparticle's magnetization in the case when the anisotropy axis orientation oscillations are close to the *z*-direction (parallel to dc magnetic field) and close to the *x*-direction (transverse to dc magnetic field), respectively. The hysteresis loops, which are shown in the figures, result from the computer simulation of a simplified model of a carbon coated magnetic nanoparticle where the coating is represented by C60 molecule. In the model, the magnetic nanoparticle is represented by magnetic anisotropy axis and its magnetization follows the Landau-Lifshitz equation (Eq. (8)). The carbon atoms in C60 molecule vibrate according to the molecular dynamics method. The rotational oscillations of a fullerene (and by this the magnetic anisotropy axis rotations) are harmonically bonded to the *z*-direction and *x*-direction, respectively, with a given spring constant. The latter means that the magnetic nanoparticle cannot rotate freely. The larger temperature is the larger the rotational oscillations are. Besides the spring force the anisotropy axis experiences the

4 Will-be-set-by-IN-TECH

A rotating external magnetic field −→*<sup>H</sup>* ac is transverse to −→*<sup>H</sup>* dc. We assume that the external dc magnetic field is oriented in the *z*-direction and the external ac magnetic field in the *x*-direction (Jung et al., 2002). Then, for the effective magnetic field defined in Eq. (1) the ferromagnetic

> *<sup>f</sup>* <sup>=</sup> *<sup>γ</sup>* 2*π*

where *<sup>γ</sup>* <sup>=</sup> 2.21 <sup>×</sup> 105*s*−1(*A*/*m*)−<sup>1</sup> denotes the gyromagnetic ratio. In practice, the spectrometers EPR/FMR are built for one value of frequency *f* and then the dc magnetic field becomes a parameter to be changed to get the resonance condition. In our case the ac magnetic field frequency *f* = 9.37 GHz. Note that even in the case of a single magnetic nanoparticle (N=1) its resonance frequency strongly depends on the orientation of the magnetic anisotropy

It turns out that the magnetic nanoparticle's magnetization dynamics can be modeled with the help of the classical spin model which represents stochastic version of the Landau-Lifshitz

where *<sup>i</sup>* <sup>=</sup> 1, 2, . . . , *<sup>N</sup>*, and *<sup>α</sup>* denotes the damping constant. The symbol −→*<sup>B</sup> <sup>i</sup>* represents the white-noise field fluctuations (e.g. (Jönsson, 2003), (Usadel, 2006)). Then the thermal averages

*<sup>γ</sup>MsV <sup>δ</sup>q*,*pδ*(*<sup>t</sup>* <sup>−</sup> *<sup>t</sup>*

The magnetic properties of the magnetic nanoparticles can be described with the help of the solutions −→*Mi*(*t*) of this set of equations.They strongly depend on the magnetic anisotropy axis orientation. In particular, the shape of the magnetic hysteresis loop can change from the almost square like to the case when it vanishes depending on the orientation of the external dc magnetic field with respect to the orientation of the magnetic anisotropy axis. This can be seen in Fig. 2 and Fig. 3 in which the magnetic hysteresis loops are presented for the *z*-component of the nanoparticle's magnetization in the case when the anisotropy axis orientation oscillations are close to the *z*-direction (parallel to dc magnetic field) and close to the *x*-direction (transverse to dc magnetic field), respectively. The hysteresis loops, which are shown in the figures, result from the computer simulation of a simplified model of a carbon coated magnetic nanoparticle where the coating is represented by C60 molecule. In the model, the magnetic nanoparticle is represented by magnetic anisotropy axis and its magnetization follows the Landau-Lifshitz equation (Eq. (8)). The carbon atoms in C60 molecule vibrate according to the molecular dynamics method. The rotational oscillations of a fullerene (and by this the magnetic anisotropy axis rotations) are harmonically bonded to the *z*-direction and *x*-direction, respectively, with a given spring constant. The latter means that the magnetic nanoparticle cannot rotate freely. The larger temperature is the larger the rotational oscillations are. Besides the spring force the anisotropy axis experiences the

*MsV*

−→*Mi* <sup>×</sup> (

�

−→*Mi* <sup>×</sup> [

�*Bq*,*i*(*t*)� = 0, *q* = *x*, *y*, *z*, (9)

−→*H*eff,i <sup>+</sup> −→*<sup>B</sup> <sup>i</sup>*] <sup>−</sup> *<sup>α</sup> <sup>γ</sup>*

)� <sup>=</sup> <sup>2</sup>*αkBT*

*H*eff (7)

−→*H*eff,i <sup>+</sup> −→*<sup>B</sup> <sup>i</sup>*]), (8)

), *p* = *x*, *y*, *z*. (10)

resonance condition can be expressed as follows:

axis with respect to the dc magnetic field direction.

equation ((Gilbert, 1955; Landau & Lifshitz, 1953)) :

of −→*<sup>B</sup> <sup>i</sup>* = (*Bx*,*i*, *By*,*i*, *Bz*,*i*) fulfill the relations:

−→*Mi* <sup>×</sup> [

�*Bq*,*i*(*t*)*Bp*,*i*(*t*

�

*d* −→*Mi dt* <sup>=</sup> <sup>−</sup>*<sup>γ</sup>*

Fig. 2. Magnetic hysteresis loop of the *z*-component of the magnetic nanoparticle's magnetization in the case when the orientation of the magnetic anisotropy axis undergoes the small oscillations around the *z*-direction (parallel to the external dc magnetic field). Some parameters of the computer simulation: demagnetizing factor in shape anisotropy *D* = 0.15 (*Ka* <sup>=</sup> *<sup>μ</sup>*0(<sup>1</sup> <sup>−</sup> <sup>3</sup>*D*)*M*<sup>2</sup> *<sup>s</sup>* /4), *α* = 0.066, *R* = 2nm, *Ms* = 450*kA*/*m*, T=10K.

Fig. 3. The same as in Fig. 2 but the magnetic anisotropy axis orientation oscillates around the *x*-direction (transverse to the external dc magnetic field).

where *χ*�� denotes total hysteresis losses per volume of magnetic nanoparticle through a cycle of the magnetization. For the chosen magnetic fields *Hz* = *Hdc* and *Hx* = *Hac* the components of the complex ac susceptibility (Eq. (12)) can be calculated by performing the

<sup>379</sup> Thermal Effects on the Ferromagnetic Resonance

where *τ* = 1/ *f* . In the case of theoretical modeling , the values *Mx*(*t*) can be obtained from the Landau-Lifshitz equation (Eq. 8). In real FMR experiments, the absorption lines derivatives, *dχ*��/*dH*dc (the derivative of the out-of-phase susceptibility) are measured instead of direct measuring *χ*��. In Fig. 5 there are presented the absorption lines derivatives obtained for the

*dtMx*(*t*)*e*


dc dc

Fig. 5. Absorption lines derivatives, *dχ*��/*dH*dc resulting from the computer simulations in the case when the magnetic anisotropy axis orientation oscillates around the direction parallel and transverse to the external dc magnetic field. The parameters of the computer

model of the carbon coated nanoparticles shown in Fig. 4 in the case when their magnetic anisotropy axis oscillations are controlled by the harmonic forces applied to the ends of the axis and the forces are coupled with the *z*-direcion and *x*-direction, respectively. Note that if the magnetic anisotropy axis is linked to the direction which is tranverse to the direction of *H*dc then the corresponding resonance magnetic field *Hr* becomes shifted to higher values of *H*dc compared with the case when it is linked to the direction which is parallel. At the value of *H*dc = *Hr* the dynamic susceptibility *χ*�� takes its maximum value. It is worth emphasizing that the energy absorbed by the magnetic nanoparticles from the external AC magnetic field


0

100

200

<sup>−</sup>*i*2*<sup>π</sup> f t*, (13)

0 0.2 0.4 0.6 0.8 1 H (Tesla)

Fourier transform on the time averaged *x*-component of the magnetization, i.e.,

 *τ* 0

*<sup>χ</sup>* <sup>=</sup> <sup>1</sup> *τH*<sup>0</sup> ac

in Polymer Composites with Magnetic Nanoparticles Fillers

0 0.2 0.4 0.6 0.8 1 H (Tesla)


simulation are the same as in Fig. 2.


0

d "/dH

dc

χ 100

200

magnetic torque which is represented by two opposite point forces (Dudek et al., 2010) applied to the anisotropy axis with the strength

$$\begin{array}{c} \mid \ \overline{F} \ \mid = \frac{1}{R} \mid K\_d V \sin(2\Psi) \ \mid \tag{11} \end{array} \tag{11}$$

where *R* is the fullerene's radius, and the greater the angle Ψ between the easy axis, represented by vector −→*n* , and magnetization −→*M*, the greater the magnetic torque. The model of the magnetic nanoparticles used in the computer simulations has been shown in Fig. 4 in the case when the magnetic anisotropy axis is, respectively, parallel and perpendicular to the external dc magnetic field.

Fig. 4. Model of carbon coated magnetic nanoparticle in the case when the coating is represented by C60 molecule. The magnetic nanoparticle is represented by the anisotropy axis which, in the model, passes through the center of the fulleren and the carbon atom painted green, in the figure. The magnetic nanoparticle was not drawn with clarity reasons. The cartesian coordinate system has been plotted and the blue axis represents the *z*-direction which is the direction of the external dc magnetic field and the white axis represents the *x*-direction.

The same features of the magnetic hysteresis loops as those presented in Fig. 2 and Fig. 3 can be observed in magnetic nanowires, e.g. (Sorop et al., 2004), where the similar relationship between the shape anisotropy of a nanowire and the external dc magnetic is observed. In low temperatures, much below 100K, the large agglomerates of the *γ*-Fe2O3 (maghemite) ferrimagnetic nanoparticles embedded in a multiblock poly(ether-ester) copolymer nonmagnetic matrix Guskos et al. (2006; 2008) are practically frozen into the matrix with a random orientation of the magnetic anisotropy axes. Then, the observed magnetic hysteresis loop represents the averaged one which is approximately a mixture of the cases discussed in Fig. 2 and Fig. 3. It is worth to add that in high temperatures, where the block copolymer is dissolved, the magnetic properties resemble the properties of ferrofluids and there is no observed magnetic hysteresis loop.

Much more information on the magnetic properties of the polymers filled with nanoparticles can be get from the analyses of the absorption lines in FMR experiment. They can be represented by the imaginary part of the dynamic magnetic susceptibility

$$
\chi = \chi' - i\chi''. \tag{12}
$$

6 Will-be-set-by-IN-TECH

magnetic torque which is represented by two opposite point forces (Dudek et al., 2010) applied

where *R* is the fullerene's radius, and the greater the angle Ψ between the easy axis, represented by vector −→*n* , and magnetization −→*M*, the greater the magnetic torque. The model of the magnetic nanoparticles used in the computer simulations has been shown in Fig. 4 in the case when the magnetic anisotropy axis is, respectively, parallel and perpendicular to the

*<sup>R</sup>* <sup>|</sup> *KaV* sin(2Ψ) <sup>|</sup> (11)


−→*<sup>F</sup>* <sup>|</sup><sup>=</sup> <sup>1</sup>

Fig. 4. Model of carbon coated magnetic nanoparticle in the case when the coating is represented by C60 molecule. The magnetic nanoparticle is represented by the anisotropy axis which, in the model, passes through the center of the fulleren and the carbon atom painted green, in the figure. The magnetic nanoparticle was not drawn with clarity reasons. The cartesian coordinate system has been plotted and the blue axis represents the *z*-direction which is the direction of the external dc magnetic field and the white axis represents the

The same features of the magnetic hysteresis loops as those presented in Fig. 2 and Fig. 3 can be observed in magnetic nanowires, e.g. (Sorop et al., 2004), where the similar relationship between the shape anisotropy of a nanowire and the external dc magnetic is observed. In low temperatures, much below 100K, the large agglomerates of the *γ*-Fe2O3 (maghemite) ferrimagnetic nanoparticles embedded in a multiblock poly(ether-ester) copolymer nonmagnetic matrix Guskos et al. (2006; 2008) are practically frozen into the matrix with a random orientation of the magnetic anisotropy axes. Then, the observed magnetic hysteresis loop represents the averaged one which is approximately a mixture of the cases discussed in Fig. 2 and Fig. 3. It is worth to add that in high temperatures, where the block copolymer is dissolved, the magnetic properties resemble the properties of ferrofluids and

Much more information on the magnetic properties of the polymers filled with nanoparticles can be get from the analyses of the absorption lines in FMR experiment. They can be

*χ* = *χ*� − *iχ*��, (12)

represented by the imaginary part of the dynamic magnetic susceptibility

to the anisotropy axis with the strength

external dc magnetic field.

*x*-direction.

there is no observed magnetic hysteresis loop.

where *χ*�� denotes total hysteresis losses per volume of magnetic nanoparticle through a cycle of the magnetization. For the chosen magnetic fields *Hz* = *Hdc* and *Hx* = *Hac* the components of the complex ac susceptibility (Eq. (12)) can be calculated by performing the Fourier transform on the time averaged *x*-component of the magnetization, i.e.,

$$\chi = \frac{1}{\pi H\_{\text{ac}}^0} \int\_0^\tau dt M\_{\text{x}}(t) e^{-i2\pi ft} \,\prime \,\tag{13}$$

where *τ* = 1/ *f* . In the case of theoretical modeling , the values *Mx*(*t*) can be obtained from the Landau-Lifshitz equation (Eq. 8). In real FMR experiments, the absorption lines derivatives, *dχ*��/*dH*dc (the derivative of the out-of-phase susceptibility) are measured instead of direct measuring *χ*��. In Fig. 5 there are presented the absorption lines derivatives obtained for the

Fig. 5. Absorption lines derivatives, *dχ*��/*dH*dc resulting from the computer simulations in the case when the magnetic anisotropy axis orientation oscillates around the direction parallel and transverse to the external dc magnetic field. The parameters of the computer simulation are the same as in Fig. 2.

model of the carbon coated nanoparticles shown in Fig. 4 in the case when their magnetic anisotropy axis oscillations are controlled by the harmonic forces applied to the ends of the axis and the forces are coupled with the *z*-direcion and *x*-direction, respectively. Note that if the magnetic anisotropy axis is linked to the direction which is tranverse to the direction of *H*dc then the corresponding resonance magnetic field *Hr* becomes shifted to higher values of *H*dc compared with the case when it is linked to the direction which is parallel. At the value of *H*dc = *Hr* the dynamic susceptibility *χ*�� takes its maximum value. It is worth emphasizing that the energy absorbed by the magnetic nanoparticles from the external AC magnetic field

0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 6. The temperature dependence of *dχ*/*dH*dc for 0.1% *γ*-Fe2O3 dispersed in

3.5 K


PEN-block-PTMO matrix.

0.2

concentrations of nanoparticles of 0.1% and 0.3%.

0.25

0.3

H (Tesla)

r

0.35

0.4


absorption derivative (arbitrary units)

0

0.002

0.004

in Polymer Composites with Magnetic Nanoparticles Fillers

Hdc (T)

0 50 100 150 200 250 300 temperature (K)

Fig. 7. An example of the dependence of the resonance field *Hr* on temperature for magnetic

nanoparticles *γ*-Fe2O3 in PEN-block-PTMO matrix. The plots correspond to two

60 K

80 K

224 K

<sup>381</sup> Thermal Effects on the Ferromagnetic Resonance

35 K

0.1% 0.3%

10.5 K

is proportional to *χ*. After the energy is converted into heat there is observed an increase Δ*T* of temperature which can be estimated at each cycle of the applied AC magnetic field with a given frequency *ω* = 2*π f* as follows (Sellmyer & Skomski, 2006):

$$
\Delta T = \frac{\mu\_0 V H\_0^2}{c \, m\_{\text{ferro}}} f \chi'' \tag{14}
$$

where *c* is the average specific heat of carbon and magnetic nanoparticle *c* = (*c*carbon + *c*ferro)/2, *m*ferro represents mass of magnetic nanoparticle. The remote heating of the magnetic nanoparticles can be important in viscous materials in low temperatures for reorientation processes among the magnetic nanoparticles. This particular feature of the magnetic nanoparticles to posses the different values of *Hr* for different orientations of their magnetic anisotropy axis (Fig. 5) becomes another interesting property of materials filled with magnetic nanoparticles where the static magnetic field *H*dc can be used as a remote switcher for the local heating different groups of nanoparticles.

#### **3. Temperature dependence of the spectral lines in viscous magnetic materials**

In the case when the magnetic nanoparticles are placed in a viscous material for which the viscosity varies significantly depending on temperature, magnetic properties of such materials are also beginning to significantly depend on temperature. This special property of viscous magnetic materials has been studied experimentally for maghemite nanoparticles embedded in a multiblock poly(ether-ester) copolymer nonmagnetic matrix Guskos et al. (2006; 2008). The experiments were performed in a wide range of temperatures, 3.5-288 K. In addition to the experimental results were also carried out theoretical studies Dudek et al. (2010). Several examples of spectral lines discussed in Dudek et al. (2010) are presented in Fig. 6 for concetration of 0.1% of *γ*-Fe2O3 nanoparticles dispersed in the polymer matrix. The figure shows the completely different FMR spectra in the range of low temperatures and high temperatures. These two ranges of temperatures are also evident in the resonance field *Hr* (Fig. 7) as a function of temperature, where at low temperatures a marked decrement of *Hr* is observed. In the latter case the experimental results for two different concentrations of magnetic nanoparticles are presented and up to 50 K there is no signicant difference between them. This could mean that the thermal properties of non-magnetic matrix, in this case of a multiblock poly(ether-ester) copolymer, are of decisive importance for the magnetic properties of the magnetic agglomerates and not the reorientation processes between magnetic nanoparticles.

In low temperature region we have solid-like nonmagnetic matrix where magnetic relaxation takes place through the process of magnetization relaxation (Neél relaxation). Once the magnetic anisotropy axes are oriented randomly some additional peaks appear on the spectral lines at the higher values of *H*dc. This property of spectral lines is shown in the previous section on the example of a single magnetic nanoparticle. The presence of many magnetic agglomerates consisting of different numbers of magnetic nanoparticles is one of the mechanisms for observing the broadening of the spectral lines. At higher temperatures the magnetic relaxation takes place both through the magnetization relaxation and rotation of the whole nanoparticle in a nonmagnetic surrounding and the additional peaks observed on spectral lines at low temepratures do vanish.

A simplified theoretical model was constructed in (Dudek et al., 2010) where a cluster consisting of *N* magnetic nanograins is placed randomly into a non-magnetic polymer matrix. 8 Will-be-set-by-IN-TECH

is proportional to *χ*. After the energy is converted into heat there is observed an increase Δ*T* of temperature which can be estimated at each cycle of the applied AC magnetic field with a

where *c* is the average specific heat of carbon and magnetic nanoparticle *c* = (*c*carbon + *c*ferro)/2, *m*ferro represents mass of magnetic nanoparticle. The remote heating of the magnetic nanoparticles can be important in viscous materials in low temperatures for reorientation processes among the magnetic nanoparticles. This particular feature of the magnetic nanoparticles to posses the different values of *Hr* for different orientations of their magnetic anisotropy axis (Fig. 5) becomes another interesting property of materials filled with magnetic nanoparticles where the static magnetic field *H*dc can be used as a remote switcher for the

0 *c m*ferro

*f χ* (14)

<sup>Δ</sup>*<sup>T</sup>* <sup>=</sup> *<sup>μ</sup>*0*VH*<sup>2</sup>

**3. Temperature dependence of the spectral lines in viscous magnetic materials**

In the case when the magnetic nanoparticles are placed in a viscous material for which the viscosity varies significantly depending on temperature, magnetic properties of such materials are also beginning to significantly depend on temperature. This special property of viscous magnetic materials has been studied experimentally for maghemite nanoparticles embedded in a multiblock poly(ether-ester) copolymer nonmagnetic matrix Guskos et al. (2006; 2008). The experiments were performed in a wide range of temperatures, 3.5-288 K. In addition to the experimental results were also carried out theoretical studies Dudek et al. (2010). Several examples of spectral lines discussed in Dudek et al. (2010) are presented in Fig. 6 for concetration of 0.1% of *γ*-Fe2O3 nanoparticles dispersed in the polymer matrix. The figure shows the completely different FMR spectra in the range of low temperatures and high temperatures. These two ranges of temperatures are also evident in the resonance field *Hr* (Fig. 7) as a function of temperature, where at low temperatures a marked decrement of *Hr* is observed. In the latter case the experimental results for two different concentrations of magnetic nanoparticles are presented and up to 50 K there is no signicant difference between them. This could mean that the thermal properties of non-magnetic matrix, in this case of a multiblock poly(ether-ester) copolymer, are of decisive importance for the magnetic properties of the magnetic agglomerates and not the reorientation processes

In low temperature region we have solid-like nonmagnetic matrix where magnetic relaxation takes place through the process of magnetization relaxation (Neél relaxation). Once the magnetic anisotropy axes are oriented randomly some additional peaks appear on the spectral lines at the higher values of *H*dc. This property of spectral lines is shown in the previous section on the example of a single magnetic nanoparticle. The presence of many magnetic agglomerates consisting of different numbers of magnetic nanoparticles is one of the mechanisms for observing the broadening of the spectral lines. At higher temperatures the magnetic relaxation takes place both through the magnetization relaxation and rotation of the whole nanoparticle in a nonmagnetic surrounding and the additional peaks observed on

A simplified theoretical model was constructed in (Dudek et al., 2010) where a cluster consisting of *N* magnetic nanograins is placed randomly into a non-magnetic polymer matrix.

given frequency *ω* = 2*π f* as follows (Sellmyer & Skomski, 2006):

local heating different groups of nanoparticles.

between magnetic nanoparticles.

spectral lines at low temepratures do vanish.

Fig. 6. The temperature dependence of *dχ*/*dH*dc for 0.1% *γ*-Fe2O3 dispersed in PEN-block-PTMO matrix.

Fig. 7. An example of the dependence of the resonance field *Hr* on temperature for magnetic nanoparticles *γ*-Fe2O3 in PEN-block-PTMO matrix. The plots correspond to two concentrations of nanoparticles of 0.1% and 0.3%.

0 0.1 0.2 0.3 0.4 0.5 H (Tesla)

20 40 60 80 100 120 140 temperature (K)

Fig. 9. Computer simulations of the dependence of the resonance field *Hr* on temperature for agglomerates of magnetic nanoparticles (Dudek et al., 2010). The agglomerates consisting of *N* = 30 magnetic nanoparticles represent two cases: when all magnetic nanoparticles are randomly oriented and when 70% of them is aligned with the dc magnetic field. In the case of a single magnetic nanoparticle (N=1) its magnetic anisotropy axis is aligned with the dc

dc

<sup>383</sup> Thermal Effects on the Ferromagnetic Resonance

Fig. 8. Computer simulations of the temperature dependence of *dχ*/*dH*dc calculated for N=30 magnetic nanoparticles in the case when their magnetic anisotropy axes are randomly oriented (Dudek et al., 2010). The parameters of the computer simulation are the same as in

10 K 100 K 120 K


0.16

0.17

H (Tesla)

r

magnetic field.

0.18

N=30, 70% with bias N=30, no bias N=1, with bias


0.000

d "/dH (arbitrary units)

dc

χ

Fig. 2.

0.002

0.004

in Polymer Composites with Magnetic Nanoparticles Fillers

They occupy a permanent position but may rotate. Each of the magnetic nanograins *i* = 1, 2, . . . , *N* has magnetization *Mi* which dynamics is described with the help of the stochastic version of the Landau-Lifshitz equation in Eq. (8). The rotational dynamics of magnetic nanoparticles is described with the help of the Langevin equations for the magnetic anisotropy axis orientation. These equations take the following form (Dudek et al., 2010; 2008):

$$\frac{d\rho\_i}{dt} = -\frac{2}{R\ \tilde{\xi}} \left| K\_{\text{il}} V \sin(2\psi\_i) \right| \sin(\varphi\_i - \varphi\_i') - \frac{K\_{\text{el}}}{\tilde{\xi}} \sin(\varphi\_i - \varphi\_{0,i}) + \frac{1}{\tilde{\xi}} \lambda\_{\varphi\_i \prime} \tag{15}$$

$$\frac{d\theta\_i}{dt} = -\frac{2}{R\ \xi} \left| K\_d V \sin(2\psi\_i) \right| \sin(\theta\_i - \theta'\_i) - \frac{K\_{\text{el}}}{\xi} \sin(\theta\_i - \theta\_{0,i}) + \frac{1}{\xi} \lambda\_{\theta\_l}.\tag{16}$$

in the diffusion limit, where *ξ* represents the friction of the *i*-th nanoparticle in the elastic non-magnetic polymer matrix and *λϕ*,*<sup>i</sup>* and *λθ*,*<sup>i</sup>* represent the white-noise driving torque (Coffey et al., 1984; Gardiner, 1983) for *i*-th nanoparticle, and *K*el represents the spring constant which controls the rotational oscillations of the magnetic anisotropy axis. In the above stochastic equations the thermal rotational fluctuations of the *i*-th magnetic nanoparticle are characterized by temperature *T* and *λϕ<sup>i</sup>* and *λθ<sup>i</sup>* and they fulfill the relations:

$$
\langle \lambda\_q(t) \rangle = 0 \tag{17}
$$

$$
\langle \lambda\_q(t)\lambda\_{q'}(t')\rangle = 2k\_B T \xi \delta(t - t'),
\tag{18}
$$

where *<sup>q</sup>* <sup>=</sup> *<sup>ϕ</sup>i*, *<sup>θ</sup>i*. The angles *<sup>ϕ</sup>*� and *<sup>θ</sup>*� represent the angles which the magnetization −→*<sup>M</sup>* makes with *z*-axis and *x*-axis, and the angles *ϕ*<sup>0</sup> and *θ*<sup>0</sup> are the initial angles of the easy axis after the magnetic nanoparticle has been built into polymer matrix. The numerical scheme applied to the stochastic equations in (Dudek et al., 2010) is the Euler-Maruyama method. The theoretical model introduced in (Dudek et al., 2010) reproduces qualitatively the results of the experiment (Guskos et al., 2006; 2008). In particular, the FMR spectrum and the dependence of *Hr* on temperature have qualitatively the same properties. It is evident from Fig. 8 and Fig. 9 if we compare them with Fig. 6 and Fig. 7.

The results of the theoretical model have been obtained by two assumptions. The first one is assuming an empirical model for the viscosity parameter *ν*, the Arrhenius law,

$$\nu(T) = \nu\_0 \mathbf{e}^{\mathbf{E}/\mathbf{k\_B T}} \tag{19}$$

where E is the activation energy. In the model, the viscosity parameter *ν*(*T*) is related to the rotational friction parameter *ξ* of magnetic nanoparticles in a polymer surounding (used in Eqs. (15) and (16)), as follows:

$$
\xi = 8\pi\nu(T)r^3,\tag{20}
$$

where *r* = *R*/2 denotes the radius of a sphere representing magnetic nanoparticle and its polymer coating. Hence the simple assumption in Eq. (19) and not the presence of a phase transition is responsible for the qualitatively different behavior of *Hr* in the low and high temperatures in the theoretical model ( Fig. 9).

The second assumption is introducing the Bloch law approximation

$$M\_s(T) = M\_0(0)\left(1 - \left(\frac{T}{T\_0}\right)^\delta\right) \tag{21}$$

10 Will-be-set-by-IN-TECH

They occupy a permanent position but may rotate. Each of the magnetic nanograins *i* = 1, 2, . . . , *N* has magnetization *Mi* which dynamics is described with the help of the stochastic version of the Landau-Lifshitz equation in Eq. (8). The rotational dynamics of magnetic nanoparticles is described with the help of the Langevin equations for the magnetic anisotropy

in the diffusion limit, where *ξ* represents the friction of the *i*-th nanoparticle in the elastic non-magnetic polymer matrix and *λϕ*,*<sup>i</sup>* and *λθ*,*<sup>i</sup>* represent the white-noise driving torque (Coffey et al., 1984; Gardiner, 1983) for *i*-th nanoparticle, and *K*el represents the spring constant which controls the rotational oscillations of the magnetic anisotropy axis. In the above stochastic equations the thermal rotational fluctuations of the *i*-th magnetic nanoparticle are

*i* ) <sup>−</sup> *<sup>K</sup>*el

)� = 2*kBTξδ*(*t* − *t*

where *<sup>q</sup>* <sup>=</sup> *<sup>ϕ</sup>i*, *<sup>θ</sup>i*. The angles *<sup>ϕ</sup>*� and *<sup>θ</sup>*� represent the angles which the magnetization −→*<sup>M</sup>* makes with *z*-axis and *x*-axis, and the angles *ϕ*<sup>0</sup> and *θ*<sup>0</sup> are the initial angles of the easy axis after the magnetic nanoparticle has been built into polymer matrix. The numerical scheme applied to the stochastic equations in (Dudek et al., 2010) is the Euler-Maruyama method. The theoretical model introduced in (Dudek et al., 2010) reproduces qualitatively the results of the experiment (Guskos et al., 2006; 2008). In particular, the FMR spectrum and the dependence of *Hr* on temperature have qualitatively the same properties. It is evident from Fig. 8 and Fig. 9 if we

The results of the theoretical model have been obtained by two assumptions. The first one is

where E is the activation energy. In the model, the viscosity parameter *ν*(*T*) is related to the rotational friction parameter *ξ* of magnetic nanoparticles in a polymer surounding (used in

where *r* = *R*/2 denotes the radius of a sphere representing magnetic nanoparticle and its polymer coating. Hence the simple assumption in Eq. (19) and not the presence of a phase transition is responsible for the qualitatively different behavior of *Hr* in the low and high

> 1 − *T T*0 *δ*

assuming an empirical model for the viscosity parameter *ν*, the Arrhenius law,

*<sup>i</sup>*) <sup>−</sup> *<sup>K</sup>*el

*<sup>ξ</sup>* sin(*ϕ<sup>i</sup>* <sup>−</sup> *<sup>ϕ</sup>*0,*i*) + <sup>1</sup>

*<sup>ξ</sup> sin*(*θ<sup>i</sup>* <sup>−</sup> *<sup>θ</sup>*0,*i*) + <sup>1</sup>

�*λq*(*t*)� = 0 (17)

*ν*(*T*) = *ν*0eE/kBT (19)

*ξ* = 8*πν*(*T*)*r*3, (20)

�

*ξ λϕ<sup>i</sup>*

*ξ λθi*

), (18)

, (15)

. (16)

(21)

axis orientation. These equations take the following form (Dudek et al., 2010; 2008):

*<sup>R</sup> <sup>ξ</sup>* <sup>|</sup>*KaV* sin(2*ψi*)<sup>|</sup> sin(*ϕ<sup>i</sup>* <sup>−</sup> *<sup>ϕ</sup>*�

*<sup>R</sup> <sup>ξ</sup>* <sup>|</sup>*KaV* sin(2*ψi*)<sup>|</sup> sin(*θ<sup>i</sup>* <sup>−</sup> *<sup>θ</sup>*�

characterized by temperature *T* and *λϕ<sup>i</sup>* and *λθ<sup>i</sup>* and they fulfill the relations:

�

�*λq*(*t*)*λq*�(*t*

*dϕ<sup>i</sup> dt* <sup>=</sup> <sup>−</sup> <sup>2</sup>

> *dθ<sup>i</sup> dt* <sup>=</sup> <sup>−</sup> <sup>2</sup>

compare them with Fig. 6 and Fig. 7.

Eqs. (15) and (16)), as follows:

temperatures in the theoretical model ( Fig. 9).

The second assumption is introducing the Bloch law approximation

*Ms*(*T*) = *M*0(0)

Fig. 8. Computer simulations of the temperature dependence of *dχ*/*dH*dc calculated for N=30 magnetic nanoparticles in the case when their magnetic anisotropy axes are randomly oriented (Dudek et al., 2010). The parameters of the computer simulation are the same as in Fig. 2.

Fig. 9. Computer simulations of the dependence of the resonance field *Hr* on temperature for agglomerates of magnetic nanoparticles (Dudek et al., 2010). The agglomerates consisting of *N* = 30 magnetic nanoparticles represent two cases: when all magnetic nanoparticles are randomly oriented and when 70% of them is aligned with the dc magnetic field. In the case of a single magnetic nanoparticle (N=1) its magnetic anisotropy axis is aligned with the dc magnetic field.

corresponding to different orientations of their magnetic easy axis. This property of the dependence of a maximum of *χ* on the orientation of the magnetic anisotropy axis with respect to the external dc magnetic field may be useful in designing new materials such as multi-functional magnetic nanocapsules. The thermal effects on the FMR spectrum in polymer composites filled with magnetic nanoparticles provide additional information about

<sup>385</sup> Thermal Effects on the Ferromagnetic Resonance

Some of the computer simulations have been performed in Wroclaw Centre for Networking

Coffey, W., Evans, M. & Grigolini, P. (1984). *Molecular Diffusion and Spectra*, Wiley, New York. Dudek, M., N.Guskos, Senderek, E. & Rosłaniec, Z. (2010). Temperature dependence of the fmr

Dudek, M. R., Guskos, N., Grabiec, B. & Maryniak, M. (2008). Magnetization dynamics

Dudek, M. & Wojciechowski, K. (2008). Magnetic films of negative poisson's ratio in rotating

Dutta, P., Manivannan, A., Seehra, M. S., Shah, N. & Huffman, G. P. (2004). Magnetic

Evans, K., Nikansah, M., Hutchinson, I. & Rogers, S. (1991). Molecular network design, *Nature*

Gilbert, T. (1955). A lagrangian formulation of the gyromagnetic equation of the magnetization

Guskos, N., Glenis, S., Likodimos, V., Typek, J., Maryniak, M., Rosłaniec, Z., Kwiatkowska,

Guskos, N., Likodimos, V., Glenis, S., Maryniak, M., M.Baran, Szymczak, R.,

Jönsson, P. E. (2003). Superparamagnetism and spin glass dynamics of interacting magnetic

Jung, S., Ketterson, J. & Chandrasekhar, V. (2002). Micromagnetic calculations of

Lakes, R. (1987). Foam structures with a negative poisson's ratio, *Science* Vol.235: 1038–1040. Landau, L. & Lifshitz, E. (1953). On the theory of the dispersion of magnetic permeability in

nanoparticle systems, *arXiv:cond-mat/0310684v2* .

ferromagnetic bodies, *Phys. Z. Sowjetunion* Vol.8: 153.

M., Baran, M., Szymczak, R. & Petridis, D. (2006). Matrix effects on the magnetic properties of *γ*-fe2o3 nanoparticles dispersed in a multiblock copolymer, *J. Appl. Phys.*

Roslaniec, Z., Kwiatkowska, M. & Petridis, D. (2008). Magnetic properties of *γ*-fe2o3/poly(esther-ester) copolymer nanocomposites, *Nanosci. Nanotech.*

ferromagnetic resonance in submicron ferromagnetic particles, *Phys. Rev. B*

Füzi, J. (2006). Magnetic characteristics of dipole clusters, *Physica B* Vol.372: 239–242. Gao, J. & Xu, B. (2009). Applications of nanomaterials inside cells, *Nano Today* Vol.4: 37–51. Gardiner, C. (1983). *Handbook of Stochastic Methods for Physics, Chemistry and the Natural*

magnetic fields, *J. Non-Cryst. Solids* Vol.354: 4304–4308.

absorption lines in viscoelastic magnetic materials, *J. Alloy Compd.* Vol.504: 289–295.

in landau-lifshitz-gilbert formulation. fmr experiment modeling, *J. Non-Cryst. Solids*

properties of nearly defect-free maghemite nanocrystals, *Phys. Rev. B* Vol.70: 174428.

the magnetic structure of the material.

in Polymer Composites with Magnetic Nanoparticles Fillers

Vol.354: 4146–4150.

Vol.353: 124.

Vol.99: 084307.

(No.8): 2127.

Vol.66: 132405.

*Sciences*, Springer-Verlag.

field, *Phys. Rev.* Vol.100: 1243.

**5. Acknowledgments**

**6. References**

and Supercomputing, Poland.

for the magnetization of the magnetic nanoparticles where T is temperature, *δ* = 1/3 and *T*<sup>0</sup> is some constant. The value of *α* is a parameter of the model under consideration. Another value of *α* can be also found in publications on magnetic materials.

The complexity of the FMR spectral lines can be seen in the example in Fig. 10 where the absorption lines derivatives *dχ*/*dH*dc have been plotted for a single magnetic nanoparticle in the case when its easy magnetic axis oscillates around the direction perpendicular to the external dc magnetic field in a surrounding with temperature-dependent viscosity *ν*(*T*). In low temperatures the magnetic resonance field *Hr* moves towards the lower values of *H*dc with increasing temperature instead to move towards the higher values of *H*dc as it is in the case of magnetic nanoparticles oscillating around the direction of the dc magnetic field. Only above a certain temperature there is no qualitative difference in the FMR spectrum for magnetic nanoparticles with magnetic easy axis oriented parallel or perpendicular to the external dc magnetic field.

Fig. 10. Absorption lines derivatives, *dχ*/*dH*dc in theoretical model (Dudek et al., 2010) for a single (*N* = 1) magnetic nanograin in the case when its magnetic anisotropy axis oscillates around the direction transverse to the direction of the external dc magnetic field. The plotted curves correspond to temperatures *T* = 10, 105, 120*K*, respectively. In low temperatures the magnetic resonance field *Hr* moves towards the lower values of *H*dc with increasing temperature and only above a certain temperature it begins to move toward the higher values of *H*dc.

In the case of magnetic agglomerates dispersed in a viscous medium and which consist of a large number of magnetic nanoparticles with randomly oriented axes relative to the field *H*dc the mechanism shown in Fig. 10 can be important in low temperatures.

#### **4. Conclusions**

Both the discussion in section 2 and FMR spectrum in Fig. 5 show that the static magnetic field *H*dc can be used as a remote switcher for the local heating different groups of nanoparticles corresponding to different orientations of their magnetic easy axis. This property of the dependence of a maximum of *χ* on the orientation of the magnetic anisotropy axis with respect to the external dc magnetic field may be useful in designing new materials such as multi-functional magnetic nanocapsules. The thermal effects on the FMR spectrum in polymer composites filled with magnetic nanoparticles provide additional information about the magnetic structure of the material.

## **5. Acknowledgments**

Some of the computer simulations have been performed in Wroclaw Centre for Networking and Supercomputing, Poland.

## **6. References**

12 Will-be-set-by-IN-TECH

for the magnetization of the magnetic nanoparticles where T is temperature, *δ* = 1/3 and *T*<sup>0</sup> is some constant. The value of *α* is a parameter of the model under consideration. Another

The complexity of the FMR spectral lines can be seen in the example in Fig. 10 where the absorption lines derivatives *dχ*/*dH*dc have been plotted for a single magnetic nanoparticle in the case when its easy magnetic axis oscillates around the direction perpendicular to the external dc magnetic field in a surrounding with temperature-dependent viscosity *ν*(*T*). In low temperatures the magnetic resonance field *Hr* moves towards the lower values of *H*dc with increasing temperature instead to move towards the higher values of *H*dc as it is in the case of magnetic nanoparticles oscillating around the direction of the dc magnetic field. Only above a certain temperature there is no qualitative difference in the FMR spectrum for magnetic nanoparticles with magnetic easy axis oriented parallel or perpendicular to the

> 0 0.1 0.2 0.3 0.4 0.5 H (Tesla)

dc

Fig. 10. Absorption lines derivatives, *dχ*/*dH*dc in theoretical model (Dudek et al., 2010) for a single (*N* = 1) magnetic nanograin in the case when its magnetic anisotropy axis oscillates around the direction transverse to the direction of the external dc magnetic field. The plotted curves correspond to temperatures *T* = 10, 105, 120*K*, respectively. In low temperatures the magnetic resonance field *Hr* moves towards the lower values of *H*dc with increasing temperature and only above a certain temperature it begins to move toward the higher

In the case of magnetic agglomerates dispersed in a viscous medium and which consist of a large number of magnetic nanoparticles with randomly oriented axes relative to the field *H*dc

Both the discussion in section 2 and FMR spectrum in Fig. 5 show that the static magnetic field *H*dc can be used as a remote switcher for the local heating different groups of nanoparticles

the mechanism shown in Fig. 10 can be important in low temperatures.

value of *α* can be also found in publications on magnetic materials.

T = 10 K T = 105 K T = 120 K

external dc magnetic field.

d "/dH (arbitrary units)

dc

χ

values of *H*dc.

**4. Conclusions**



0

0.0002

0.0004

Coffey, W., Evans, M. & Grigolini, P. (1984). *Molecular Diffusion and Spectra*, Wiley, New York.


**18** 

*Italy* 

**Nanoparticle Dynamics in Polymer Melts** 

*Dept. of Materials and Production Engineering, University of Naples Federico II* 

Adding solid particles to polymeric materials is a common way to reduce the costs and to impart desired mechanical and transport properties. This makes polymers potential substitutes for more expensive non-polymeric materials. The advantages of filled polymers are normally offset by the increased complexity in the rheological behaviour of the resulting composite. Usually, a compromise has to be made between the benefits ensured by the filler, the increased difficulties in melt processing, the problems in achieving a uniform dispersion of the solid particulate, and the economics of the process due to the added step of compounding [Shenoy, 1999]. Filled polymers can be described as a suspension of particles and particle aggregates dispersed in the polymer matrix. Interactions between individual particles or aggregates and the matrix, as well as between particles, hinder the material deformability modifying both the solid- and melt-state behaviour of the host polymer. In polymer-based microcomposites, these effects only become significant at relatively high filler contents, i.e. when the filler particles are sufficiently close to each other to form a network that spans large sections of the polymer matrix. Over the last fifteen years, the same reinforcing and thixotropic effects have been observed with the use of very small amounts of inorganic nanoparticles, which has resulted in extensive research in the field of polymer-based nanocomposites (PNCs) [Usuki et al., 1993; Kojima et al., 1993]. In order to fully understand the exceptional properties of PNCs, the morphological and structural implications stemming from the nanometric sizes of the filler have to be taken into account. With respect to traditional microcomposites, nanocomposites show very high specific interface area, typically of order of ~102 m2 g-1. The matrix properties are significantly affected in the vicinity of the reinforcement, varying continuously from the interface towards the bulk polymer. As a consequence, the large amount of reinforcement surface area means that a relatively small amount of nanoscale reinforcement can have remarkable effects on the macroscale

A noticeable consequence of the nanometric dimensions of the filler is the extremely high numerical density of particles, or alternatively the very small inter-particles distances. If N monodisperse spherical particles with radius *r* are randomly distributed in a volume *V*, the distance between the centres of the particles can be approximated to *h*=(*V*/*N*)1/3. Introducing the particle volume fraction *Φ*=*Nv*/*V*, where *v*=4π*r*3/3 is the volume of the

single particle, the wall-to-wall distance between contiguous particles is:

**1. Introduction** 

properties of the composite material.

Giovanni Filippone and Domenico Acierno


## **Nanoparticle Dynamics in Polymer Melts**

Giovanni Filippone and Domenico Acierno

*Dept. of Materials and Production Engineering, University of Naples Federico II Italy* 

## **1. Introduction**

14 Will-be-set-by-IN-TECH

386 Smart Nanoparticles Technology

Liu, T.-Y., Hu, S.-H., Liu, D.-M., Chen, S.-Y. & Chen, I.-W. (2009). Biomedical nanoparticle carriers with combined thermal and magnetic responses, *Nano Today* Vol.4: 52–65. Owens, F. J. (2003). Ferromagnetic resonance of magnetic field oriented fe3o4 nanoparticles in

Sellmyer, D. & Skomski, R. (2006). *Advanced Magnetic Materials*, Springer Science+Business

Smith, C. & Wojciechowski, K. (2008). Preface: phys. stat. sol. (b), *Phys. Status Solidi b*

Sorop, T., Nielsch, K., Göring, P., Kröll, M., Blau, W., Werspohn, R., Gösele, U. & de Jongh, L.

Sukhov, A., Usadel, K. & Nowak, U. (2008). Ferromagnetic resonance in an ensemble of

Usadel, K. D. (2006). Temperature-dependent dynamical behavior of nanoparticles as probed

Vleck, J. V. (1950). Concerning the theory of ferromagnetic resonance absorption, *Phys. Rev.*

Wilson, J., Poddar, P., Frey, N., Srikanth, H., Mohomed, K., Harmon, J., Kotha, S. &

Wood, D. & Camp, P. (2011). Modeling the properties of ferrogels in uniform magnetic fields,

Zahn, M. (2001). Magnetic fluid and nanoparticle applications to nanotechnology, *J. Nanopart.*

with embedded iron nanoparticles, *J. Appl. Phys.* Vol.95: 1439–1443.

(2004). Study of the magnetic hysteresis in arrays of ferromagnetic fe nanowires as a function of the template filling fraction, *J. Magn. Magn. Mater.* Vol.272-276: 1656–1657.

nanoparticles with randomly distributed anisotropy axes, *J. Magn. Magn. Mater.*

by ferromagnetic resonance using landau-lifshitz-gilbert dynamics in a classical spin

Wachsmuth, J. (2004). Synthesis and magnetic properties of polymer nanocomposites

frozen ferrofluids, *J. Phys. Chem. Solids* Vol.64: 2289–2292.

Shliomis, M. I. (1975). Magnetic fluids, *Sov. Phys. Usp.* Vol.17: 153–169.

Media, Inc., Place of publication.

model, *Phys. Rev. B* Vol.73: 212405.

*Phys. Rev. E* Vol.83: 011402.

Vol.245: 486–488.

Vol.320: 31–35.

Vol.78: 266–274.

*Res.* Vol.3: 73–78.

Adding solid particles to polymeric materials is a common way to reduce the costs and to impart desired mechanical and transport properties. This makes polymers potential substitutes for more expensive non-polymeric materials. The advantages of filled polymers are normally offset by the increased complexity in the rheological behaviour of the resulting composite. Usually, a compromise has to be made between the benefits ensured by the filler, the increased difficulties in melt processing, the problems in achieving a uniform dispersion of the solid particulate, and the economics of the process due to the added step of compounding [Shenoy, 1999]. Filled polymers can be described as a suspension of particles and particle aggregates dispersed in the polymer matrix. Interactions between individual particles or aggregates and the matrix, as well as between particles, hinder the material deformability modifying both the solid- and melt-state behaviour of the host polymer. In polymer-based microcomposites, these effects only become significant at relatively high filler contents, i.e. when the filler particles are sufficiently close to each other to form a network that spans large sections of the polymer matrix. Over the last fifteen years, the same reinforcing and thixotropic effects have been observed with the use of very small amounts of inorganic nanoparticles, which has resulted in extensive research in the field of polymer-based nanocomposites (PNCs) [Usuki et al., 1993; Kojima et al., 1993]. In order to fully understand the exceptional properties of PNCs, the morphological and structural implications stemming from the nanometric sizes of the filler have to be taken into account. With respect to traditional microcomposites, nanocomposites show very high specific interface area, typically of order of ~102 m2 g-1. The matrix properties are significantly affected in the vicinity of the reinforcement, varying continuously from the interface towards the bulk polymer. As a consequence, the large amount of reinforcement surface area means that a relatively small amount of nanoscale reinforcement can have remarkable effects on the macroscale properties of the composite material.

A noticeable consequence of the nanometric dimensions of the filler is the extremely high numerical density of particles, or alternatively the very small inter-particles distances. If N monodisperse spherical particles with radius *r* are randomly distributed in a volume *V*, the distance between the centres of the particles can be approximated to *h*=(*V*/*N*)1/3. Introducing the particle volume fraction *Φ*=*Nv*/*V*, where *v*=4π*r*3/3 is the volume of the single particle, the wall-to-wall distance between contiguous particles is:

Nanoparticle Dynamics in Polymer Melts 389

interactions, this phase behaviour is modified due to interplay between *Φ* and the energy of interaction, *U*. We are mainly interested in weakly attractive colloidal dispersions, which are reminiscent of a large number of PNCs in which Van der Waals forces between nanoparticles and aggregates are of major importance. In such systems, aggregation results in disordered clusters of particles. These mesostructures may or may not span the whole space depending on *Φ* and *U* [Prasad, 2003]. The rheological behaviour of weakly interacting colloidal dispersions can be rationalized with a simple two-phase model that combines the elasticity of the disordered particle network and the Newtonian viscosity of the suspending liquid [Cipelletti et al., 2000; Trappe & Weitz, 2000; Trappe et al., 2001]. Despite the complexities stemming from the intrinsic non-Newtonian feature of polymer matrices, in this chapter we show that a similar approach can be successfully applied to a series of model PNCs with weak polymer-filler interaction. We emphasize that many PNCs of technological interest fall in this family. The two-phase model is validated through the building of a master curve of the elastic modulus of samples at different composition. A refinement of the model is also presented, which accounts for hydrodynamic effects. The dynamics of de-structuring and reforming of the filler network are studied by analysing the effects of large amplitude deformations. Besides simplifying the viscoelastic analysis of complex systems such as PNCs, the proposed approach can be extended to a wide variety of complex fluids where the elasticity of the components can be superimposed. In particular, the elastic modulus has been recently suggested to follow a universal behaviour with volume fraction also in case of interacting systems in which polymer bridging mechanisms exist [Surve et al., 2006]. This suggests a possible general

We start our analysis dealing with the implications of Brownian motion in simple model systems constituted by polymer melts filled with small amounts of different kinds of spherical particles. Specifically, we discuss the effect of particle size and matrix viscosity on the ability of the filler to aggregate and eventually assemble in a three-dimensional network. Then, a two-phase model firstly proposed for weakly attractive particles suspended in a Newtonian medium is presented [Trappe & Weitz, 2000]. The physical picture of an elastic particle network interspersed in a background fluid qualitatively accounts for the viscoelastic behaviour of the suspension. Afterwards, the relations between structure and viscoelasticity of two model PNCs is described in the framework of the two-phase model. A refinement of the model is therefore presented, which accounts for hydrodynamic effects successfully capturing the frequency dependent viscoelastic behaviour of simple PNCs. Finally, the dynamics of de-structuring and reforming of the filler network are studied by

**2.1 Brownian motion in polymer melts filled with nanoparticles – Gelation and ageing** 

Untreated inorganic particles are difficult to disperse in polymer matrices due to the typically poor polymer-filler affinity. Such incompatibility clearly emerges in the case of PNCs, where the specific surface of the particles is very high. The hydrodynamic forces

feature for the proposed approach.

**2. Viscoelasticity and structure of PNCs** 

analysing the effects of large amplitude deformations.

**2.1.1 Preliminary considerations** 

$$h = \left[\sqrt[3]{\frac{4\pi}{3\cdot 6}} - 2\right]r\tag{1}$$

Once fixed the filler content, *h* linearly scales with *r*. In addition, we observe that, for diluted systems (*Φ*<0.1) such those we are interested in, Eq. 1 gives *h*~2*r*. This means that, if the filler particles are well dispersed within the host polymer, nanometric inter-particles distances are expected for nanocomposites. In such systems a large fraction of polymer is in contact with the filler. At the most, if the particle radius is of the same order as the mean radius of gyration of host polymer chains, *Rg*, each single chain potentially interacts with more than one nanoparticle, and there is no bulk polymer [Jancar & Recman, 2010]. Two scenarios are possible when inter-particles distances are so small: if a good affinity exists between the polymer and the filler, then a polymer-mediated transient network between the particles set up [Ozmusul et al., 2005; Saint-Michel et al., 2003; Zhang & Archer, 2002]; on the other hand, if the polymer-filler interactions are weak, the nanoparticles aggregate forming flocs, which eventually assemble into a space-spanning filler network [Filippone et al. 2009; Inoubli et al., 2006; Ren et al., 2000]. In both cases, the presence of a threedimensional mesostructure has a profound effect on the composite rheology.

The formation of the network, either polymer-mediated or formed by bare nanoparticles, originates from local rearrangements of the filler occurring in the melt both during flow and at rest. Nanoparticles, in fact, are subjected to relevant Brownian motion even in highly viscous mediums such as polymer melts. To get an idea about the relevance of such a phenomenon, we estimate the self-diffusion time of a spherical particle of radius *r*, *τs*, that is the time required for the particle moves of a length equal to its radius [Russel et al., 1989]:

$$
\pi\_s = \frac{6\pi\eta\_s r^3}{k\_B T} \tag{2}
$$

Here *ηs* is the viscosity of the suspending medium, *kB* is the Boltzmann's constant and *T* is the temperature. For a simple low viscosity (*ηs*~10-2 Pa\*s) Newtonian liquid at room temperature, Eq. 2 gives the well-known result that particles of a few microns in size experience appreciable Brownian motions. Setting *T*=400°K and *ηs*~103 Pa\*s as typical values for melted polymers, we obtain the noteworthy result that particles of a few tens of nanometers display Brownian motions on timescales of order of a 101÷102 seconds. Such durations are typically accessed in many transforming processes of the polymer industry, as well as during rheological analyses. The result is that, unlike polymer microcomposites, PNCs can be depicted as "living systems", in which the particles are free to move and rearrange in the melt, both in flow and even at rest, towards more favourable thermodynamic states. In this sense, PNCs are reminiscent of colloidal suspensions. Therefore, these simpler systems can be considered as the natural starting point to understand the much more complex rheological behaviour of PNCs.

The simplest case of colloidal dispersion is represented by a Newtonian suspension of hard spheres. The inter-particles interaction is zero at all separations and infinitely repulsive at contact. Coupled with thermal fluctuations, this kind of interaction results in a wide variety of possible structures. The suspension may behave like a gas, a liquid, a crystal or a glass depending on the particle volume fraction *Φ* [Pusey & van Megen, 1986]. In the presence of

<sup>3</sup> <sup>4</sup> <sup>2</sup> 3 

Once fixed the filler content, *h* linearly scales with *r*. In addition, we observe that, for diluted systems (*Φ*<0.1) such those we are interested in, Eq. 1 gives *h*~2*r*. This means that, if the filler particles are well dispersed within the host polymer, nanometric inter-particles distances are expected for nanocomposites. In such systems a large fraction of polymer is in contact with the filler. At the most, if the particle radius is of the same order as the mean radius of gyration of host polymer chains, *Rg*, each single chain potentially interacts with more than one nanoparticle, and there is no bulk polymer [Jancar & Recman, 2010]. Two scenarios are possible when inter-particles distances are so small: if a good affinity exists between the polymer and the filler, then a polymer-mediated transient network between the particles set up [Ozmusul et al., 2005; Saint-Michel et al., 2003; Zhang & Archer, 2002]; on the other hand, if the polymer-filler interactions are weak, the nanoparticles aggregate forming flocs, which eventually assemble into a space-spanning filler network [Filippone et al. 2009; Inoubli et al., 2006; Ren et al., 2000]. In both cases, the presence of a three-

The formation of the network, either polymer-mediated or formed by bare nanoparticles, originates from local rearrangements of the filler occurring in the melt both during flow and at rest. Nanoparticles, in fact, are subjected to relevant Brownian motion even in highly viscous mediums such as polymer melts. To get an idea about the relevance of such a phenomenon, we estimate the self-diffusion time of a spherical particle of radius *r*, *τs*, that is the time required for the particle moves of a length equal to its radius [Russel et al., 1989]:

> <sup>3</sup> <sup>6</sup> *<sup>s</sup> <sup>s</sup> B r*

Here *ηs* is the viscosity of the suspending medium, *kB* is the Boltzmann's constant and *T* is the temperature. For a simple low viscosity (*ηs*~10-2 Pa\*s) Newtonian liquid at room temperature, Eq. 2 gives the well-known result that particles of a few microns in size experience appreciable Brownian motions. Setting *T*=400°K and *ηs*~103 Pa\*s as typical values for melted polymers, we obtain the noteworthy result that particles of a few tens of nanometers display Brownian motions on timescales of order of a 101÷102 seconds. Such durations are typically accessed in many transforming processes of the polymer industry, as well as during rheological analyses. The result is that, unlike polymer microcomposites, PNCs can be depicted as "living systems", in which the particles are free to move and rearrange in the melt, both in flow and even at rest, towards more favourable thermodynamic states. In this sense, PNCs are reminiscent of colloidal suspensions. Therefore, these simpler systems can be considered as the natural starting point to

The simplest case of colloidal dispersion is represented by a Newtonian suspension of hard spheres. The inter-particles interaction is zero at all separations and infinitely repulsive at contact. Coupled with thermal fluctuations, this kind of interaction results in a wide variety of possible structures. The suspension may behave like a gas, a liquid, a crystal or a glass depending on the particle volume fraction *Φ* [Pusey & van Megen, 1986]. In the presence of

dimensional mesostructure has a profound effect on the composite rheology.

understand the much more complex rheological behaviour of PNCs.

*h r* (1)

*k T* (2)

interactions, this phase behaviour is modified due to interplay between *Φ* and the energy of interaction, *U*. We are mainly interested in weakly attractive colloidal dispersions, which are reminiscent of a large number of PNCs in which Van der Waals forces between nanoparticles and aggregates are of major importance. In such systems, aggregation results in disordered clusters of particles. These mesostructures may or may not span the whole space depending on *Φ* and *U* [Prasad, 2003]. The rheological behaviour of weakly interacting colloidal dispersions can be rationalized with a simple two-phase model that combines the elasticity of the disordered particle network and the Newtonian viscosity of the suspending liquid [Cipelletti et al., 2000; Trappe & Weitz, 2000; Trappe et al., 2001]. Despite the complexities stemming from the intrinsic non-Newtonian feature of polymer matrices, in this chapter we show that a similar approach can be successfully applied to a series of model PNCs with weak polymer-filler interaction. We emphasize that many PNCs of technological interest fall in this family. The two-phase model is validated through the building of a master curve of the elastic modulus of samples at different composition. A refinement of the model is also presented, which accounts for hydrodynamic effects. The dynamics of de-structuring and reforming of the filler network are studied by analysing the effects of large amplitude deformations. Besides simplifying the viscoelastic analysis of complex systems such as PNCs, the proposed approach can be extended to a wide variety of complex fluids where the elasticity of the components can be superimposed. In particular, the elastic modulus has been recently suggested to follow a universal behaviour with volume fraction also in case of interacting systems in which polymer bridging mechanisms exist [Surve et al., 2006]. This suggests a possible general feature for the proposed approach.

## **2. Viscoelasticity and structure of PNCs**

We start our analysis dealing with the implications of Brownian motion in simple model systems constituted by polymer melts filled with small amounts of different kinds of spherical particles. Specifically, we discuss the effect of particle size and matrix viscosity on the ability of the filler to aggregate and eventually assemble in a three-dimensional network. Then, a two-phase model firstly proposed for weakly attractive particles suspended in a Newtonian medium is presented [Trappe & Weitz, 2000]. The physical picture of an elastic particle network interspersed in a background fluid qualitatively accounts for the viscoelastic behaviour of the suspension. Afterwards, the relations between structure and viscoelasticity of two model PNCs is described in the framework of the two-phase model. A refinement of the model is therefore presented, which accounts for hydrodynamic effects successfully capturing the frequency dependent viscoelastic behaviour of simple PNCs. Finally, the dynamics of de-structuring and reforming of the filler network are studied by analysing the effects of large amplitude deformations.

#### **2.1 Brownian motion in polymer melts filled with nanoparticles – Gelation and ageing**

#### **2.1.1 Preliminary considerations**

Untreated inorganic particles are difficult to disperse in polymer matrices due to the typically poor polymer-filler affinity. Such incompatibility clearly emerges in the case of PNCs, where the specific surface of the particles is very high. The hydrodynamic forces

Nanoparticle Dynamics in Polymer Melts 391

set to 250 s for all the samples. The polymer and the filler were previously dried under vacuum for sixteen hours at 70°C. The neat polymers used as reference materials were extruded in the same conditions to allow for an accurate comparison with the filled samples.

The morphology of the composites was examined by transmission electron microscopy (TEM mod. EM 208, Philips). The observations were performed on slices with thickness ~150 nm, which were randomly cut from the extruded pellets using a diamond knife at

Rheological tests were carried out by means of either a strain-controlled rotational rheometer (ARES L.S, Rheometric Scientific) or a stress-controlled rotational rheometer (ARG2, TA Instruments). The tests were carried out using parallel plates with diameter of 25 mm for the nanocomposites, while plates of 50 mm were used for the neat polymers because of their low viscosity. All measurements were performed in an atmosphere of dry nitrogen. The testing temperature was T=190°C for the PP/TiO2 samples and T=200°C for the PS/SiO2 samples. The viscoelastic moduli display a range of strain-independence, i.e. a range of linear viscoelasticity, which depends on the filler content. In order to determine the limits of the linear viscoelastic regime, oscillatory strain scans were performed on each sample at a fixed frequency of 0.063 rad s-1. Low-frequency (*ω*=0.063 rad s-1) time-sweep experiments were performed to study the evolution of the linear viscoelastic properties during time. The frequency-dependent elastic (*G′*) and viscous (*G′′*) moduli of the samples were measured by oscillatory shear scans in the linear regime. To account for the marked sensitivity of the rheological response on filler content, we evaluated the effective amount of filler of each sample used for the rheological experiments through thermogravimetrical analyses (TGA).

 *p f pf c*

where *c* is filler weight fraction as deduced from TGA and *ρp* and *ρf* are the densities of

The internal structure of the as extruded sample PP/TiO2 at *Φ*=0.038 is shown in the TEM micrograph of Figure 1.a. Well distributed nanoparticle aggregates of a few hundreds of nanometers are suspended in the polymer matrix. The magnification of one of these aggregates is reported in Figure 1.b. A few hundreds of individual TiO2 nanoparticles are

The sample was subjected to a thermal annealing at 190°C in quasi-quiescent conditions, i.e. by submitting it to shear oscillations in the rheometer at small strain amplitude (*γ*=2%) and frequency (*ω*=0.063 rad s-1). This allows to monitor the evolutions during time of slow dynamic populations, relaxing in timescales of order of *τ*=1/*ω*≈16 sec, without altering the

*c( )* (3)

**2.1.3 Characterization** 

room temperature.

The filler volume fraction *Φ* was estimated as:

**2.1.4 Effect of the filler mobility on the linear viscoelasticity** 

closely packed into dense clusters with irregular shape.

polymer and filler, respectively.

internal structure of the sample.

developed during intense melt mixing processes breakup the large aggregates down to clusters of few tens of particles [Baird & Collias, 1998]. Above the melting or glass transition temperature of the polymer matrix, however, these aggregates may reassemble into bigger structures because of the inter-particles attraction forces. Since the refractive indexes of polymers and inorganic fillers are typically very different, Van der Waals forces becomes of major importance leading to formation of aggregates and particle gels. The two most simple experimental techniques to follow the rearrangements of the filler in the melt are: (i) direct visualization of the particles through electron microscopy performed on solid samples; (ii) monitoring of rheological parameters sensitive to the material internal structure. Both these techniques have been applied to several model PNC systems constituted by polymer matrices filled with different kinds of inorganic nanoparticles with spherical symmetry. The rational for selecting such model systems originates from the intrinsic high complexity of other technologically relevant PNCs. The properties of such systems, often based on layered or tubular nanoparticles, are too sensitive to the state of dispersion of the filler and the wide variety of the possible nanostructures achievable during processing. The materials, the compounding procedures and the experimental details about the characterization of the composites are described in detail in the following paragraphs. Many of the results have been taken from papers previously published by our group, wherein further experimental details can be found [Acierno et al., 2007a, 2007b; Romeo et al., 2008; Filippone et al., 2010; Romeo et al., 2009].

#### **2.1.2 Materials and sample preparation**

Nano- and microcomposites were prepared using two different polymeric matrices. The first one is polypropylene (PP Moplen HP563N by Basell; weight average molecular weight *Mw*=245 KDa; zero shear viscosity *η0*=1.9\*103 Pa\*s at 190°C; terminal relaxation time *τt*≈0.4 s) with glass transition temperature *Tg*=6°C and melting temperature *Tm*=169°C. The second polymer matrix is atactic polystyrene (PS, kindly supplied by Polimeri Europa). In particular, we used two PS matrices at different molecular weight, coded as PS-low (*Mw*=125 KDa; *η0*=1.7\*103 Pa\*s at 200°C; *τt*≈0.1 s) and PS-high (*Mw*=268 KDa; *η0*=2.1\*104 Pa\*s at 200°C; *τt*≈100 s), both having glass transition temperatures *Tg*=100°C.

Three kinds of nanoparticles were used as fillers: titanium dioxide (TiO2 by Sigma Aldrich; density *ρ*=3.9 g/mL; surface area ~190÷290 m2/g; average primary particles diameter *d*=15 nm) and alumina nanospheres (Al2O3 by Sigma Aldrich; *ρ*=4.00 g/mL; surface area: 35–43 m2/g; *d*≈40 nm) were used to prepare PP/TiO2 and PP/Al2O3 nanocomposites with filler volume fractions up to *Φ*=0.064; fumed silica (SiO2 by Degussa; *ρ*=2.2 g/mL; surface area ~135-165 m2/g; *d*=14 nm) was mixed with the two PS matrices up to *Φ*=0.041. PP/TiO2 microcomposites were also prepared by using titanium dioxide microparticles (TiO2 by Sigma Aldrich; *ρ*=3.9 g/mL; surface area ~0.14-0.04 m2/g; *d*≈4 μm).

Nano- and microcomposites were prepared by melt compounding the constituents using a co-rotating extruder (Minilab Microcompounder, ThermoHaake) equipped with a capillary die (diameter 2 mm). The extrusions were carried out at 190°C. The screw speed was set to ~100 rpm, corresponding to an average shear rate of order of 50 s-1 inside the extrusion chamber. A feedback chamber allowed an accurate control of the residence time, which was set to 250 s for all the samples. The polymer and the filler were previously dried under vacuum for sixteen hours at 70°C. The neat polymers used as reference materials were extruded in the same conditions to allow for an accurate comparison with the filled samples.

#### **2.1.3 Characterization**

390 Smart Nanoparticles Technology

developed during intense melt mixing processes breakup the large aggregates down to clusters of few tens of particles [Baird & Collias, 1998]. Above the melting or glass transition temperature of the polymer matrix, however, these aggregates may reassemble into bigger structures because of the inter-particles attraction forces. Since the refractive indexes of polymers and inorganic fillers are typically very different, Van der Waals forces becomes of major importance leading to formation of aggregates and particle gels. The two most simple experimental techniques to follow the rearrangements of the filler in the melt are: (i) direct visualization of the particles through electron microscopy performed on solid samples; (ii) monitoring of rheological parameters sensitive to the material internal structure. Both these techniques have been applied to several model PNC systems constituted by polymer matrices filled with different kinds of inorganic nanoparticles with spherical symmetry. The rational for selecting such model systems originates from the intrinsic high complexity of other technologically relevant PNCs. The properties of such systems, often based on layered or tubular nanoparticles, are too sensitive to the state of dispersion of the filler and the wide variety of the possible nanostructures achievable during processing. The materials, the compounding procedures and the experimental details about the characterization of the composites are described in detail in the following paragraphs. Many of the results have been taken from papers previously published by our group, wherein further experimental details can be found [Acierno et al., 2007a, 2007b; Romeo et al., 2008; Filippone et al., 2010;

Nano- and microcomposites were prepared using two different polymeric matrices. The first one is polypropylene (PP Moplen HP563N by Basell; weight average molecular weight *Mw*=245 KDa; zero shear viscosity *η0*=1.9\*103 Pa\*s at 190°C; terminal relaxation time *τt*≈0.4 s) with glass transition temperature *Tg*=6°C and melting temperature *Tm*=169°C. The second polymer matrix is atactic polystyrene (PS, kindly supplied by Polimeri Europa). In particular, we used two PS matrices at different molecular weight, coded as PS-low (*Mw*=125 KDa; *η0*=1.7\*103 Pa\*s at 200°C; *τt*≈0.1 s) and PS-high (*Mw*=268 KDa; *η0*=2.1\*104 Pa\*s at 200°C;

Three kinds of nanoparticles were used as fillers: titanium dioxide (TiO2 by Sigma Aldrich; density *ρ*=3.9 g/mL; surface area ~190÷290 m2/g; average primary particles diameter *d*=15 nm) and alumina nanospheres (Al2O3 by Sigma Aldrich; *ρ*=4.00 g/mL; surface area: 35–43 m2/g; *d*≈40 nm) were used to prepare PP/TiO2 and PP/Al2O3 nanocomposites with filler volume fractions up to *Φ*=0.064; fumed silica (SiO2 by Degussa; *ρ*=2.2 g/mL; surface area ~135-165 m2/g; *d*=14 nm) was mixed with the two PS matrices up to *Φ*=0.041. PP/TiO2 microcomposites were also prepared by using titanium dioxide microparticles (TiO2 by

Nano- and microcomposites were prepared by melt compounding the constituents using a co-rotating extruder (Minilab Microcompounder, ThermoHaake) equipped with a capillary die (diameter 2 mm). The extrusions were carried out at 190°C. The screw speed was set to ~100 rpm, corresponding to an average shear rate of order of 50 s-1 inside the extrusion chamber. A feedback chamber allowed an accurate control of the residence time, which was

Romeo et al., 2009].

**2.1.2 Materials and sample preparation** 

*τt*≈100 s), both having glass transition temperatures *Tg*=100°C.

Sigma Aldrich; *ρ*=3.9 g/mL; surface area ~0.14-0.04 m2/g; *d*≈4 μm).

The morphology of the composites was examined by transmission electron microscopy (TEM mod. EM 208, Philips). The observations were performed on slices with thickness ~150 nm, which were randomly cut from the extruded pellets using a diamond knife at room temperature.

Rheological tests were carried out by means of either a strain-controlled rotational rheometer (ARES L.S, Rheometric Scientific) or a stress-controlled rotational rheometer (ARG2, TA Instruments). The tests were carried out using parallel plates with diameter of 25 mm for the nanocomposites, while plates of 50 mm were used for the neat polymers because of their low viscosity. All measurements were performed in an atmosphere of dry nitrogen. The testing temperature was T=190°C for the PP/TiO2 samples and T=200°C for the PS/SiO2 samples. The viscoelastic moduli display a range of strain-independence, i.e. a range of linear viscoelasticity, which depends on the filler content. In order to determine the limits of the linear viscoelastic regime, oscillatory strain scans were performed on each sample at a fixed frequency of 0.063 rad s-1. Low-frequency (*ω*=0.063 rad s-1) time-sweep experiments were performed to study the evolution of the linear viscoelastic properties during time. The frequency-dependent elastic (*G′*) and viscous (*G′′*) moduli of the samples were measured by oscillatory shear scans in the linear regime. To account for the marked sensitivity of the rheological response on filler content, we evaluated the effective amount of filler of each sample used for the rheological experiments through thermogravimetrical analyses (TGA). The filler volume fraction *Φ* was estimated as:

$$\Phi = \frac{c\mathfrak{p}\_p}{\mathfrak{p}\_f + c(\mathfrak{p}\_p - \mathfrak{p}\_f)} \tag{3}$$

where *c* is filler weight fraction as deduced from TGA and *ρp* and *ρf* are the densities of polymer and filler, respectively.

#### **2.1.4 Effect of the filler mobility on the linear viscoelasticity**

The internal structure of the as extruded sample PP/TiO2 at *Φ*=0.038 is shown in the TEM micrograph of Figure 1.a. Well distributed nanoparticle aggregates of a few hundreds of nanometers are suspended in the polymer matrix. The magnification of one of these aggregates is reported in Figure 1.b. A few hundreds of individual TiO2 nanoparticles are closely packed into dense clusters with irregular shape.

The sample was subjected to a thermal annealing at 190°C in quasi-quiescent conditions, i.e. by submitting it to shear oscillations in the rheometer at small strain amplitude (*γ*=2%) and frequency (*ω*=0.063 rad s-1). This allows to monitor the evolutions during time of slow dynamic populations, relaxing in timescales of order of *τ*=1/*ω*≈16 sec, without altering the internal structure of the sample.

Nanoparticle Dynamics in Polymer Melts 393

time for two clusters of radius *R* to come in contact, *τa* [Russel et al., 1989]. This characteristic time depends on on the self-diffusion time of each aggregate, given by Equation 2, and on the

> <sup>3</sup> *<sup>s</sup> <sup>a</sup> B R*

 is the actual filler volume fraction, i.e. the volume of the particles in a cluster plus the free volume enclosed between them. These regions are actually inaccessible to the polymer, and depends on how primary particles are assembled together inside the aggregates. As shown in Figure 1.b, the TiO2 clusters appear rather compact. As a consequence, we can reasonably assume that the primary particles are packed at a volume fraction of ~60%, which is close to random close packing. The actual filler volume fraction of the PP/TiO2 nanocomposites can be consequently estimated as ≈*Φ*/0.6. Assuming *R*=*Dn*/2≈65 nm, Equation 4 gives *τa*~4\*103 s, in good agreement with the data shown in Figure 2. This result suggests that the increasing of the sample elasticity during time is related to cluster-cluster aggregation. In order to support the previous conclusion, we increase *τa* by increasing either the size of primary particles or aggregates or the viscosity of the suspending medium. According to Equation 2, in these conditions we expect that the elasticity of the samples

*k T* (4)

*L* , *df* being the fractal dimension [Weitz &

average inter-aggregates distance, inversely proportional to the filler amount:

cannot increase significantly because of the reduced particle mobility.

Fig. 2. Time evolution of *G′* (full) and *G′′* (empty) at *ω*=0.063 rad s-1 and *T*=190°C for the

As first test, we investigate the time evolutions of the linear viscoelastic moduli at *ω*=0.063 rad s-1 for a PP/TiO2 microcomposite (particles radius *R*≈2 μm) at *Φ*≈0.035. Based on Equation 4, we expect that two micron-sized particles should come at contact after timescales of order of ~107 s. As a matter of fact, the results shown in Figure 3.a indicate that

As second test, we monitor the moduli of a nanocomposite based on a high viscosity matrix such as PS-high (*η0*=2.1\*104 Pa\*s at 200°C) filled with SiO2 particles at *Φ*≈0.035. Silica aggregates exhibits the typical open and branched structure of fractal objects. In such

Oliveira, 1984]. The actual filler volume fraction thus becomes [Wolthers et al., 1997]:

nanocomposite PP/TiO2 at *Φ*=0.038 (image taken from Romeo et al., 2009).

both moduli remain stable during the aging test until ~104 s.

systems the mass *M* scales with length *L* as *M*~ *<sup>f</sup> <sup>d</sup>*

Fig. 1. (a) TEM micrograph of the as extruded sample PP/TiO2 at *Φ*=0.045. (b) Magnification of an aggregate of TiO2 nanoparticles. (c) TEM micrograph of the same sample as in (a) after a three-hours thermal annealing at T=190°C. (d) CSD of the samples shown in (a) and (c) (images taken from Acierno et al., 2007a).

The microstructure of the annealed sample is shown in Figure 1.c. A visual comparison with the morphology of the as extruded sample reveals the presence of bigger aggregates and the disappearance of the smaller ones. An analysis of the TEM micrographs was carried out to quantify the effect of the thermal annealing. An equivalent diameter for the aggregates was defined as *Di*=(*πAi*)0.5, where *Ai* is the measured area of the *i*-th cluster. Once the sizes of the aggregates are available, the cumulative size distribution (CSD) and the number average size of the TiO2 aggregates, *Dn*=*ΣniDi*/*Σni* (*ni* clusters with size *Di*), was determined for each sample. The comparison between the CSDs is shown in Figure 1.d. The lowering of the cumulative CSD curves indicates an increase of the cluster sizes occurred during the thermal conditioning. In particular, the average size of the TiO2 aggregates increases from *Dn*≈125 nm to *Dn*≈170 nm.

The coarsening of the microstructure is a consequence of the diffusion of the clusters under the push of Van der Waals attraction. Rheological parameters such as the linear viscoelastic moduli are extremely sensitive to the internal microstructure. Thus, we use them to follow such internal rearrangements. The time evolutions of *G′* and *G′′* at *ω*=0.063 rad s-1 are shown in Figure 2.

The elastic modulus, which at the beginning is lower than the viscous one, increases during the first stage and then it reaches a plateau after a certain time; on the other hand, the loss modulus remains essentially constant. Preliminary investigations revealed that the neat matrices display a constant value of the moduli in the analysed time window. Thus, the increase in the sample elasticity is related to the structuring of the inorganic phase. The characteristic timescale for such a phenomenon can be roughly estimated as the Smoluchowski

Fig. 1. (a) TEM micrograph of the as extruded sample PP/TiO2 at *Φ*=0.045. (b) Magnification of an aggregate of TiO2 nanoparticles. (c) TEM micrograph of the same sample as in (a) after a three-hours thermal annealing at T=190°C. (d) CSD of the samples shown in (a) and (c)

The microstructure of the annealed sample is shown in Figure 1.c. A visual comparison with the morphology of the as extruded sample reveals the presence of bigger aggregates and the disappearance of the smaller ones. An analysis of the TEM micrographs was carried out to quantify the effect of the thermal annealing. An equivalent diameter for the aggregates was defined as *Di*=(*πAi*)0.5, where *Ai* is the measured area of the *i*-th cluster. Once the sizes of the aggregates are available, the cumulative size distribution (CSD) and the number average size of the TiO2 aggregates, *Dn*=*ΣniDi*/*Σni* (*ni* clusters with size *Di*), was determined for each sample. The comparison between the CSDs is shown in Figure 1.d. The lowering of the cumulative CSD curves indicates an increase of the cluster sizes occurred during the thermal conditioning. In particular, the average size of the TiO2 aggregates increases from *Dn*≈125

The coarsening of the microstructure is a consequence of the diffusion of the clusters under the push of Van der Waals attraction. Rheological parameters such as the linear viscoelastic moduli are extremely sensitive to the internal microstructure. Thus, we use them to follow such internal rearrangements. The time evolutions of *G′* and *G′′* at *ω*=0.063 rad s-1 are

The elastic modulus, which at the beginning is lower than the viscous one, increases during the first stage and then it reaches a plateau after a certain time; on the other hand, the loss modulus remains essentially constant. Preliminary investigations revealed that the neat matrices display a constant value of the moduli in the analysed time window. Thus, the increase in the sample elasticity is related to the structuring of the inorganic phase. The characteristic timescale for such a phenomenon can be roughly estimated as the Smoluchowski

(images taken from Acierno et al., 2007a).

nm to *Dn*≈170 nm.

shown in Figure 2.

time for two clusters of radius *R* to come in contact, *τa* [Russel et al., 1989]. This characteristic time depends on on the self-diffusion time of each aggregate, given by Equation 2, and on the average inter-aggregates distance, inversely proportional to the filler amount:

$$
\pi\_a = \frac{\pi \eta\_s R^3}{\overline{\Phi k} k\_B T} \tag{4}
$$

 is the actual filler volume fraction, i.e. the volume of the particles in a cluster plus the free volume enclosed between them. These regions are actually inaccessible to the polymer, and depends on how primary particles are assembled together inside the aggregates. As shown in Figure 1.b, the TiO2 clusters appear rather compact. As a consequence, we can reasonably assume that the primary particles are packed at a volume fraction of ~60%, which is close to random close packing. The actual filler volume fraction of the PP/TiO2 nanocomposites can be consequently estimated as ≈*Φ*/0.6. Assuming *R*=*Dn*/2≈65 nm, Equation 4 gives *τa*~4\*103 s, in good agreement with the data shown in Figure 2. This result suggests that the increasing of the sample elasticity during time is related to cluster-cluster aggregation. In order to support the previous conclusion, we increase *τa* by increasing either the size of primary particles or aggregates or the viscosity of the suspending medium. According to Equation 2, in these conditions we expect that the elasticity of the samples cannot increase significantly because of the reduced particle mobility.

Fig. 2. Time evolution of *G′* (full) and *G′′* (empty) at *ω*=0.063 rad s-1 and *T*=190°C for the nanocomposite PP/TiO2 at *Φ*=0.038 (image taken from Romeo et al., 2009).

As first test, we investigate the time evolutions of the linear viscoelastic moduli at *ω*=0.063 rad s-1 for a PP/TiO2 microcomposite (particles radius *R*≈2 μm) at *Φ*≈0.035. Based on Equation 4, we expect that two micron-sized particles should come at contact after timescales of order of ~107 s. As a matter of fact, the results shown in Figure 3.a indicate that both moduli remain stable during the aging test until ~104 s.

As second test, we monitor the moduli of a nanocomposite based on a high viscosity matrix such as PS-high (*η0*=2.1\*104 Pa\*s at 200°C) filled with SiO2 particles at *Φ*≈0.035. Silica aggregates exhibits the typical open and branched structure of fractal objects. In such systems the mass *M* scales with length *L* as *M*~ *<sup>f</sup> <sup>d</sup> L* , *df* being the fractal dimension [Weitz & Oliveira, 1984]. The actual filler volume fraction thus becomes [Wolthers et al., 1997]:

Nanoparticle Dynamics in Polymer Melts 395

size is too big, the filler is unable to rearrange and only produce a small perturbation of the composite viscoelastic response. Conversely, when mobility of the inorganic phase is high enough, random motion and attractive Van der Waals forces lead to the structuring of the primary aggregates. This eventually results in the formation of a whole space-spanning filler network. Since this network exhibits the connotation of an elastic solid, a drastic slowing

Fig. 4. (a) *G′* (full) and *G′′* (empty) for the samples PP/TiO2 at *Φ*≈0.035 filled with

micrometric (circles) and nanometric (diamonds) particles. Solid and dashed lines represent the elastic and viscous modulus of the neat PP, respectively. (b) *G′* (full) and *G′′* (empty) for the nanocomposite samples PS-low/SiO2 (diamonds, left axis) and PS-high/SiO2 (circles,

**2.2.1 Weakly attractive particles suspended in Newtonian fluids – A two-phase model**  Colloids are typically nanometer to micron sized particles forming a dispersed phase in a suspending medium. Colloidal dispersions exhibit a wide spectrum of rheological properties, ranging from simply viscous fluids to highly elastic pastes depending on the amount of particles and the sign and magnitude of inter-particles interactions. Here we are interested in weakly attractive systems, where the particles are inclined to assemble together into more or less branched flocs. In these systems, the *ω*-dependent storage and loss modulus typically exhibit a strong dependence on both *Φ* and *U*. Such a high variability makes extremely difficult a general description of the viscoelastic behaviour of colloidal dispersions. A drastic simplification has been introduced by Trappe and Weitz, which showed that modelling the suspension above the particle percolation threshold as an elastic filler network interspersed in a background fluid (two-phase model) qualitatively accounts for the viscoelasticity of their samples [Trappe & Weitz, 2000]. The authors studied a dispersion of carbon black in base stock oil as a function of particle volume fraction and interaction potential. The *U* was tuned by adding a dispersant that acts as a surfactant. Without dispersant carbon black particles are rather strongly attractive, and flocs of ~100 μm in size form even at very low amounts of particles. The linear viscoelastic moduli of samples at different *Φ* were measured as a function of frequency with a strain-controlled rheometer with Couette geometry. The authors found that a rheological transition occurs at *Φc*=0.053: at *Φ*>*Φc* the suspension is clearly elastic and *G′* is nearly independent on *ω*; at

down of relaxation dynamics occurs at low frequencies.

right axis) at *Φ*≈0.035 (image taken from Romeo et al., 2009).

**2.2 Linear viscoelasticity of PNCs** 

$$
\overline{\Phi} = \Phi \times \left(\mathbf{L} \;/\; d\right)^{\mathbf{\hat{3}} - d\_f} \tag{5}
$$

Setting *L*=*Dn*≈125 nm as emerged from the analysis of many TEM micrographs, and taking *df*=2.2 as a typical fractal dimension of fumed silica aggregates [Kammler et al., 2004], Equation 4 gives *τa*~105 s. This is in agreement with the results of the time sweep experiment shown in Figure 3.b, which indicate that cluster assembling phenomena, if any, are negligible in the timescale of the test. Obviously, the not structured sample keeps a predominantly viscous connotation, i.e. *G′′*>>*G′*.

Fig. 3. Time evolution of *G′* (full) and *G′′* (empty) at *ω*=0.063 rad s-1 for the microcomposite PP/TiO2 at *Φ*=0.035 and *T*=190°C (a), and the nanocomposite PS-high/SiO2 at *Φ*=0.035 and *T*=200°C (b) (images taken from Romeo et al., 2009).

Particle rearrangements eventually give rise to mesoscopic structures, such as branched aggregates or space-spanning filler network, which strongly alter the frequency response of the sample. The *ω*-dependent *G′* and *G′′* of two PP/TiO2 samples filled with micro- and nanoparticles both at *Φ*≈0.035 are compared in Figure 4.a. In both cases the matrix governs the high-frequency response. This suggests that the relaxation modes of the polymer chains and sub-chains are only slightly affected by the presence of the filler at these high frequencies. The presence of microparticles negligibly affects the whole response of the composite. On the contrary, the nanoparticles significantly alter the low-frequency moduli of the material, and in particular the elastic one.

The flattening of *G′* over long timescales is a general feature characterizing different kinds of PNCs [Krishnamoorti & Yurekli, 2001; Du et al., 2004]. Such a behaviour, however, is not a direct consequence of the nanometric size of the particles, but rather it originates from particle mobility. To emphasize this point, in Figure 4.b the frequency response of the threehours aged samples PS-low/SiO2 and PS-high/SiO2 at *Φ*≈0.035 are compared. The nanocomposite with high viscosity matrix displays a liquid-like behaviour at low frequency reminiscent of that of the neat polymer (not shown). Differently, the PS-low/SiO2 sample exhibits a predominant elastic connotation, the low-frequency plateau of *G′* being indicative of the presence of a space-spanning filler network formed during the ageing process.

To summarize, the viscoelastic response of a filled polymer is greatly affected by particle mobility. When the characteristic diffusion time of the particles and/or aggregates resulting from the extrusion process is too high, either because the matrix is too viscous or the particle

Setting *L*=*Dn*≈125 nm as emerged from the analysis of many TEM micrographs, and taking *df*=2.2 as a typical fractal dimension of fumed silica aggregates [Kammler et al., 2004], Equation 4 gives *τa*~105 s. This is in agreement with the results of the time sweep experiment shown in Figure 3.b, which indicate that cluster assembling phenomena, if any, are negligible in the timescale of the test. Obviously, the not structured sample keeps a

Fig. 3. Time evolution of *G′* (full) and *G′′* (empty) at *ω*=0.063 rad s-1 for the microcomposite PP/TiO2 at *Φ*=0.035 and *T*=190°C (a), and the nanocomposite PS-high/SiO2 at *Φ*=0.035 and

Particle rearrangements eventually give rise to mesoscopic structures, such as branched aggregates or space-spanning filler network, which strongly alter the frequency response of the sample. The *ω*-dependent *G′* and *G′′* of two PP/TiO2 samples filled with micro- and nanoparticles both at *Φ*≈0.035 are compared in Figure 4.a. In both cases the matrix governs the high-frequency response. This suggests that the relaxation modes of the polymer chains and sub-chains are only slightly affected by the presence of the filler at these high frequencies. The presence of microparticles negligibly affects the whole response of the composite. On the contrary, the nanoparticles significantly alter the low-frequency moduli

The flattening of *G′* over long timescales is a general feature characterizing different kinds of PNCs [Krishnamoorti & Yurekli, 2001; Du et al., 2004]. Such a behaviour, however, is not a direct consequence of the nanometric size of the particles, but rather it originates from particle mobility. To emphasize this point, in Figure 4.b the frequency response of the threehours aged samples PS-low/SiO2 and PS-high/SiO2 at *Φ*≈0.035 are compared. The nanocomposite with high viscosity matrix displays a liquid-like behaviour at low frequency reminiscent of that of the neat polymer (not shown). Differently, the PS-low/SiO2 sample exhibits a predominant elastic connotation, the low-frequency plateau of *G′* being indicative

of the presence of a space-spanning filler network formed during the ageing process.

To summarize, the viscoelastic response of a filled polymer is greatly affected by particle mobility. When the characteristic diffusion time of the particles and/or aggregates resulting from the extrusion process is too high, either because the matrix is too viscous or the particle

predominantly viscous connotation, i.e. *G′′*>>*G′*.

*T*=200°C (b) (images taken from Romeo et al., 2009).

of the material, and in particular the elastic one.

<sup>3</sup> *<sup>f</sup> <sup>d</sup> (L / d)* (5)

size is too big, the filler is unable to rearrange and only produce a small perturbation of the composite viscoelastic response. Conversely, when mobility of the inorganic phase is high enough, random motion and attractive Van der Waals forces lead to the structuring of the primary aggregates. This eventually results in the formation of a whole space-spanning filler network. Since this network exhibits the connotation of an elastic solid, a drastic slowing down of relaxation dynamics occurs at low frequencies.

Fig. 4. (a) *G′* (full) and *G′′* (empty) for the samples PP/TiO2 at *Φ*≈0.035 filled with micrometric (circles) and nanometric (diamonds) particles. Solid and dashed lines represent the elastic and viscous modulus of the neat PP, respectively. (b) *G′* (full) and *G′′* (empty) for the nanocomposite samples PS-low/SiO2 (diamonds, left axis) and PS-high/SiO2 (circles, right axis) at *Φ*≈0.035 (image taken from Romeo et al., 2009).

#### **2.2 Linear viscoelasticity of PNCs**

#### **2.2.1 Weakly attractive particles suspended in Newtonian fluids – A two-phase model**

Colloids are typically nanometer to micron sized particles forming a dispersed phase in a suspending medium. Colloidal dispersions exhibit a wide spectrum of rheological properties, ranging from simply viscous fluids to highly elastic pastes depending on the amount of particles and the sign and magnitude of inter-particles interactions. Here we are interested in weakly attractive systems, where the particles are inclined to assemble together into more or less branched flocs. In these systems, the *ω*-dependent storage and loss modulus typically exhibit a strong dependence on both *Φ* and *U*. Such a high variability makes extremely difficult a general description of the viscoelastic behaviour of colloidal dispersions. A drastic simplification has been introduced by Trappe and Weitz, which showed that modelling the suspension above the particle percolation threshold as an elastic filler network interspersed in a background fluid (two-phase model) qualitatively accounts for the viscoelasticity of their samples [Trappe & Weitz, 2000]. The authors studied a dispersion of carbon black in base stock oil as a function of particle volume fraction and interaction potential. The *U* was tuned by adding a dispersant that acts as a surfactant. Without dispersant carbon black particles are rather strongly attractive, and flocs of ~100 μm in size form even at very low amounts of particles. The linear viscoelastic moduli of samples at different *Φ* were measured as a function of frequency with a strain-controlled rheometer with Couette geometry. The authors found that a rheological transition occurs at *Φc*=0.053: at *Φ*>*Φc* the suspension is clearly elastic and *G′* is nearly independent on *ω*; at

Nanoparticle Dynamics in Polymer Melts 397

Fig. 5. Scheme of the viscoelasticity of a PNC at *Φ*> *Φc*. For fully relaxed polymer matrix, the

To test the validity of the previous considerations, we focus on the *ω*-dependence of the moduli of PP/TiO2 and PS-low/SiO2 nanocomposite samples at *Φ*>*Φc*, i.e. in which the filler rearranges in experimentally accessible timescales forming a space-spanning network. All these samples share a similar pseudo solid-like behaviour at low frequency, with weak *ω*dependences of both moduli and *G′* greater than *G′′*. Since the filler mainly affects the elastic modulus of the samples, *G′* increases with *Φ* more rapidly than *G′′*. As a consequence, a further crossover between *G′* and *G′′* occurs at intermediate frequencies in addition to that at high *ω* related to the relaxation of the neat polymer. The coordinates of such additional crossing point, (*ωc*; *Gc*), shift towards higher and higher frequencies and moduli with increasing the filler content. This is shown in Figure 6 for three samples PS-

Fig. 6. *G′* (full, red) and *G′′* (empty, blu) for the nanocomposite samples PS-low/SiO2 at

The additional low-frequency crossover can be interpreted as the point at which the network elasticity equals the viscous contribution of the polymer. As a consequence,

increasing filler content. The additional crossover is indicated by the arrows.

filler network is the only responsible for the elastic connotation of the system.

low/SiO2 at different composition.

*Φ*<*Φc* the viscous feature definitely prevails over the elastic one, and the suspension rheology looks like that of the suspending fluid. Microscopic analyses reveal that the rheological transition reflects the state of dispersion of the filler: isolated carbon black flocs are suspended in the background fluid below *Φc*, whereas above this threshold the aggregates assemble in a three-dimensional space spanning network.

Despite their marked differences, the moduli of the samples at *Φ*>*Φc* can be scaled onto a single pair of master curves. The authors qualitatively accounted for the observed scaling by assuming that the carbon black forms a solid but tenuous network with a purely elastic, *ω*independent modulus. The elasticity of this network, *G′0*, increases with *Φ* as the network becomes more and more robust. Interspersed throughout this structure is the purely viscous suspending fluid, which *G′′* linearly increases with *ω* and is substantially independent of *Φ*. Consequently, the elasticity of the network prevails at low *ω*, while the viscosity of the fluid dominates at high *ω*. Within this simplified picture, scaling the elasticity of each sample along the viscosity of the matrix results in the collapse of data of samples at different composition onto a single pair of master curves.

Although the proposed approach can account for the basic scaling behaviour, many issue remain unresolved. For example, the behaviour of the weaker of the two moduli in each regime is not addressed. At low frequencies, *G′′*(*ω*) must be determined by the loss modulus of the network, which is larger than that of the suspending fluid. Similarly, at the highest frequencies *G′*(*ω*) must reflect the storage component of the suspending fluid with the solid network in it. In addition, the model does not take into account hydrodynamic effects. Despite these limitations, the good quality of the scaling supports the reliability of the approach, indicating that there is a strong similarity in the structures of the networks that form at different *Φ*. This also implies some predictive feature of the model: the tiny elasticity of samples at low *Φ* (as long as greater than *Φc*), which networks are too tenuous to be appreciated through direct dynamic-mechanical analyses, can be predicted with good approximation by simply referring to the master curve of *G′*.

### **2.2.2 Weakly attractive nanoparticles suspended in non-Newtonian mediums – Recovering the two-phase model**

The relatively high mobility of nanoparticles even in highly viscous fluids such as polymer melts makes PNCs similar to colloidal dispersions. The main difference with these simpler systems is the non-Newtonian feature of the suspending medium. According to Trappe and Weitz, the viscoelasticity of a colloidal suspension above *Φc* originates from the combination of the responses of an *elastic* particle gel that of the *purely viscous* background fluid. In the case of a PNC, instead, the suspending medium is viscoelastic by itself, and its response combines with that of the space-spanning network giving rise to a more complex *ω*- and *Φ*dependent viscoelastic behaviour. It follows that a separation of the effects of the solid and fluid phases is no more possible in the case of PNCs. However, we argue that a recovery of the two-phase model is possible if the elasticity of the polymer is neglected with respect to that of the filler network. Under this assumption, the viscoelasticity of the PNC can be split into the independent responses of an *elastic* particle network and that of the *predominantly viscous* polymer. The former contribution depends on the filler content and governs the long timescale response of the composite, whereas the latter is responsible for the high-frequency behaviour (Figure 5).

*Φ*<*Φc* the viscous feature definitely prevails over the elastic one, and the suspension rheology looks like that of the suspending fluid. Microscopic analyses reveal that the rheological transition reflects the state of dispersion of the filler: isolated carbon black flocs are suspended in the background fluid below *Φc*, whereas above this threshold the

Despite their marked differences, the moduli of the samples at *Φ*>*Φc* can be scaled onto a single pair of master curves. The authors qualitatively accounted for the observed scaling by assuming that the carbon black forms a solid but tenuous network with a purely elastic, *ω*independent modulus. The elasticity of this network, *G′0*, increases with *Φ* as the network becomes more and more robust. Interspersed throughout this structure is the purely viscous suspending fluid, which *G′′* linearly increases with *ω* and is substantially independent of *Φ*. Consequently, the elasticity of the network prevails at low *ω*, while the viscosity of the fluid dominates at high *ω*. Within this simplified picture, scaling the elasticity of each sample along the viscosity of the matrix results in the collapse of data of samples at different

Although the proposed approach can account for the basic scaling behaviour, many issue remain unresolved. For example, the behaviour of the weaker of the two moduli in each regime is not addressed. At low frequencies, *G′′*(*ω*) must be determined by the loss modulus of the network, which is larger than that of the suspending fluid. Similarly, at the highest frequencies *G′*(*ω*) must reflect the storage component of the suspending fluid with the solid network in it. In addition, the model does not take into account hydrodynamic effects. Despite these limitations, the good quality of the scaling supports the reliability of the approach, indicating that there is a strong similarity in the structures of the networks that form at different *Φ*. This also implies some predictive feature of the model: the tiny elasticity of samples at low *Φ* (as long as greater than *Φc*), which networks are too tenuous to be appreciated through direct dynamic-mechanical analyses, can be predicted with good

**2.2.2 Weakly attractive nanoparticles suspended in non-Newtonian mediums –** 

The relatively high mobility of nanoparticles even in highly viscous fluids such as polymer melts makes PNCs similar to colloidal dispersions. The main difference with these simpler systems is the non-Newtonian feature of the suspending medium. According to Trappe and Weitz, the viscoelasticity of a colloidal suspension above *Φc* originates from the combination of the responses of an *elastic* particle gel that of the *purely viscous* background fluid. In the case of a PNC, instead, the suspending medium is viscoelastic by itself, and its response combines with that of the space-spanning network giving rise to a more complex *ω*- and *Φ*dependent viscoelastic behaviour. It follows that a separation of the effects of the solid and fluid phases is no more possible in the case of PNCs. However, we argue that a recovery of the two-phase model is possible if the elasticity of the polymer is neglected with respect to that of the filler network. Under this assumption, the viscoelasticity of the PNC can be split into the independent responses of an *elastic* particle network and that of the *predominantly viscous* polymer. The former contribution depends on the filler content and governs the long timescale response of the composite, whereas the latter is responsible for the high-frequency

aggregates assemble in a three-dimensional space spanning network.

composition onto a single pair of master curves.

approximation by simply referring to the master curve of *G′*.

**Recovering the two-phase model** 

behaviour (Figure 5).

Fig. 5. Scheme of the viscoelasticity of a PNC at *Φ*> *Φc*. For fully relaxed polymer matrix, the filler network is the only responsible for the elastic connotation of the system.

To test the validity of the previous considerations, we focus on the *ω*-dependence of the moduli of PP/TiO2 and PS-low/SiO2 nanocomposite samples at *Φ*>*Φc*, i.e. in which the filler rearranges in experimentally accessible timescales forming a space-spanning network. All these samples share a similar pseudo solid-like behaviour at low frequency, with weak *ω*dependences of both moduli and *G′* greater than *G′′*. Since the filler mainly affects the elastic modulus of the samples, *G′* increases with *Φ* more rapidly than *G′′*. As a consequence, a further crossover between *G′* and *G′′* occurs at intermediate frequencies in addition to that at high *ω* related to the relaxation of the neat polymer. The coordinates of such additional crossing point, (*ωc*; *Gc*), shift towards higher and higher frequencies and moduli with increasing the filler content. This is shown in Figure 6 for three samples PSlow/SiO2 at different composition.

Fig. 6. *G′* (full, red) and *G′′* (empty, blu) for the nanocomposite samples PS-low/SiO2 at increasing filler content. The additional crossover is indicated by the arrows.

The additional low-frequency crossover can be interpreted as the point at which the network elasticity equals the viscous contribution of the polymer. As a consequence,

Nanoparticle Dynamics in Polymer Melts 399

Despite the good quality of the scaling shown in Figure 7, unresolved issues exist regarding the physical meaning of the shift factors. The underlying physics of the model lies on the independent rheological responses of the *neat polymer* and the particle network. Actually, the coordinates of the crossover point of the moduli of the nanocomposite, identified by Trappe and Weitz as the shift factors for their system, do not rigorously reflect the properties of the two pristine phases of the model. In addition, the presence of the particles implies hydrodynamic effects, which cannot be eluded for a correct scaling of the data. To account for these issues, the procedure to get the shift factors for the building of the master curve has to be revisited. For this aim, hereinafter we only refer to the system PS-low/SiO2,

Hydrodynamic effects reflect the perturbation of the flow lines in proximity of the filler. In a liquid filled with a solid particulate, the suspending fluid flows in the narrow gap between contiguous particles or aggregates, locally experiencing a greater flow rate than what externally imposed or measured. Gleissle and Hochstein quantitatively accounted for hydrodynamic effects in oscillatory shear experiments by introducing an empiric amplification factor, representing the ratio between the complex moduli of the filled sample over that of the neat matrix: *\* \* B( ) G ( ) GPS* [Gleissle & Hochstein, 2003]. In the case of microparticles, *B*(*Φ*) well describe the increase of *G\** of the suspension in the whole range of accessible frequencies. Differently, non-continuum effects emerge over long timescales in the case of PNCs. Consequently, the hydrodynamic effects only are appreciable at high frequencies, i.e. where the rheological response is governed by the polymer matrix. This is shown in Figure 8, where the complex moduli of various PS-low/SiO2 nanocomposites at

Fig. 8. (a) Complex modulus of PS-low/SiO2 nanocomposite at various filler content. The regions in which non-continuum and hydrodynamic effects are dominant are emphasized. (b) Amplification factor for the data shown in (a) (images taken from Filippone et al., 2010).

After the hydrodynamic contribution has been quantified for each sample, then new and more rigorous shift factors can be identified. Specifically, we now refer to the point at which the elasticity of the filler network, given by the plateau modulus of the nanocomposite, *G'0*(*Φ*), equals the viscous modulus of the neat matrix amplified by *B*(*Φ*) to account for

**2.2.3 Refining the two-phase model – Role of the hydrodynamic effects** 

which particle network exhibits a truly solid-like behaviour at low frequency.

different composition are reported together with the resulting *B*(*Φ*).

hydrodynamic effects, *B*(*Φ*)·*G\**.

normalizing the moduli of samples at different *Φ* by their elasticity, and doing so along the background fluid viscosity, the curves should collapse onto a single pair of master curves. Accordingly, the scaling has to be done by shifting the curves both horizontally and vertically using as shift factors *a*=1/*ωc* and *b*=1/*Gc*, respectively. The resulting master curves are shown in Figure 7 for both the PP/TiO2 and PS-low/SiO2 nanocomposites.

Fig. 7. Master curves of G′ (full, left axis) and G′′ (empty, right axis) for the systems PP/TiO2 (a) and PS-LOW/SiO2 (b). Each colour corresponds to a composition. Note that only curves at Φ>Φc have been used to build the master curves. The TEM micrographs shown in the insets represent the microstructures of samples at Φ≈0.035 (image taken from Romeo et al., 2009).

The scaled moduli lie on top of each other in about five decades of frequencies, supporting the validity of the adopted approach. Deviations are observed for the viscous moduli at high scaled frequencies. This is not unexpected, since the relaxation modes of the polymers are independent on the filler content and cannot be scaled using *a* and *b* as scaling factors.

Once the master curves are built, the differences in elasticity and dynamic of the particle networks become evident. The SiO2 network is characterized by an *ω*-independent elastic modulus at low frequency, which emphasizes its truly solid-like feature. Differently, the TiO2 network displays a slow relaxation dynamic with *G′*~*ω*0.3. These differences are related to the differences in network structures formed in the two composites. The TEM images reported in the insets of Figure 7 show that the SiO2 nanoparticles form a tenuous, fractal network of sub-micron sized, branched flocs interspersed within the host PS. Differently, the TiO2 nanoparticles are assembled into dense clusters, which mobility is presumably slowed down by the surrounding aggregates. The transient character of the latter network emerges as a glassy-like decrease of *G′*, which reflects the internal rearrangements of the TiO2 clusters. Such slow relaxation dynamics are characteristic of colloidal glasses [Shikata & Pearson, 1994; Mason & Weitz, 1995] and has been observed in many other soft materials [Sollich et al., 1997].

normalizing the moduli of samples at different *Φ* by their elasticity, and doing so along the background fluid viscosity, the curves should collapse onto a single pair of master curves. Accordingly, the scaling has to be done by shifting the curves both horizontally and vertically using as shift factors *a*=1/*ωc* and *b*=1/*Gc*, respectively. The resulting master curves

Fig. 7. Master curves of G′ (full, left axis) and G′′ (empty, right axis) for the systems PP/TiO2 (a) and PS-LOW/SiO2 (b). Each colour corresponds to a composition. Note that only curves at Φ>Φc have been used to build the master curves. The TEM micrographs shown in the insets represent the microstructures of samples at Φ≈0.035 (image taken from Romeo et al.,

The scaled moduli lie on top of each other in about five decades of frequencies, supporting the validity of the adopted approach. Deviations are observed for the viscous moduli at high scaled frequencies. This is not unexpected, since the relaxation modes of the polymers are independent on the filler content and cannot be scaled using *a* and *b* as scaling factors.

Once the master curves are built, the differences in elasticity and dynamic of the particle networks become evident. The SiO2 network is characterized by an *ω*-independent elastic modulus at low frequency, which emphasizes its truly solid-like feature. Differently, the TiO2 network displays a slow relaxation dynamic with *G′*~*ω*0.3. These differences are related to the differences in network structures formed in the two composites. The TEM images reported in the insets of Figure 7 show that the SiO2 nanoparticles form a tenuous, fractal network of sub-micron sized, branched flocs interspersed within the host PS. Differently, the TiO2 nanoparticles are assembled into dense clusters, which mobility is presumably slowed down by the surrounding aggregates. The transient character of the latter network emerges as a glassy-like decrease of *G′*, which reflects the internal rearrangements of the TiO2 clusters. Such slow relaxation dynamics are characteristic of colloidal glasses [Shikata & Pearson, 1994; Mason & Weitz, 1995] and has been observed in many other soft materials

2009).

[Sollich et al., 1997].

are shown in Figure 7 for both the PP/TiO2 and PS-low/SiO2 nanocomposites.

#### **2.2.3 Refining the two-phase model – Role of the hydrodynamic effects**

Despite the good quality of the scaling shown in Figure 7, unresolved issues exist regarding the physical meaning of the shift factors. The underlying physics of the model lies on the independent rheological responses of the *neat polymer* and the particle network. Actually, the coordinates of the crossover point of the moduli of the nanocomposite, identified by Trappe and Weitz as the shift factors for their system, do not rigorously reflect the properties of the two pristine phases of the model. In addition, the presence of the particles implies hydrodynamic effects, which cannot be eluded for a correct scaling of the data. To account for these issues, the procedure to get the shift factors for the building of the master curve has to be revisited. For this aim, hereinafter we only refer to the system PS-low/SiO2, which particle network exhibits a truly solid-like behaviour at low frequency.

Hydrodynamic effects reflect the perturbation of the flow lines in proximity of the filler. In a liquid filled with a solid particulate, the suspending fluid flows in the narrow gap between contiguous particles or aggregates, locally experiencing a greater flow rate than what externally imposed or measured. Gleissle and Hochstein quantitatively accounted for hydrodynamic effects in oscillatory shear experiments by introducing an empiric amplification factor, representing the ratio between the complex moduli of the filled sample over that of the neat matrix: *\* \* B( ) G ( ) GPS* [Gleissle & Hochstein, 2003]. In the case of microparticles, *B*(*Φ*) well describe the increase of *G\** of the suspension in the whole range of accessible frequencies. Differently, non-continuum effects emerge over long timescales in the case of PNCs. Consequently, the hydrodynamic effects only are appreciable at high frequencies, i.e. where the rheological response is governed by the polymer matrix. This is shown in Figure 8, where the complex moduli of various PS-low/SiO2 nanocomposites at different composition are reported together with the resulting *B*(*Φ*).

Fig. 8. (a) Complex modulus of PS-low/SiO2 nanocomposite at various filler content. The regions in which non-continuum and hydrodynamic effects are dominant are emphasized. (b) Amplification factor for the data shown in (a) (images taken from Filippone et al., 2010).

After the hydrodynamic contribution has been quantified for each sample, then new and more rigorous shift factors can be identified. Specifically, we now refer to the point at which the elasticity of the filler network, given by the plateau modulus of the nanocomposite, *G'0*(*Φ*), equals the viscous modulus of the neat matrix amplified by *B*(*Φ*) to account for hydrodynamic effects, *B*(*Φ*)·*G\**.

Nanoparticle Dynamics in Polymer Melts 401

Fig. 10. TEM micrographs of the as extruded PP/Al2O3 sample at *Φ*=4.2% at various

Fig. 11. TEM micrographs of the 3-hours thermal annealed PP/Al2O3 sample at *Φ*=4.2% at

Pristine individual aggregates are now assembled into a disordered network that spans large sections of the sample. The particles and aggregates are essentially kept together by Van der Waals attractions and/or other kinds of weak bonds between the functional sites located at the particle surfaces. The application of large strains provides an excess energy to overcome such attractive interactions, thus destroying the network. After that, the particles may or may not aggregate again depending on the strength of inter-particle

The relaxation dynamics of a viscoelastic fluid can be indifferently monitored by frequency scans or stress relaxation tests. In the latter kind of experiment, a constant strain, *γ0*, is imposed to the sample in the linear regime, and the transient stress, *σ*(*t*), is measured as a function of time. The stress relaxation modulus, *G*(*t*)=*σ*(*t*)/*γ0*, is shown in Figure 12 after the application of large amplitude oscillatory shear (LAOS) at a constant frequency *ω*=0.0628

Large deformations have a drastic effect on the relaxation spectrum: the bigger the strain amplitude, the faster the relaxation dynamics. Time sweep tests in linear regime were performed after each LAOS to test the viscoelastic behaviour of the sheared sample, and the results are shown in the inset of Figure 12. The elastic feature progressively vanishes with increasing the deformation amplitude. Interestingly, the steadiness of the elastic modulus during time suggests an irreversibility of the network break-up process, at least within the experimental time window. Moreover, a polymer-like behaviour is recovered after the LAOS at the largest amplitude (*γ0*=500%). In such case, the inorganic phase does not affect

magnifications (image taken from Acierno et al., 2007b).

various magnifications (image taken from Acierno et al., 2007b).

rad s-1 and different *γ0* on the 3-hours aged sample at *Φ*=4.2%.

the rheological response of the nanocomposite at all.

interactions.

The comparison between the old (*a*; *b*) and new (*a'*; *b'*) shift factors is shown in Figure 9.a for the sample at *Φ*=2.9%; in Figure 9.b the new master curve is reported.

Fig. 9. (a) Comparison of the shift factors for the samples-low/SiO2 at Φ=2.8%. (b) Master curve of G′ built using a′ and b′ as shift factors; the inset shows a magnifications at low scaled frequencies of the master curves obtained using as shift factors (a′; b′) (red) and (a; b) (blu) (images taken from Filippone et al., 2010).

The elastic moduli scaled using *a′* and *b′* as shift factors lies on top of each other over about seven decades of scaled frequencies, confirming the validity of the adopted approach. Again, the slight deviations at *ω*/*a′* greater than ~101 do not invalidate the consistency of the scaling, being a consequence of the intrinsic viscoelastic feature of the suspending fluid.

Besides exactly capturing the underlying physics of the two-phase model, the refined model guarantees a better scaling of the elasticity of samples at different composition. This is shown in the inset of Figure 9.b, where the master curves built using the two pairs of shift factors are compared. The lower scattering of the data scaled using *a′* and *b′* confirms the importance of properly accounting for hydrodynamic contributions when dealing with PNCs.

## **2.3 Strength and reversibility of the filler network in PP/Al2O3 PNCs**

Aim of this paragraph is the study of the relationships between the rheology and structure of PP/Al2O3 nanocomposites. The structuring (during a quiescent annealing process) and de-structuring (promoted by large amplitude shear flows) of the filler network are investigated by means of both rheological and TEM analyses. The internal morphology of the sample PP/Al2O3 at *Φ*=4.2% at the end of the extrusion process is shown in Figure 10.

Although a homogeneous distribution can be observed on microscale, the presence of aggregates of a few hundred nanometers is noticed at higher magnifications. The aggregates appear as open structures formed of tens of nanospheres of different sizes. Such nonequilibrium structures rearrange towards a more favourable thermodynamic state during a subsequent aging above the PP melting temperature. The morphology of a sample at *Φ*=4.2% after a 3-hours annealing at *T*=190°C is shown in Figure 11.

The comparison between the old (*a*; *b*) and new (*a'*; *b'*) shift factors is shown in Figure 9.a for

Fig. 9. (a) Comparison of the shift factors for the samples-low/SiO2 at Φ=2.8%. (b) Master curve of G′ built using a′ and b′ as shift factors; the inset shows a magnifications at low scaled frequencies of the master curves obtained using as shift factors (a′; b′) (red) and (a; b)

The elastic moduli scaled using *a′* and *b′* as shift factors lies on top of each other over about seven decades of scaled frequencies, confirming the validity of the adopted approach. Again, the slight deviations at *ω*/*a′* greater than ~101 do not invalidate the consistency of the scaling, being a consequence of the intrinsic viscoelastic feature of the suspending fluid.

Besides exactly capturing the underlying physics of the two-phase model, the refined model guarantees a better scaling of the elasticity of samples at different composition. This is shown in the inset of Figure 9.b, where the master curves built using the two pairs of shift factors are compared. The lower scattering of the data scaled using *a′* and *b′* confirms the importance of properly accounting for hydrodynamic contributions when dealing with

Aim of this paragraph is the study of the relationships between the rheology and structure of PP/Al2O3 nanocomposites. The structuring (during a quiescent annealing process) and de-structuring (promoted by large amplitude shear flows) of the filler network are investigated by means of both rheological and TEM analyses. The internal morphology of the sample PP/Al2O3 at *Φ*=4.2% at the end of the extrusion process is shown in Figure 10.

Although a homogeneous distribution can be observed on microscale, the presence of aggregates of a few hundred nanometers is noticed at higher magnifications. The aggregates appear as open structures formed of tens of nanospheres of different sizes. Such nonequilibrium structures rearrange towards a more favourable thermodynamic state during a subsequent aging above the PP melting temperature. The morphology of a sample at

**2.3 Strength and reversibility of the filler network in PP/Al2O3 PNCs** 

*Φ*=4.2% after a 3-hours annealing at *T*=190°C is shown in Figure 11.

the sample at *Φ*=2.9%; in Figure 9.b the new master curve is reported.

(blu) (images taken from Filippone et al., 2010).

PNCs.

Fig. 10. TEM micrographs of the as extruded PP/Al2O3 sample at *Φ*=4.2% at various magnifications (image taken from Acierno et al., 2007b).

Fig. 11. TEM micrographs of the 3-hours thermal annealed PP/Al2O3 sample at *Φ*=4.2% at various magnifications (image taken from Acierno et al., 2007b).

Pristine individual aggregates are now assembled into a disordered network that spans large sections of the sample. The particles and aggregates are essentially kept together by Van der Waals attractions and/or other kinds of weak bonds between the functional sites located at the particle surfaces. The application of large strains provides an excess energy to overcome such attractive interactions, thus destroying the network. After that, the particles may or may not aggregate again depending on the strength of inter-particle interactions.

The relaxation dynamics of a viscoelastic fluid can be indifferently monitored by frequency scans or stress relaxation tests. In the latter kind of experiment, a constant strain, *γ0*, is imposed to the sample in the linear regime, and the transient stress, *σ*(*t*), is measured as a function of time. The stress relaxation modulus, *G*(*t*)=*σ*(*t*)/*γ0*, is shown in Figure 12 after the application of large amplitude oscillatory shear (LAOS) at a constant frequency *ω*=0.0628 rad s-1 and different *γ0* on the 3-hours aged sample at *Φ*=4.2%.

Large deformations have a drastic effect on the relaxation spectrum: the bigger the strain amplitude, the faster the relaxation dynamics. Time sweep tests in linear regime were performed after each LAOS to test the viscoelastic behaviour of the sheared sample, and the results are shown in the inset of Figure 12. The elastic feature progressively vanishes with increasing the deformation amplitude. Interestingly, the steadiness of the elastic modulus during time suggests an irreversibility of the network break-up process, at least within the experimental time window. Moreover, a polymer-like behaviour is recovered after the LAOS at the largest amplitude (*γ0*=500%). In such case, the inorganic phase does not affect the rheological response of the nanocomposite at all.

Nanoparticle Dynamics in Polymer Melts 403

under the push of the inter-particle attractive interactions. The resulting filler network breaks up when the sample is subjected to LAOS, and a remarkable sharpening of the CSD

Fig. 14. CSDs for the PP/Al2O3 sample at *Φ*=4.2% as extruded (black circles), 3-hours aged (blue diamonds) and 3-hours aged after LAOS at *γ0*=500% (red triangles) (image taken from

Interestingly, the strength of the filler network depends on whether the LAOS is applied before or after the thermal annealing. This is shown in Figure 15, where the loss factor *tanδ*=*G''*/*G'* (15.a) and the complex moduli (15.b) of the samples at *Φ*=4.2% submitted to LAOS (*γ0*=500%) are reported before and after the ageing; the curves of the 3-hours aged but

If the LAOS is applied to the sample before the formation of the particle network, the system quickly evolves to a more elastic structure and the *tanδ* asymptotically reaches values close to those of the not sheared sample. However, the comparison between the *G\** shown in

Fig. 15. Loss factor (a) and complex moduli (b) of the samples at *Φ*=4.2% submitted to LAOS (*γ0*=500%) before (diamonds) and after (squares) the thermal annealing. The curves of the 3-hours aged and not sheared sample (circles) are also reported for comparison (image taken

is observed.

Acierno et al., 2007b).

from Acierno et al., 2007b).

not sheared sample are also reported for comparison.

Fig. 12. *G*(*t*) of the 3-hours aged PP/Al2O3 sample at *Φ*=4,5% after LAOS at different strain amplitudes *γ0*: 0.8% (solid circles), 10% (open circles), 25% (triangles), 50% (squares), 100% (crosses), 250% (reverse triangles), 500% (diamonds). Solid diamonds represents the *G*(*t*) of the neat polymer. The time evolutions of *G′* after each LAOS are shown in the inset. Symbols are the same of stress relaxation moduli (image taken from Acierno et al., 2007b).

The morphology of the 3-hours aged sample after the LAOS at *γ0*=500% is reported in Figure 13. The network formed during aging is no more visible, and the presence of many small clusters characterizes the sheared system. The flocs show a more open structure than that of a not sheared sample, either aged or not, suggesting a weaker tendency to the clustering for the Al2O3 nanoparticles after the large deformations. The cumulative cluster size distributions were determined through the analysis of TEM micrographs. The results are shown in Figure 14 for the as extruded, 3-hours annealed and sheared after aging samples at *Φ*=4.2%. The number average equivalent diameters of the clusters are reported in the same figure.

Fig. 13. TEM morphology of the 3-hours aged sample at Φ=4.2% after the LAOS at γ=500% (image taken from Acierno et al., 2007b).

The CSD of the as extruded sample is rather sharp, indicating a good dispersion efficiency of the extrusion process. The thermal annealing results in a significant widening of the CSD, with the appearance of very large clusters (*Dn* greater than 800 nm). This confirms the metastable feature of the samples, which quickly evolve toward states of less free energy

Fig. 12. *G*(*t*) of the 3-hours aged PP/Al2O3 sample at *Φ*=4,5% after LAOS at different strain amplitudes *γ0*: 0.8% (solid circles), 10% (open circles), 25% (triangles), 50% (squares), 100% (crosses), 250% (reverse triangles), 500% (diamonds). Solid diamonds represents the *G*(*t*) of the neat polymer. The time evolutions of *G′* after each LAOS are shown in the inset. Symbols are the same of stress relaxation moduli (image taken from Acierno et al., 2007b).

The morphology of the 3-hours aged sample after the LAOS at *γ0*=500% is reported in Figure 13. The network formed during aging is no more visible, and the presence of many small clusters characterizes the sheared system. The flocs show a more open structure than that of a not sheared sample, either aged or not, suggesting a weaker tendency to the clustering for the Al2O3 nanoparticles after the large deformations. The cumulative cluster size distributions were determined through the analysis of TEM micrographs. The results are shown in Figure 14 for the as extruded, 3-hours annealed and sheared after aging samples at *Φ*=4.2%. The number average equivalent diameters of the clusters are reported in the same

Fig. 13. TEM morphology of the 3-hours aged sample at Φ=4.2% after the LAOS at γ=500%

The CSD of the as extruded sample is rather sharp, indicating a good dispersion efficiency of the extrusion process. The thermal annealing results in a significant widening of the CSD, with the appearance of very large clusters (*Dn* greater than 800 nm). This confirms the metastable feature of the samples, which quickly evolve toward states of less free energy

figure.

(image taken from Acierno et al., 2007b).

under the push of the inter-particle attractive interactions. The resulting filler network breaks up when the sample is subjected to LAOS, and a remarkable sharpening of the CSD is observed.

Fig. 14. CSDs for the PP/Al2O3 sample at *Φ*=4.2% as extruded (black circles), 3-hours aged (blue diamonds) and 3-hours aged after LAOS at *γ0*=500% (red triangles) (image taken from Acierno et al., 2007b).

Interestingly, the strength of the filler network depends on whether the LAOS is applied before or after the thermal annealing. This is shown in Figure 15, where the loss factor *tanδ*=*G''*/*G'* (15.a) and the complex moduli (15.b) of the samples at *Φ*=4.2% submitted to LAOS (*γ0*=500%) are reported before and after the ageing; the curves of the 3-hours aged but not sheared sample are also reported for comparison.

If the LAOS is applied to the sample before the formation of the particle network, the system quickly evolves to a more elastic structure and the *tanδ* asymptotically reaches values close to those of the not sheared sample. However, the comparison between the *G\** shown in

Fig. 15. Loss factor (a) and complex moduli (b) of the samples at *Φ*=4.2% submitted to LAOS (*γ0*=500%) before (diamonds) and after (squares) the thermal annealing. The curves of the 3-hours aged and not sheared sample (circles) are also reported for comparison (image taken from Acierno et al., 2007b).

Nanoparticle Dynamics in Polymer Melts 405

and to other technologically relevant PNCs, such as nanocomposites based on layered

Acierno, D.; Filippone, G.; Romeo, G.; Russo, P. (2007). Rheological aspects of PP-TiO2 nanocomposites: a preliminary investigation. *Macromol. Symp.*, Vol. 247, pp. 59-66 Acierno, D.; Filippone, G.; Romeo, G.; Russo, P. (2007). Dynamics of stress bearing particle

Baird, D. G.; Collias D. I. (1995). In: *Polymer Processing Principles and Design*, John Wiley and

Bicerano, J.; Douglas, J. F.; Brune, D. A. (1999). Model for the viscosity of particle

Cipelletti, L.; Manley, S.; Ball, R. C.; Weitz, D. A. (2000). Universal aging features in

Du, F.; Scogna, R. C.; Zhou, W.; Brand, S.; Fischer, J. E.; Winey, K. I. (2004). Nanotube

Filippone, G.; Romeo, G.; Acierno, D. (2010). Viscoelasticity and structure of

Gleissle, W.; Hochstein, B. (2003). Validity of the Cox–Merz rule for concentrated

Inoubli, R.; Dagréou, S.; Lapp, A.; Billon, L.; Peyrelasse, J. (2006). Nanostructure and

Israelachvili, J. (1991). In: *Intermolecular and surface forces*, Academic Press, ISBN 0-12-375181-

Jancar, J.; Recman, L. (2010). Particle size dependence of the elastic modulus of particulate filled PMMA near its Tg, *Polymer*, Vol. 51, No. 17, (August 2010), pp. 3826-3828 Kammler, H. K.; Beucage, G.; Mueller, R.; Pratsinis S. E. (2004). Structure of flame-made

Kojima Y, Usuki A, Kawasumi M, Okada A, Fukushima Y, Kurauchi T, Kamigaito O. (1993) Mechanical properties of nylon 6-clay hybrid, *J Mat Res* Vol. 8, pp. 1185-1189 Krishnamoorti, R.; Yurekli, K. (2001). Rheology of polymer layered silicate nanocomposites,

Mason, T. G.; Weitz, D. A. (1995) Linear viscoelasticity of colloidal hard sphere suspensions

Ozmusul, M. S.; Picu, R. C.; Sternstein, S. S.; Kumar, S. (2005). Lattice Monte Carlo

Prasad, V.; Trappe, V.; Dinsmore, A. D.; Segrè, P. N.; Cipelletti, L.; Weitz, D. A. (2003)

simulations of chain conformations in polymer nanocomposites , *Macromolecules*,

Universal features of the fluid to solid transition for attractive colloidal particles.

*Curr. Opin. Colloid Interface Sci.* Vol. 6, No. 5-6, pp. 464-470

near the glass transition. *Phys. Rev. Lett.*, Vol. 75, pp. 2770-2773

Sons, Inc., ISBN: 978-0-471-25453-9, New York (USA)

Contributions. *Langmuir*, Vol. 26, No. 4, pp. 2714–2720

networks in poly(propilene)/alumina nanohybrids, *Macromol. Mater. Eng.*, Vol. 292,

dispersions. *J. Macromol. Sci.: Rev. Macromol. Chem. Phys.* Vol. 39, No. 4, pp. 5611-642

restructuring of fractal colloidal gels. *Phys. Rev. Lett.*, Vol. 84, No. 10, pp. 2275-2278

networks in polymer nanocomposites: rheology and electrical conductivity,

polystyrene/fumed silica nanocomposites: Filler Network and Hydrodynamic

mechanical properties of polybutylacrylate filled with grafted silica particles.

silica nanoparticles by ultra-small-angle X-ray scattering. *Langmuir*, Vol. 20, pp.

silicates or carbon nanotubes, still remains to be proved.

*Macromolecules*, Vol. 37, pp. 9048-9055

suspensions. *J. Rheol.*, Vol. 47, pp. 897-910

*Langmuir*, Vol. 22, No. 15, pp. 6683-6689

Vol. 38, No. 10, pp. 4495-4500

*Faraday Discuss.*, Vol. 123, pp. 1-12

**4. References** 

pp. 347-353

0, London, UK

1915-1921

Figure 15.b reveals that the strength of the network formed after the LAOS is much lower than that of the not sheared sample.

Such a result can be explained by assuming some rearrangement of the reactive sites of the particle surfaces after the network break-up, which may weaken the surface activity of the particles. This reduces the intensity of inter-particle interactions and, as a consequence, the strength of the filler network [Bicerano et al., 1999]. On the other hand, if a "strong" network forms and then it is destroyed by LAOS, the restoration of new bonds required for the reformation of the network can results inhibited. This could explain the irreversibility of the structuring process noticed after the LAOS performed on the aged sample.

## **3. Conclusions**

The effect of small amounts of nanoparticles on the melt-state linear viscoelastic behaviour has been investigated for different polymer-nanoparticles model systems characterized by poor polymer-particles interactions and low particle contents. The drastic increase of the rheological properties with respect to the matrices has been related to the formation of a filler network above a critical particles volume fraction. This is a consequence of particles and clusters rearrangements taking place during a thermal annealing. The filler mobility depends on both particle size and viscosity of the suspending medium. Once formed, the filler network exhibits an elastic feature that mixes with the intrinsic viscoelastic response of the polymer matrix, resulting in a complex *Φ*- and *ω*-dependent viscoelastic response of the nanocomposite. However, starting from a two-phase model proposed for colloidal suspensions in Newtonian fluids, we have shown that the contributions of filler network and suspending medium can be decoupled due to the weak polymer-particle interactions and the differences in temporal relaxation scales. The adopted approach has been validated through the building of a master curve of the moduli, which reflects the scaling of the elasticity of composites along the viscosity of the suspending medium. The two-phase model well works irrespective of the structure of the filler network, making evident the strict interrelationships between the structure, both on nano- and micro-scale, and the meltstate behaviour of the studied PNCs. The physical meaning of the two-phase model clearly emerges once hydrodynamic effects have been properly taken into account. Besides clarifying the various timescales of PNCs, the proposed model allows for predicting the modulus of particle networks which are too tenuous to be appreciated through simple frequency scans. The application of a large amplitude oscillatory shear flows provides an excess energy for the system to escape from the metastable configuration in which it is trapped. This destroys the network formed during the thermal annealing, leading to a more tenuous structure which is unable to significantly contribute to the system elasticity. After the network has been destroyed the sample cannot recover its previous solid-like feature during a subsequent thermal annealing. This is probably due to some rearrangement of the reactive sites of the particle surfaces occurring after the rupture of the inter-particles bonds formed during annealing.

Besides well describing the behaviour of PNCs in the framework of simpler systems such as Newtonian colloidal suspensions, the analysis proposed in this chapter is expected to be useful to understand a wide variety of complex fluids in which a superposition of the elasticity of the components is possible. The generalization of our approach to such systems and to other technologically relevant PNCs, such as nanocomposites based on layered silicates or carbon nanotubes, still remains to be proved.

## **4. References**

404 Smart Nanoparticles Technology

Figure 15.b reveals that the strength of the network formed after the LAOS is much lower

Such a result can be explained by assuming some rearrangement of the reactive sites of the particle surfaces after the network break-up, which may weaken the surface activity of the particles. This reduces the intensity of inter-particle interactions and, as a consequence, the strength of the filler network [Bicerano et al., 1999]. On the other hand, if a "strong" network forms and then it is destroyed by LAOS, the restoration of new bonds required for the reformation of the network can results inhibited. This could explain the irreversibility of the

The effect of small amounts of nanoparticles on the melt-state linear viscoelastic behaviour has been investigated for different polymer-nanoparticles model systems characterized by poor polymer-particles interactions and low particle contents. The drastic increase of the rheological properties with respect to the matrices has been related to the formation of a filler network above a critical particles volume fraction. This is a consequence of particles and clusters rearrangements taking place during a thermal annealing. The filler mobility depends on both particle size and viscosity of the suspending medium. Once formed, the filler network exhibits an elastic feature that mixes with the intrinsic viscoelastic response of the polymer matrix, resulting in a complex *Φ*- and *ω*-dependent viscoelastic response of the nanocomposite. However, starting from a two-phase model proposed for colloidal suspensions in Newtonian fluids, we have shown that the contributions of filler network and suspending medium can be decoupled due to the weak polymer-particle interactions and the differences in temporal relaxation scales. The adopted approach has been validated through the building of a master curve of the moduli, which reflects the scaling of the elasticity of composites along the viscosity of the suspending medium. The two-phase model well works irrespective of the structure of the filler network, making evident the strict interrelationships between the structure, both on nano- and micro-scale, and the meltstate behaviour of the studied PNCs. The physical meaning of the two-phase model clearly emerges once hydrodynamic effects have been properly taken into account. Besides clarifying the various timescales of PNCs, the proposed model allows for predicting the modulus of particle networks which are too tenuous to be appreciated through simple frequency scans. The application of a large amplitude oscillatory shear flows provides an excess energy for the system to escape from the metastable configuration in which it is trapped. This destroys the network formed during the thermal annealing, leading to a more tenuous structure which is unable to significantly contribute to the system elasticity. After the network has been destroyed the sample cannot recover its previous solid-like feature during a subsequent thermal annealing. This is probably due to some rearrangement of the reactive sites of the particle surfaces occurring after the rupture of the inter-particles bonds

Besides well describing the behaviour of PNCs in the framework of simpler systems such as Newtonian colloidal suspensions, the analysis proposed in this chapter is expected to be useful to understand a wide variety of complex fluids in which a superposition of the elasticity of the components is possible. The generalization of our approach to such systems

structuring process noticed after the LAOS performed on the aged sample.

than that of the not sheared sample.

**3. Conclusions** 

formed during annealing.


**19** 

*Russia* 

**Dielectric and Transport Properties** 

*1Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow,* 

Currently, there is steady scientific interest in structures formed by nanocrystalline silicon particles (*nc*-Si). This interest is to a large extent caused by the fact that efficient methods for fabricating silicon nanoparticles capable of bright and stable photoluminescence in the visible region of the spectrum with high quantum yield were developed over the last decade (Jurbergs at al., 2006). The main carriers of such nanoparticles are colloidal solutions (sols) based on methanol, chloroform, hexane, etc. Such sols are very promising objects for developing technologies for applying highly uniform thin *nc*-Si films onto various substrates. The use of such films seems very promising for developing light emitting elements based on *nc*-Si electroluminescence (Anopchenko at al., 2009 ). Furthermore, *nc*-Si films are very promising as elements of solar panels (De la Torre at al., 2006), thin film transistors (Min at al., 2002), and single electronic devices (Tsu, 2000). In the case in which films consist of nanoparticles with a diameter smaller than 10 nm, their total characteristics are controlled not only by their material, but also by properties of atoms on the surface of these particles. In other words, in general, such films should be considered as a multicomponent medium the properties of which are controlled by both crystalline cores of nanoparticles and surface atoms and molecules and air voids being a film component.

In the modern scientific literature, most papers are devoted to the study of properties of amorphous silicon (a-Si) films with introduced silicon nanocrystals (Conte at al., 2006; Wang at al., 2003). Such films can be deposited, e.g., in the high frequency discharge in a mixture of gases SiH4, Ar, or H2 (PECVD method), followed by high temperature annealing

Recently, we showed that homogeneous thin films (with a thickness up to 30 nm) can be grown by size selective precipitation sols containing nanocrystalline silicon particles (Dorofeev at al., 2009). Such films (*nc*-Si) are formed by closely adjacent crystalline Si nanoparticles; therefore, their physical characteristics to a certain extent should be similar to characteristics of films based on porous silicon (por-Si). The optical absorption and photoluminescence ability of por-Si films have been very comprehensively studied to date (see, e.g., Kovalev at al., 1996; Brus at al., 1995); however, the number of studies of transport

**1. Introduction** 

(Saadane at al., 2003).

**of Thin Films Deposited from Sols** 

Nickolay N. Kononov1 and Sergey G. Dorofeev2

*2Faculty of Chemistry, Moscow State University, Moscow,* 

**with Silicon Nanoparticles** 


## **Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles**

Nickolay N. Kononov1 and Sergey G. Dorofeev2 *1Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 2Faculty of Chemistry, Moscow State University, Moscow, Russia* 

## **1. Introduction**

406 Smart Nanoparticles Technology

Pusey, P. N.; van Megen, W. (1986). Phase behaviour of concentrated suspensions of nearly

Ren, J.; Silva, A. S.; Krishnamoorti, R. (2000). Linear viscoelasticity of disordered

Romeo, G.; Filippone, G.; Fernández-Nieves, A.; Russo, P.; Acierno, D. (2008). Elasticiy and dynamics of particle gels in non-Newtonian melts. *Rheol. Acta*, Vol. 47, pp. 989-997 Romeo, G.; Filippone, G.; Russo, P.; Acierno, D. (2010). Effects of particle dimension and

Russel, W. B.; Saville, D. A.; Schowalter, W. R. (1989). In: *Colloidal dispersions*, Cambridge

Saint-Michel, F.; Pignon, F.; Magnin, A. (2003). Fractal behavior and scaling law of hydrophobic silica in polyol. *J. Colloid* space *face Sci.*, Vol. 267, No. 2, pp. 314-319 Shenoy, A. V. (1999). In: *Rheology of filled polymer systems*, Kluwer Academic Publishers,

Shikata, T.; Pearson, D.S. (1994). Viscoelastic behavior of concentrated spherical

Sollich, P.; Lequeux, F.; Hébraud, P.; Cates, M. E. (1997). Rheology of soft glassy materials.

Surve, M.; Pryamitsyn, V.; Ganesan, V. (2006). Universality in structure and elasticity of polymer-nanoparticle gels. *Phys. Rev. Lett.*, Vol. 96, No. 17, pp. 1778051-1778054 Trappe, V.; Weitz, D. A. (2000). Scaling of the viscoelasticity of weakly attractive particles.

Trappe, V.; Prasad, V.; Cipelletti, L.; Segrè, P.N.; Weitz, D. A. (2001). Jamming phase

Usuki A.; Kojima Y.; Kawasumi M.; Okada A.; Fukushima Y.; Kurauchi T.; Kamigaito O. (1993). Synthesis of nylon 6-clay hybrid. *J Mat Res*, Vol. 8, pp. 1179-1184 Weitz, D. A.; Oliveira, M. (1984). Fractal structures formed by kinetic aggregation of

Wolthers, W.; van den Ende, D.; Bredveld, V.; Duits, M. H. G.; Potanin, A. A.; Wientjens, R.

Zhang, Q.; Archer, L. A. (2002). Poly(ethylene oxide)/silica nanocomposites: structure and

H. W.; Mellema, J. (1997). Linear viscoelastic behavior of aggregated colloidal

diagram for attractive particles. *Nature*, Vol. 411, pp. 772-775

aqueous gold colloids. *Phys. Rev. Lett.*, Vol. 52, pp. 1433-1436

polystyrene−polyisoprene block copolymer based layered-silicate nanocomposites.

matrix viscosity on the colloidal aggregation in weakly interacting polymernanoparticle composites: a linear viscoelastic analysis. *Polym. Bull.*, Vol. 63, No.6,

hard colloidal spheres. *Nature*, Vol. 320, pp. 340-342

University Press, ISBN 0-521-34188-4, Cambridge, UK

ISBN 0-4112-83100-7, Dordrecht, The Netherlands

suspensions. *J. Rheol.*, Vol. 38, pp. 601-613

*Phys. Rev. Lett.*, Vol. 85, No. 2, pp. 449-452

dispersions. *Phys. Rev. E*, Vol. 56, pp. 5726-5733

rheology. *Langmuir*, Vol. 18, No. 26, pp. 10435-10442

*Phys. Rev. Lett.* 78, 2020-2023

*Macromolecules*, Vol. 33, No. 10, pp. 3739-3746

pp. 883-895

Currently, there is steady scientific interest in structures formed by nanocrystalline silicon particles (*nc*-Si). This interest is to a large extent caused by the fact that efficient methods for fabricating silicon nanoparticles capable of bright and stable photoluminescence in the visible region of the spectrum with high quantum yield were developed over the last decade (Jurbergs at al., 2006). The main carriers of such nanoparticles are colloidal solutions (sols) based on methanol, chloroform, hexane, etc. Such sols are very promising objects for developing technologies for applying highly uniform thin *nc*-Si films onto various substrates. The use of such films seems very promising for developing light emitting elements based on *nc*-Si electroluminescence (Anopchenko at al., 2009 ). Furthermore, *nc*-Si films are very promising as elements of solar panels (De la Torre at al., 2006), thin film transistors (Min at al., 2002), and single electronic devices (Tsu, 2000). In the case in which films consist of nanoparticles with a diameter smaller than 10 nm, their total characteristics are controlled not only by their material, but also by properties of atoms on the surface of these particles. In other words, in general, such films should be considered as a multicomponent medium the properties of which are controlled by both crystalline cores of nanoparticles and surface atoms and molecules and air voids being a film component.

In the modern scientific literature, most papers are devoted to the study of properties of amorphous silicon (a-Si) films with introduced silicon nanocrystals (Conte at al., 2006; Wang at al., 2003). Such films can be deposited, e.g., in the high frequency discharge in a mixture of gases SiH4, Ar, or H2 (PECVD method), followed by high temperature annealing (Saadane at al., 2003).

Recently, we showed that homogeneous thin films (with a thickness up to 30 nm) can be grown by size selective precipitation sols containing nanocrystalline silicon particles (Dorofeev at al., 2009). Such films (*nc*-Si) are formed by closely adjacent crystalline Si nanoparticles; therefore, their physical characteristics to a certain extent should be similar to characteristics of films based on porous silicon (por-Si). The optical absorption and photoluminescence ability of por-Si films have been very comprehensively studied to date (see, e.g., Kovalev at al., 1996; Brus at al., 1995); however, the number of studies of transport

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 409

It is found that the function ε'(ω) in this frequency range is well approximated by the semiempirical Cole–Cole dependence (Cole–Cole dielectric relaxation) ( Cole, K. S. & Cole, R. H., 1941). At the same time, the ε''(ω) spectra of *nc*-Si films are well approximated by the Cole–Cole dependence only at frequencies higher than 2 × 102 Hz. In the low frequency spectral region, good approximation is achieved by combining the Cole–Cole dependence and the term associated with the presence of free electric charges. From analysis of the approximating dependences, the average room temperature relaxation times of dipole

The conductivity σac of the studied films I in an ac electric field depends only on its frequency according to the power law; the exponent is 0.74 in the entire frequency range under study. Such behavior of σac suggests that the electrical transport mechanism in films is hopping. Comparison of the measured frequency dependence σac(ν) with similar dependences following from various models of hopping conductivity shows that the σac(ν) behavior is most accurately described in the diffusion cluster approximation (DCA) (Dyre &

Analysis of the dependences of the dark conductivity of films on humidity of ambient air and the temperature dependence of absorption bands caused by associated Si–OH groups on the film surface allowed the conclusion to be drawn that conductivity at frequencies lower than 2×102 Hz is associated with proton transport through the hydrogen bound

For films II and III we present measurements of the *nc*-Si film permittivity and ac conductivity (σac) in the frequency range of 1 ≤ν≤106Hz. The dielectric properties of the films II and III were

We found that in films II and III, a double dielectric relaxation exists and to adequately describe the spectra of ε 'and ε'' of these films should use not only the Cole-Cole

By a total approximation of the experimental spectra of the films II and III the values of static dielectric constant ε0 have obtained. These values are equal 11.5 and 67 respectively. Value ε<sup>0</sup> ≈ 11,5 characteristic of film II is close to the static permittivity of crystalline silicon, but the magnitude of ε<sup>0</sup> ≈ 67 of films III significantly higher than this value. Next, we

In contrast to the conductivity of the films I σAS of films II and III are not subject to a power law over the entire range of measured frequencies. Next, we show that such a deviation from the law σAS ~ ωs associated with the appearance in the spectra ε "(ω) of the films II and

**2.1 Films deposited from freshly prepared sols of silicon nanoparticles ( films I )** 

The *nc*-Si films were deposited from silicon nanoparticles produced by CO2 laser pyrolysis of silane. The system for synthesis of the *nc*-Si powders and conditions of the process are described in detail elsewhere (Kononov at al., *2005*; Kuz'min at al., 2000). In what follows,

studied by impedance spectroscopy only in the frequency range 1 ≤ ν ≤ 106Hz.

moments in *nc*-Si films were determined as 6 ×10–2 s.

hydroxyl groups on the silicon nanoparticle surface.

analyze this fact.

III Debye's components.

**2. The films from silicon nanoparticles** 

**2.1.1 Samples and measurement procedures** 

relationship, but and the law of Debye's dielectric relaxation.

Schrøder, 2000; Schrøder & Dyre, 2002; Schrøder & Dyre, 2008).

and dielectric properties of such films in an ac electric field is extremely small. Here we indicate papers (Axelrod at al., 2002; Ben-Chorin at al., 1995; Urbach at al., 2007) devoted to such studies of por-Si.

A similar situation exists as applied to *nc*-Si films; however, we are not aware of results of studies on the conductivity in an ac electric field (ac conductivity and dielectric relaxation in such films).

In this chapter we analyze the dielectric and transport properties of nc-Si films deposited on a glass and quartz substrates from the sol containing nanoparticles of silicon. Silicon nanoparticles were synthesized in the process of laser pyrolysis of silane and placed in ethanol or methanol, repeatedly centrifuged resulting in a colloidal solution (sol) in which the silicon nanoparticles could be a long time (over two years). We analyze three kinds of films. The films deposited on a substrate by centrifugation of sols of nanoparticles in a week after their synthesis. Films deposited on a substrate of sols in which the nanoparticles were 2 years after their synthesis and films deposited from two-year-old sol in which has been added the conductive tetra-aniline. More circumstantial experimental details we will present in the following sections. In the future of the films deposited on a substrate of silicon nanoparticles in a week after their synthesis we call films I, films obtained from similar nanoparticles, but two years after their synthesis (aged nanoparticles) - films II and films deposited of sols with aged nanoparticles and with the tetra aniline addition - films III.

For films I we present measurements of the *nc*-Si film permittivity in the optical range (5×1014 ≤ν≤1015 Hz) and in the frequency range of 10 ≤ν≤106Hz. In the latter range, the ac conductivity (σac) of *nc*-Si films is also determined.

In the optical region, the real ε' and imaginary ε'' components of the complex permittivity were determined from an ellipsometric analysis of light beams incident and reflected from the free boundary of the *nc*-Si film. In the frequency range of 10 ≤ν≤106 Hz, the ε' and ε'' spectra, were determined from an analysis of the frequency dependence of the *nc*-Si film impedance.

In an optical spectral region, ε' and ε'' varied within 2.1–1.1 and 0.25–0.75, respectively, as the frequency increased. We attribute such low values of ε' and ε'' to the *nc*-Si film structure. The *nc*-Si particles forming such films consist of crystalline cores surrounded by a SiOx shell (0 ≤ *x* ≤ 2). The SiOx shell results from the interaction of the Si nanoparticle surface with ambient air. On the basis of the analysis of the Raman spectra, it is suggested that the amorphous component is involved in the *nc*-Si powders and films due to oxygen atoms arranged at the nanoparticle surface.

Using the Bruggeman effective medium approximation (EMA) (Bruggeman, 1935), the structural composition of *nc*-Si film was simulated. It was shown that good agreement between the frequency dependences of ε' and ε'' obtained from the EMA and the ε' and ε'' spectra determined from ellipsometric data is achieved when *nc*-Si films are considered as a two component medium consisting of SiO and air voids existing in it. In the frequency range of 10–106 Hz, the ε' and ε'' dispersion was determined from an analysis of the frequency dependences of the capacitance of *nc*-Si films and their impedance spectra. It was found that ε' and ε'' vary within 6.2–3.4 and 1.8–0.08, respectively, as the frequency increases.

and dielectric properties of such films in an ac electric field is extremely small. Here we indicate papers (Axelrod at al., 2002; Ben-Chorin at al., 1995; Urbach at al., 2007) devoted to

A similar situation exists as applied to *nc*-Si films; however, we are not aware of results of studies on the conductivity in an ac electric field (ac conductivity and dielectric relaxation in

In this chapter we analyze the dielectric and transport properties of nc-Si films deposited on a glass and quartz substrates from the sol containing nanoparticles of silicon. Silicon nanoparticles were synthesized in the process of laser pyrolysis of silane and placed in ethanol or methanol, repeatedly centrifuged resulting in a colloidal solution (sol) in which the silicon nanoparticles could be a long time (over two years). We analyze three kinds of films. The films deposited on a substrate by centrifugation of sols of nanoparticles in a week after their synthesis. Films deposited on a substrate of sols in which the nanoparticles were 2 years after their synthesis and films deposited from two-year-old sol in which has been added the conductive tetra-aniline. More circumstantial experimental details we will present in the following sections. In the future of the films deposited on a substrate of silicon nanoparticles in a week after their synthesis we call films I, films obtained from similar nanoparticles, but two years after their synthesis (aged nanoparticles) - films II and films deposited of sols with aged nanoparticles and with the tetra aniline addition - films III.

For films I we present measurements of the *nc*-Si film permittivity in the optical range (5×1014 ≤ν≤1015 Hz) and in the frequency range of 10 ≤ν≤106Hz. In the latter range, the ac

In the optical region, the real ε' and imaginary ε'' components of the complex permittivity were determined from an ellipsometric analysis of light beams incident and reflected from the free boundary of the *nc*-Si film. In the frequency range of 10 ≤ν≤106 Hz, the ε' and ε'' spectra, were determined from an analysis of the frequency dependence of the *nc*-Si film

In an optical spectral region, ε' and ε'' varied within 2.1–1.1 and 0.25–0.75, respectively, as the frequency increased. We attribute such low values of ε' and ε'' to the *nc*-Si film structure. The *nc*-Si particles forming such films consist of crystalline cores surrounded by a SiOx shell (0 ≤ *x* ≤ 2). The SiOx shell results from the interaction of the Si nanoparticle surface with ambient air. On the basis of the analysis of the Raman spectra, it is suggested that the amorphous component is involved in the *nc*-Si powders and films due to oxygen atoms

Using the Bruggeman effective medium approximation (EMA) (Bruggeman, 1935), the structural composition of *nc*-Si film was simulated. It was shown that good agreement between the frequency dependences of ε' and ε'' obtained from the EMA and the ε' and ε'' spectra determined from ellipsometric data is achieved when *nc*-Si films are considered as a two component medium consisting of SiO and air voids existing in it. In the frequency range of 10–106 Hz, the ε' and ε'' dispersion was determined from an analysis of the frequency dependences of the capacitance of *nc*-Si films and their impedance spectra. It was found that

ε' and ε'' vary within 6.2–3.4 and 1.8–0.08, respectively, as the frequency increases.

conductivity (σac) of *nc*-Si films is also determined.

arranged at the nanoparticle surface.

such studies of por-Si.

such films).

impedance.

It is found that the function ε'(ω) in this frequency range is well approximated by the semiempirical Cole–Cole dependence (Cole–Cole dielectric relaxation) ( Cole, K. S. & Cole, R. H., 1941). At the same time, the ε''(ω) spectra of *nc*-Si films are well approximated by the Cole–Cole dependence only at frequencies higher than 2 × 102 Hz. In the low frequency spectral region, good approximation is achieved by combining the Cole–Cole dependence and the term associated with the presence of free electric charges. From analysis of the approximating dependences, the average room temperature relaxation times of dipole moments in *nc*-Si films were determined as 6 ×10–2 s.

The conductivity σac of the studied films I in an ac electric field depends only on its frequency according to the power law; the exponent is 0.74 in the entire frequency range under study. Such behavior of σac suggests that the electrical transport mechanism in films is hopping. Comparison of the measured frequency dependence σac(ν) with similar dependences following from various models of hopping conductivity shows that the σac(ν) behavior is most accurately described in the diffusion cluster approximation (DCA) (Dyre & Schrøder, 2000; Schrøder & Dyre, 2002; Schrøder & Dyre, 2008).

Analysis of the dependences of the dark conductivity of films on humidity of ambient air and the temperature dependence of absorption bands caused by associated Si–OH groups on the film surface allowed the conclusion to be drawn that conductivity at frequencies lower than 2×102 Hz is associated with proton transport through the hydrogen bound hydroxyl groups on the silicon nanoparticle surface.

For films II and III we present measurements of the *nc*-Si film permittivity and ac conductivity (σac) in the frequency range of 1 ≤ν≤106Hz. The dielectric properties of the films II and III were studied by impedance spectroscopy only in the frequency range 1 ≤ ν ≤ 106Hz.

We found that in films II and III, a double dielectric relaxation exists and to adequately describe the spectra of ε 'and ε'' of these films should use not only the Cole-Cole relationship, but and the law of Debye's dielectric relaxation.

By a total approximation of the experimental spectra of the films II and III the values of static dielectric constant ε0 have obtained. These values are equal 11.5 and 67 respectively. Value ε<sup>0</sup> ≈ 11,5 characteristic of film II is close to the static permittivity of crystalline silicon, but the magnitude of ε<sup>0</sup> ≈ 67 of films III significantly higher than this value. Next, we analyze this fact.

In contrast to the conductivity of the films I σAS of films II and III are not subject to a power law over the entire range of measured frequencies. Next, we show that such a deviation from the law σAS ~ ωs associated with the appearance in the spectra ε "(ω) of the films II and III Debye's components.

## **2. The films from silicon nanoparticles**

## **2.1 Films deposited from freshly prepared sols of silicon nanoparticles ( films I )**

## **2.1.1 Samples and measurement procedures**

The *nc*-Si films were deposited from silicon nanoparticles produced by CO2 laser pyrolysis of silane. The system for synthesis of the *nc*-Si powders and conditions of the process are described in detail elsewhere (Kononov at al., *2005*; Kuz'min at al., 2000). In what follows,

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 411

measuring impedance spectra were prepared as follows. First, aluminum electrodes separated by a rectilinear gap 1 mm wide were deposited on a glass substrate. Then *nc*-Si particles were precipitated from the sol on the substrate prepared in such a way, which formed a film. The third aluminum electrode was deposited on the obtained *nc*-Si film. As a result, a sandwich like structure similar to that shown in Fig. 2 was obtained. To achieve the ohmic lead contacts, the structure was annealed at a temperature of 400°C and a pressure of 10–5 Torr. Impedance spectra were measured at an amplitude voltage of 100 mV; however,

the films under study can withstand a voltage to 15 V without electrical breakdown.

glass

Fig. 2. Diagram of the sandwich like sample structures for measuring impedance spectra.

Al Al

Al nc-Si film

To record the Raman spectra, we first deposited an aluminum film with the thickness ~300 μm onto the quartz substrate, and then, on top of the film, we deposited the *nc*-Si film from the sol. We proceeded in such manner in order to avoid the background scattering

spectra recorded for the initial *nc*-Si powder, for the films deposited at the second stage of centrifuging the sols of the initial *nc*-Si powder and film deposited from the sol with powder etched in the (5wt%**H**F+14wt%HNO3) water mixture. The corresponding samples are

The typical Raman spectra recorded for these samples are shown in Fig. 3. All of the experimentally recorded spectra are very similar to the Raman spectra obtained for *p-*Si in

> 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

**Intensity, a u**

250 300 350 400 450 500 550 600

а **Raman shift, cm-1** b

S2

component produced by the quartz substrate. In this section, we analyze the Raman

(Tsang at al., 1992; Tsu at al., 1992) and for the *nc*-Si clusters in (Ehbrecht at al., 1995).

**2.1.2 Experimental results 2.1.2.1 Raman scattering** 

identified as samples *S*1, *S*2, and *S*3 respectively.

250 300 350 400 450 500 550 600

**Raman shift, cm-1**

**P3**

S1

**P2**

**P1**

0,0

0,5

**P4**

1,0

**Intencity, a u**

1,5

we briefly outline the procedure of synthesis of the Si nanoparticles. In a reactor chamber filled with a buffer gas (helium or argon) to the pressure *P* = 200 Torr, a fine SiH4 jet is formed and heated by focused cw CO2 laser radiation beam crossing the jet. During pyrolysis of silane, the SiH4 molecules are decomposed, and free Si atoms are produced. When colliding with each other and with the atoms of the buffer gas, the Si atoms form particles, whose average dimensions can be in the range from 10 to 100 nm, depending on the pressure of the buffer gas. The *nc*-Si powders produced in such a manner were dispersed by ultrasonic treatment in ethanol and centrifuged for 30 min with an acceleration of 2000*g*  (*g* is the gravitational acceleration). As a result, almost all agglomerates of *nc*-Si particles are precipitated. After preliminary centrifugation, a stable colloidal solution (sol) of *nc*-Si in ethanol remains. No visible changes in the solution, including precipitations, were observed for two years. For the subsequent deposition of nanoparticles, a water solution of aluminum dihydrophosphate was added to the sol.

Fig. 1. (a) Histogram of the size distribution of particles, as obtained by processing of the TEM images of the *nc*-Si powder (b) Histogram of the size distribution of particles, as obtained by processing of the TEM images of the *nc*-Si powder etched in the (HF + HNO3) acid mixture. The dushed lines represent the normal distribution functions for two different kinds of nc-Si particles

The size distribution of *nc*-Si particles was determined from images obtained using an LEO 912 AV OMEGA transmission electron microscope. The typical spectrum of silicon nanoparticles used for precipitation is shown in the Fig. 1. The *nc*-Si film thickness was determined using a Taly Step (Taylor-Hobbson) atomic force step profilometer. Ellipsometric spectra were measured using an Ellips 1891 ellipsometer (Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences). The transmission spectra were measured using a Lambda 900 (Perkin-Elmer) spectrophotometer. The Raman spectra of the films were recorded with a microlens equipped T 64000 (Jobin Ivon) Raman triple spectrograph in the backscattering layout of measurements at the power of the excitation argon laser 2 mW.

The impedance spectra were measured using an E7-20 immittance meter (Minsk Research Instrument Making Institute) and a Z-3000X (Elins) impedance meter. Samples for measuring impedance spectra were prepared as follows. First, aluminum electrodes separated by a rectilinear gap 1 mm wide were deposited on a glass substrate. Then *nc*-Si particles were precipitated from the sol on the substrate prepared in such a way, which formed a film. The third aluminum electrode was deposited on the obtained *nc*-Si film. As a result, a sandwich like structure similar to that shown in Fig. 2 was obtained. To achieve the ohmic lead contacts, the structure was annealed at a temperature of 400°C and a pressure of 10–5 Torr. Impedance spectra were measured at an amplitude voltage of 100 mV; however, the films under study can withstand a voltage to 15 V without electrical breakdown.

## **2.1.2 Experimental results**

#### **2.1.2.1 Raman scattering**

410 Smart Nanoparticles Technology

we briefly outline the procedure of synthesis of the Si nanoparticles. In a reactor chamber filled with a buffer gas (helium or argon) to the pressure *P* = 200 Torr, a fine SiH4 jet is formed and heated by focused cw CO2 laser radiation beam crossing the jet. During pyrolysis of silane, the SiH4 molecules are decomposed, and free Si atoms are produced. When colliding with each other and with the atoms of the buffer gas, the Si atoms form particles, whose average dimensions can be in the range from 10 to 100 nm, depending on the pressure of the buffer gas. The *nc*-Si powders produced in such a manner were dispersed by ultrasonic treatment in ethanol and centrifuged for 30 min with an acceleration of 2000*g*  (*g* is the gravitational acceleration). As a result, almost all agglomerates of *nc*-Si particles are precipitated. After preliminary centrifugation, a stable colloidal solution (sol) of *nc*-Si in ethanol remains. No visible changes in the solution, including precipitations, were observed for two years. For the subsequent deposition of nanoparticles, a water solution of aluminum

Fig. 1. (a) Histogram of the size distribution of particles, as obtained by processing of the TEM images of the *nc*-Si powder (b) Histogram of the size distribution of particles, as obtained by processing of the TEM images of the *nc*-Si powder etched in the (HF + HNO3) acid mixture. The dushed lines represent the normal distribution functions for two different

**Diameter (nm)** <sup>а</sup> <sup>b</sup>

**Relative number (%)**

1 2 3 4 5 6 7 8 9 10 11 12

The size distribution of *nc*-Si particles was determined from images obtained using an LEO 912 AV OMEGA transmission electron microscope. The typical spectrum of silicon nanoparticles used for precipitation is shown in the Fig. 1. The *nc*-Si film thickness was determined using a Taly Step (Taylor-Hobbson) atomic force step profilometer. Ellipsometric spectra were measured using an Ellips 1891 ellipsometer (Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences). The transmission spectra were measured using a Lambda 900 (Perkin-Elmer) spectrophotometer. The Raman spectra of the films were recorded with a microlens equipped T 64000 (Jobin Ivon) Raman triple spectrograph in the backscattering layout of measurements at the power of the

The impedance spectra were measured using an E7-20 immittance meter (Minsk Research Instrument Making Institute) and a Z-3000X (Elins) impedance meter. Samples for

dihydrophosphate was added to the sol.

2 4 6 8 10 12 14 16 18 20 22

Diameter (nm)

kinds of nc-Si particles

Relative number (%)

excitation argon laser 2 mW.

To record the Raman spectra, we first deposited an aluminum film with the thickness ~300 μm onto the quartz substrate, and then, on top of the film, we deposited the *nc*-Si film from the sol. We proceeded in such manner in order to avoid the background scattering component produced by the quartz substrate. In this section, we analyze the Raman

spectra recorded for the initial *nc*-Si powder, for the films deposited at the second stage of centrifuging the sols of the initial *nc*-Si powder and film deposited from the sol with powder etched in the (5wt%**H**F+14wt%HNO3) water mixture. The corresponding samples are identified as samples *S*1, *S*2, and *S*3 respectively.

The typical Raman spectra recorded for these samples are shown in Fig. 3. All of the experimentally recorded spectra are very similar to the Raman spectra obtained for *p-*Si in (Tsang at al., 1992; Tsu at al., 1992) and for the *nc*-Si clusters in (Ehbrecht at al., 1995).

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 413

nanoparticle can vary in the range (0, 2π/*L*), where *L* is the particle diameter. However, if the nanoparticle core is polycrystalline and the average dimension of the elementary crystal lattice in the core is *l*, the confining condition *q* ≤ 2π/*L* should be replaced by the condition *q* ≤ 2π/*l*. Thus, it is possible that the dimensions *l* = 4–6 nm calculated in the phonon's confinement model are related to the average dimensions of elementary lattices in the polycrystalline nanoparticle cores rather than to the average nanoparticles' dimensions in the initial *nc*-Si powder. From this assumption and the fact that, for nanoparticles subjected to etching, the average dimensions determined by the above two methods are the same, it follows that, on such etching of the nanoparticles, the remaining *c-*Si cores are single crystals. The other cause can follow from the well known low contrast of the finest nanoparticles (with the diameter 3 nm in the case under study) in the TEM images. Because of the low contrast, the processing of the TEM images always reduces the relative portion of the fine grained fraction of nanoparticles in the ensemble of particles

Fig. 4. The half-width and the red shift of the *P*1 Raman peak versus the diameter of the spherical silicon nanoparticles, as obtained (solid line) in the context of the phonon's confinement model [19, 20] and (solid circles) from the approximation of the *P*1 peak in

**S3**

**S2**

**S1**

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

**cm-1**

The Raman shift of the *P*2 peak in the samples is in the range from 480 to 495 cm–1. This peak corresponds to the TO-phonon assisted scattering in *a-*Si:H. Similarly to the *P*2 peak, the *P*<sup>3</sup> and *P*4 peaks are related to the amorphous component of the structure of the Si particles and

From the comparison of the integrated intensities of the *P*1 and *P*2 peaks, *Ic* and *Ia*, we can determine the volume fraction of the crystalline phase, *Xc*, in the Si particles. To do this, we

> **<sup>c</sup> <sup>c</sup> c a**

(1)

10 8 7

9

5

6

4

**L, nm**

3

**<sup>I</sup> <sup>X</sup> I I** 

result from scattering assisted by LO and longitudinal acoustic (LA) phonons.

samples *S*1, *S*2 and *S*3, with the Lorentzian contours.

**, cm-1**

used the expression (Voutsas at al., 1995)

under consideration.

Fig. 3. Raman spectra of: a) nc-Si powder S1, b) film deposited from the sol of the initial *nc*-Si powder-S2 c) film deposited from the sol *nc*-Si powder etched in the (HF + HNO3) acid mixture –S3. The dotted line refers to the approximation of the spectrum with Lorentzian contours (the *P*1, *P*2, *P*3, and *P*4 peaks).

The Raman spectra of all of the samples studied here can be fitted with four Lorentzian bands with a rather good accuracy (Fig. 3). In what follows, these bands are referred to as the *P*1, *P*2, *P*3, and *P*4 peaks. The Raman shift of the most intense *P*1 peak with respect to the emission frequency of the probing laser is in the range of wave numbers from 515 to 517 cm– 1 for all of the samples. The Raman shift of the similar peak for *c-*Si corresponds to the wave number 520.5 cm–1. Thus, for all of the films studied here, the *P*1 peak is shifted to smaller wave numbers with respect to the peak for *c-*Si (the red shift). The *P*1 peak in the Raman spectra of the *nc*-Si particles is due to light scattering assisted by longitudinal optical (LO) and transverse optical (TO) phonons at the central point of the Brillouin zone for the *c-*Si crystal lattice. The red shift of the *P*1 peak and its half width as functions of the nanoparticle dimensions are adequately described in the context of the phonon's confinement model (Campbell & Faushet 1986; Richter at al., 1981).

The result of application of this model to spherical nanoparticles is shown in Fig. 4. From Fig. 4, it can be seen that the average dimension of the *nc*-Si particles in the samples is in the range 4–6 nm, irrespective of whether the particles of the initial *nc*-Si powder were subjected to some treatment or not. For the sols of the *nc*-Si powders etched in the (HF + HNO3) mixture, the average particle's dimensions determined in the phonon's confinement model are in good agreement with the particle dimensions corresponding to the peak of size distribution obtained for the particles by processing of the TEM images.

However, for the initial *nc*-Si powders, the average particle dimensions determined by the above mentioned two methods differ by a factor of about 2. There are two possible causes of the difference between the average particle's dimensions determined in the phonon's confinement model and by processing of the TEM images. One of the causes is associated with the fact that, in the phonon's confinement model, the nanoparticles are assumed to be single crystals. Therefore, the magnitude of the phonon wave's vector *q* in the

S3

Fig. 3. Raman spectra of: a) nc-Si powder S1, b) film deposited from the sol of the initial *nc*-Si powder-S2 c) film deposited from the sol *nc*-Si powder etched in the (HF + HNO3) acid mixture –S3. The dotted line refers to the approximation of the spectrum with Lorentzian

250 300 350 400 450 500 550 600

**Raman shift, cm-1** c

The Raman spectra of all of the samples studied here can be fitted with four Lorentzian bands with a rather good accuracy (Fig. 3). In what follows, these bands are referred to as the *P*1, *P*2, *P*3, and *P*4 peaks. The Raman shift of the most intense *P*1 peak with respect to the emission frequency of the probing laser is in the range of wave numbers from 515 to 517 cm– 1 for all of the samples. The Raman shift of the similar peak for *c-*Si corresponds to the wave number 520.5 cm–1. Thus, for all of the films studied here, the *P*1 peak is shifted to smaller wave numbers with respect to the peak for *c-*Si (the red shift). The *P*1 peak in the Raman spectra of the *nc*-Si particles is due to light scattering assisted by longitudinal optical (LO) and transverse optical (TO) phonons at the central point of the Brillouin zone for the *c-*Si crystal lattice. The red shift of the *P*1 peak and its half width as functions of the nanoparticle dimensions are adequately described in the context of the phonon's confinement model

The result of application of this model to spherical nanoparticles is shown in Fig. 4. From Fig. 4, it can be seen that the average dimension of the *nc*-Si particles in the samples is in the range 4–6 nm, irrespective of whether the particles of the initial *nc*-Si powder were subjected to some treatment or not. For the sols of the *nc*-Si powders etched in the (HF + HNO3) mixture, the average particle's dimensions determined in the phonon's confinement model are in good agreement with the particle dimensions corresponding to the peak of size distribution obtained for the particles by processing of the TEM

However, for the initial *nc*-Si powders, the average particle dimensions determined by the above mentioned two methods differ by a factor of about 2. There are two possible causes of the difference between the average particle's dimensions determined in the phonon's confinement model and by processing of the TEM images. One of the causes is associated with the fact that, in the phonon's confinement model, the nanoparticles are assumed to be single crystals. Therefore, the magnitude of the phonon wave's vector *q* in the

contours (the *P*1, *P*2, *P*3, and *P*4 peaks).

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

**Intensity, a u**

(Campbell & Faushet 1986; Richter at al., 1981).

images.

nanoparticle can vary in the range (0, 2π/*L*), where *L* is the particle diameter. However, if the nanoparticle core is polycrystalline and the average dimension of the elementary crystal lattice in the core is *l*, the confining condition *q* ≤ 2π/*L* should be replaced by the condition *q* ≤ 2π/*l*. Thus, it is possible that the dimensions *l* = 4–6 nm calculated in the phonon's confinement model are related to the average dimensions of elementary lattices in the polycrystalline nanoparticle cores rather than to the average nanoparticles' dimensions in the initial *nc*-Si powder. From this assumption and the fact that, for nanoparticles subjected to etching, the average dimensions determined by the above two methods are the same, it follows that, on such etching of the nanoparticles, the remaining *c-*Si cores are single crystals. The other cause can follow from the well known low contrast of the finest nanoparticles (with the diameter 3 nm in the case under study) in the TEM images. Because of the low contrast, the processing of the TEM images always reduces the relative portion of the fine grained fraction of nanoparticles in the ensemble of particles under consideration.

Fig. 4. The half-width and the red shift of the *P*1 Raman peak versus the diameter of the spherical silicon nanoparticles, as obtained (solid line) in the context of the phonon's confinement model [19, 20] and (solid circles) from the approximation of the *P*1 peak in samples *S*1, *S*2 and *S*3, with the Lorentzian contours.

The Raman shift of the *P*2 peak in the samples is in the range from 480 to 495 cm–1. This peak corresponds to the TO-phonon assisted scattering in *a-*Si:H. Similarly to the *P*2 peak, the *P*<sup>3</sup> and *P*4 peaks are related to the amorphous component of the structure of the Si particles and result from scattering assisted by LO and longitudinal acoustic (LA) phonons.

From the comparison of the integrated intensities of the *P*1 and *P*2 peaks, *Ic* and *Ia*, we can determine the volume fraction of the crystalline phase, *Xc*, in the Si particles. To do this, we used the expression (Voutsas at al., 1995)

$$\mathbf{X\_c = \frac{\mathbf{I\_c}}{\mathbf{I\_c + \eta I\_a}}} \tag{1}$$

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 415

effect in powder *S*1. As a result, the volume fraction of the crystal phase in film *S*2 is reduced

Etching of the *nc*-Si particles in the solution of the (HF + HNO3) acids results in a decrease in the particle dimensions. However, in this case, the total number of oxygen atoms at the nanoparticle's surface decreases, since a portion of oxygen atoms is replaced with hydrogen atoms. Therefore, in film *S*3 two opposite processes are bound to occur. One process related to the decrease in the nanoparticle's dimensions yields a decrease in *Xc*, whereas the other process related to the decrease in the number of oxygen atoms at the nanoparticle surface brings about an increase in *Xc*. In film *S*3, we experimentally observe the parameter *X*<sup>c</sup> larger than *X*<sup>c</sup> in film *S*2; therefore, we can conclude that, on etching of the *nc*-Si particles, the latter

In the experiment, the ellipsometric angles ψ and Δ were measured as functions of the wavelength of a light beam incident at the angle Φ0 on the free flat surface of the *nc*-Si film. The films under study were applied on glass and quartz substrates and on quartz substrates with preliminarily deposited aluminum films. The *nc*-Si film thicknesses (1–2 μm) were measured independently. When processing the ellipsometric data, the *nc*-Si films under study were considered as a 3D medium in air medium. The complex refractive index *N* = *n* – *ik*, where *n* is the film refractive index and *k* is the extinction coefficient, was

> 2 2

(2)

0 0 0

1

<sup>1</sup> sin 1

*N N tg*

Here, ρ = eiΔ· tgψ and *N*0 are the complex refractive index of an ambient medium (air), which was equal to unity in the case at hand. It is known that formula (2) yields accurate values only when light is reflected from a semi-infinite medium with a boundary with an atomically clean surface. If impurities or an oxide filmare on the boundary, they introduce errors to the calculated values. In (Tompkins & Irene, 2005), the values *n* and *k* were compared for crystalline silicon (*c*-Si) in the absence and presence of the oxide film on its surface. It follows from this comparison that, in the presence of a SiO2 film to 2 nm thick on the silicon surface, the value of *n* is almost identical to that of *c*-Si in the incident photon energy range of 1–3.4 eV; in the range of 3.4–5 eV, the refractive index differs from *n* of *c*-Si no more than by 20%, as well as *k*. However, in the range of 1–3.4 eV, the value of k in the

Since the real ε' and imaginary ε'' components of the medium permittivity are related to *n*  and *k* by the known expressions ε' = *n*2 – *k*2 and ε'' = 2*nk*, it can be expected that the values of ε' calculated by Eq. (2) for *nc*-Si films will be slightly systematically underestimated, while

Nevertheless, representation of the pseudo dielectric functions by relation (2) is very convenient and is quite often used to study the dielectric properties of materials. For example, dielectric parameters of *por*-Si were studied using this equation in (Pickering, 1984). As applied to the present study, an analysis of the spectra obtained using formula (2)

compared to that in *S*1.

process dominates over the former one.

determined by the expression (Azzam & Bashara, 1977)

presence of the SiO2 film almost twice exceeds the *c*-Si extinction.

the values of ε'' will be overestimated.

**2.1.2.2 Ellipsometric spectra** 

where **c a** is the ratio between the integrated backscattering's cross sections in the

crystalline and amorphous fractions (corresponding to the *P*1 and *P*2 peaks). According to (Kakinuma at al., 1991), the quantity η for silicon is η = 0.8–0.9. In the calculations, we set η = 0.8. For samples *S*1, *S*2 and *S*3, the values of the parameter *Xc* are 0.45, 0.35 and 0.50 respectively.

From these values of *Xc*, it follows that almost a half of the volume of the particles is characterized by a high degree of disorder of the crystal lattice.

From comparison of the above values, it is evident that, in film *S*2 deposited at the second stage of centrifuging from the sol with the initial *nc*-Si powder, the parameter *Xc* is smaller than *Xc* for the initial powder. The average particle's dimension in film *S*2 is smaller than that in the initial powder. Correspondingly, the surface area to volume ratio for the particles in the *S*2 film is larger than the corresponding ratio in the initial powder. Therefore, the effect of the nanoparticle surface on the general properties of the nanoparticles in film *S*2 is bound to be more pronounced that the corresponding effect in the initial powder. Consequently, the smaller value of *Xc* (the higher degree of amorphization of the particles) in film *S*2 in comparison with *Xc* in sample *S*1 suggests that the disordered regionis at the nanoparticle surface rather than in the nanoparticle core. However, for film *S*3 the value of *Xc* is larger than *Xc* for film *S*2, although the average particle's dimensions in these films are comparable. Such difference suggests that the degree of disorder of particle surfaces in film *S*3 is lower than that in film *S*2.

Since film *S*3 are deposited from the sols of the *nc*-Si powders subjected to etching, such lower degree of disorder in these films is due to the effect of the HF and HNO3 acids on the particle surface. Here, it is reasonable to mention the studies ( Luppi & Ossicini, 2005; Puzder at al., 2002), in which the effect of oxygen atoms on the structure of silicon clusters and on the degree of ordering of the Si crystal lattice in nanoparticles is analyzed, and the studies (Ma at al., 2000 Tsang at al., 1992; ), in which the changes induced in the Raman peak similar to the *P*2 peak (Fig. 3) by the effect of oxygen on the surface of *p-*Si passivated with hydrogen, are reported. The general idea of the above mentioned studies is that the crystal lattice of nanoparticles, whose surface is completely passivated with hydrogen, is practically the same as the lattice of the silicon crystal. However, if oxygen atoms appear at the nanoparticle surface, they can form the Si–O–Si and (Si=O) bonds and, thus, distort the lattice at the distances up to 0.5 nm. In this space region, the distortions of angles between the Si–Si bonds in the crystal lattice can be as large as 10° (Tsang at al., 1992). Therefore, if the surface of a nanoparticle of a diameter smaller than 3 nm is coated with the SiO2 oxide, the crystal lattice is distorted within a noticeable volume fraction of such particle. As a consequence, if the *p-*Si surface is etched in the solution of HF, the Raman spectrum involves only one peak similar to the *P*1 peak. If *p-*Si is exposed to oxygen in oxygen containing atmosphere, the Raman spectrum exhibits also the *P*2 peak along with the *P*1 peak. From the above mentioned studies and from the analysis of the Raman spectra discussed here, we can make the statement presented below. At the surface of *nc*-Si nanoparticles in all samples, there is a noticeable number of oxygen atoms, which distort the crystal lattice in these particles and bring about the appearance of the *P*2 peak in the Raman spectra. Since the average nanoparticle's dimensions in film *S*2 are smaller than those in powder *S*1, the effect of these oxygen atoms on the crystal lattice structure in film *S*2 is more pronounced than the effect in powder *S*1. As a result, the volume fraction of the crystal phase in film *S*2 is reduced compared to that in *S*1.

Etching of the *nc*-Si particles in the solution of the (HF + HNO3) acids results in a decrease in the particle dimensions. However, in this case, the total number of oxygen atoms at the nanoparticle's surface decreases, since a portion of oxygen atoms is replaced with hydrogen atoms. Therefore, in film *S*3 two opposite processes are bound to occur. One process related to the decrease in the nanoparticle's dimensions yields a decrease in *Xc*, whereas the other process related to the decrease in the number of oxygen atoms at the nanoparticle surface brings about an increase in *Xc*. In film *S*3, we experimentally observe the parameter *X*<sup>c</sup> larger than *X*<sup>c</sup> in film *S*2; therefore, we can conclude that, on etching of the *nc*-Si particles, the latter process dominates over the former one.

#### **2.1.2.2 Ellipsometric spectra**

414 Smart Nanoparticles Technology

crystalline and amorphous fractions (corresponding to the *P*1 and *P*2 peaks). According to (Kakinuma at al., 1991), the quantity η for silicon is η = 0.8–0.9. In the calculations, we set η = 0.8. For samples *S*1, *S*2 and *S*3, the values of the parameter *Xc* are 0.45, 0.35 and 0.50

From these values of *Xc*, it follows that almost a half of the volume of the particles is

From comparison of the above values, it is evident that, in film *S*2 deposited at the second stage of centrifuging from the sol with the initial *nc*-Si powder, the parameter *Xc* is smaller than *Xc* for the initial powder. The average particle's dimension in film *S*2 is smaller than that in the initial powder. Correspondingly, the surface area to volume ratio for the particles in the *S*2 film is larger than the corresponding ratio in the initial powder. Therefore, the effect of the nanoparticle surface on the general properties of the nanoparticles in film *S*2 is bound to be more pronounced that the corresponding effect in the initial powder. Consequently, the smaller value of *Xc* (the higher degree of amorphization of the particles) in film *S*2 in comparison with *Xc* in sample *S*1 suggests that the disordered regionis at the nanoparticle surface rather than in the nanoparticle core. However, for film *S*3 the value of *Xc* is larger than *Xc* for film *S*2, although the average particle's dimensions in these films are comparable. Such difference suggests that the degree of disorder of particle surfaces in film

Since film *S*3 are deposited from the sols of the *nc*-Si powders subjected to etching, such lower degree of disorder in these films is due to the effect of the HF and HNO3 acids on the particle surface. Here, it is reasonable to mention the studies ( Luppi & Ossicini, 2005; Puzder at al., 2002), in which the effect of oxygen atoms on the structure of silicon clusters and on the degree of ordering of the Si crystal lattice in nanoparticles is analyzed, and the studies (Ma at al., 2000 Tsang at al., 1992; ), in which the changes induced in the Raman peak similar to the *P*2 peak (Fig. 3) by the effect of oxygen on the surface of *p-*Si passivated with hydrogen, are reported. The general idea of the above mentioned studies is that the crystal lattice of nanoparticles, whose surface is completely passivated with hydrogen, is practically the same as the lattice of the silicon crystal. However, if oxygen atoms appear at the nanoparticle surface, they can form the Si–O–Si and (Si=O) bonds and, thus, distort the lattice at the distances up to 0.5 nm. In this space region, the distortions of angles between the Si–Si bonds in the crystal lattice can be as large as 10° (Tsang at al., 1992). Therefore, if the surface of a nanoparticle of a diameter smaller than 3 nm is coated with the SiO2 oxide, the crystal lattice is distorted within a noticeable volume fraction of such particle. As a consequence, if the *p-*Si surface is etched in the solution of HF, the Raman spectrum involves only one peak similar to the *P*1 peak. If *p-*Si is exposed to oxygen in oxygen containing atmosphere, the Raman spectrum exhibits also the *P*2 peak along with the *P*1 peak. From the above mentioned studies and from the analysis of the Raman spectra discussed here, we can make the statement presented below. At the surface of *nc*-Si nanoparticles in all samples, there is a noticeable number of oxygen atoms, which distort the crystal lattice in these particles and bring about the appearance of the *P*2 peak in the Raman spectra. Since the average nanoparticle's dimensions in film *S*2 are smaller than those in powder *S*1, the effect of these oxygen atoms on the crystal lattice structure in film *S*2 is more pronounced than the

characterized by a high degree of disorder of the crystal lattice.

is the ratio between the integrated backscattering's cross sections in the

where **c**

respectively.

**a** 

*S*3 is lower than that in film *S*2.

In the experiment, the ellipsometric angles ψ and Δ were measured as functions of the wavelength of a light beam incident at the angle Φ0 on the free flat surface of the *nc*-Si film. The films under study were applied on glass and quartz substrates and on quartz substrates with preliminarily deposited aluminum films. The *nc*-Si film thicknesses (1–2 μm) were measured independently. When processing the ellipsometric data, the *nc*-Si films under study were considered as a 3D medium in air medium. The complex refractive index *N* = *n* – *ik*, where *n* is the film refractive index and *k* is the extinction coefficient, was determined by the expression (Azzam & Bashara, 1977)

$$N = N\_0 \sin \phi\_0 \sqrt{1 + \left(\frac{1 - \rho}{1 + \rho}\right)^2 t g^2 \phi\_0} \tag{2}$$

Here, ρ = eiΔ· tgψ and *N*0 are the complex refractive index of an ambient medium (air), which was equal to unity in the case at hand. It is known that formula (2) yields accurate values only when light is reflected from a semi-infinite medium with a boundary with an atomically clean surface. If impurities or an oxide filmare on the boundary, they introduce errors to the calculated values. In (Tompkins & Irene, 2005), the values *n* and *k* were compared for crystalline silicon (*c*-Si) in the absence and presence of the oxide film on its surface. It follows from this comparison that, in the presence of a SiO2 film to 2 nm thick on the silicon surface, the value of *n* is almost identical to that of *c*-Si in the incident photon energy range of 1–3.4 eV; in the range of 3.4–5 eV, the refractive index differs from *n* of *c*-Si no more than by 20%, as well as *k*. However, in the range of 1–3.4 eV, the value of k in the presence of the SiO2 film almost twice exceeds the *c*-Si extinction.

Since the real ε' and imaginary ε'' components of the medium permittivity are related to *n*  and *k* by the known expressions ε' = *n*2 – *k*2 and ε'' = 2*nk*, it can be expected that the values of ε' calculated by Eq. (2) for *nc*-Si films will be slightly systematically underestimated, while the values of ε'' will be overestimated.

Nevertheless, representation of the pseudo dielectric functions by relation (2) is very convenient and is quite often used to study the dielectric properties of materials. For example, dielectric parameters of *por*-Si were studied using this equation in (Pickering, 1984). As applied to the present study, an analysis of the spectra obtained using formula (2)

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 417

**3**

**1**

**4**

Fig. 6. (*1*–*3*) - absorption spectra of *nc*-Si films, obtained from ellipsometric data; (*4*) - absorption spectrum of film 1, obtained from its transmission spectrum; and (*5*) -

**2**

This figure also shows the absorption spectrum of the *nc*-Si film formed by unetched nanoparticles, which was calculated from its transmission spectrum. As a reference, the absorption spectrum of crystalline silicon (Aspens & Studna, 1983) is also shown. The size distribution of unetched and etched *nc*-Si particles used to precipitate films 1 and 3 are

1,0 1,5 2,0 2,5 3,0 3,5 4,0 <sup>101</sup>

**h eV**

A comparison of the absorption spectra of the film *nc*-Si grown from unetched nanoparticles, which were obtained from ellipsometric measurements and by processing the corresponding transmission spectrum, shows that the values of α obtained by ellipsometry are higher than the similar values calculated from transmission spectra, and this difference increases with decreasing the incident photon energies. As noted above, this difference is associated with the error of the extinction coefficient calculation by formula (2). At the same time, both spectra exhibit strong absorption of the *nc*-Si film in comparison with *c*-Si at energies lower than 1.5 eV. Such absorption enhancement in the low energy photon region is also inherent to the film grown by etched nanoparticles. At energies higher than 3 eV, all spectra exhibit absorption weaker than that of *c*-Si. In the Fig. 1, we can see that the diameter of an appreciable fraction of particles used to form films is smaller than 10 nm; therefore, the most probable cause of a decrease in the film absorption in the high-energy photon region is widening of the band gap in crystalline cores of silicon nanoparticles due to quantum

The permittivity spectra of *nc*-Si films were calculated from the measured frequency dependences of the capacitance of corresponding samples and their impedances,

absorption spectrum of crystalline silicon.

102

**5**

103

 **cm-1**

104

105

106

shown in Fig. 1.

confinement.

**2.1.2.3 Dielectric dispersion** 

Z(ν) = Z′ - iZ′′, Z(ν) = U(ν) / I(ν),

was limited by the energy range of incident photons, in which films strongly absorbed incident probe radiation, which could not reach the substrate surface in this case. If probe radiation reached the substrate surface with precipitated film, an interference structure arose in the spectra, which consisted of alternating minima and maxima. Such a structure at energies lower than 2 eV is easily seen in Fig. 5 (curves *3* and *3* ').

Fig. 5. Spectra of (*1*–*3*) real and imaginary (*1*'–*3*') permittivity components of *nc*-Si films precipitated on various substrates: (*1*, *1*') film of initial (unetched) nanoparticles on the glass substrate; (*2*, *2*') film of nanoparticles preliminarily etched in a HF/HNO3 acid mixture on the quartz substrate; (*3*, *3*') *nc*-Si film of initial nanoparticles on the glass substrate with a preliminary deposited aluminum film; and (*4*, *4*') Bruggeman approximation for ε' and ε'', respectively.

We can see the spectra of pseudo dielectric functions ε' and ε'' of *nc*-Si films fabricated by precipitating initial silicon nanoparticles on the glass substrate and nanoparticles preliminary etched in a HF/HNO3 acid mixture in a water for 30 min on the quartz substrate. Figure 5 also shows the ε' and ε'' spectra of *nc-*Si films precipitated on the glass substrate with a preliminarily deposited aluminum film.

It follows from this figure that the obtained values of ε' and ε'' are significantly lower than the similar values of *c*-Si.

Figure 6 shows the absorption spectra α(*E*) of the same films, obtained by the relation:

$$\alpha(E) = \frac{4\pi\nu}{c}k = \frac{4\pi E}{c\hbar}k\tag{3}$$

where *E* = *h*ν is the energy of the incident photon and *k* is the experimentally measured extinction coefficient.

Fig. 6. (*1*–*3*) - absorption spectra of *nc*-Si films, obtained from ellipsometric data; (*4*) - absorption spectrum of film 1, obtained from its transmission spectrum; and (*5*) absorption spectrum of crystalline silicon.

This figure also shows the absorption spectrum of the *nc*-Si film formed by unetched nanoparticles, which was calculated from its transmission spectrum. As a reference, the absorption spectrum of crystalline silicon (Aspens & Studna, 1983) is also shown. The size distribution of unetched and etched *nc*-Si particles used to precipitate films 1 and 3 are shown in Fig. 1.

A comparison of the absorption spectra of the film *nc*-Si grown from unetched nanoparticles, which were obtained from ellipsometric measurements and by processing the corresponding transmission spectrum, shows that the values of α obtained by ellipsometry are higher than the similar values calculated from transmission spectra, and this difference increases with decreasing the incident photon energies. As noted above, this difference is associated with the error of the extinction coefficient calculation by formula (2). At the same time, both spectra exhibit strong absorption of the *nc*-Si film in comparison with *c*-Si at energies lower than 1.5 eV. Such absorption enhancement in the low energy photon region is also inherent to the film grown by etched nanoparticles. At energies higher than 3 eV, all spectra exhibit absorption weaker than that of *c*-Si. In the Fig. 1, we can see that the diameter of an appreciable fraction of particles used to form films is smaller than 10 nm; therefore, the most probable cause of a decrease in the film absorption in the high-energy photon region is widening of the band gap in crystalline cores of silicon nanoparticles due to quantum confinement.

#### **2.1.2.3 Dielectric dispersion**

416 Smart Nanoparticles Technology

was limited by the energy range of incident photons, in which films strongly absorbed incident probe radiation, which could not reach the substrate surface in this case. If probe radiation reached the substrate surface with precipitated film, an interference structure arose in the spectra, which consisted of alternating minima and maxima. Such a structure at

Fig. 5. Spectra of (*1*–*3*) real and imaginary (*1*'–*3*') permittivity components of *nc*-Si films precipitated on various substrates: (*1*, *1*') film of initial (unetched) nanoparticles on the glass substrate; (*2*, *2*') film of nanoparticles preliminarily etched in a HF/HNO3 acid mixture on the quartz substrate; (*3*, *3*') *nc*-Si film of initial nanoparticles on the glass substrate with a preliminary deposited aluminum film; and (*4*, *4*') Bruggeman approximation for ε' and ε'',

**2′ 3′**

4

1,5 2,0 2,5 3,0 3,5 4,0 4,5 0,0

4′

**h, eV**

**3 1**

**1′**

**2**

We can see the spectra of pseudo dielectric functions ε' and ε'' of *nc*-Si films fabricated by precipitating initial silicon nanoparticles on the glass substrate and nanoparticles preliminary etched in a HF/HNO3 acid mixture in a water for 30 min on the quartz substrate. Figure 5 also shows the ε' and ε'' spectra of *nc-*Si films precipitated on the glass

It follows from this figure that the obtained values of ε' and ε'' are significantly lower than

*c ch* 

where *E* = *h*ν is the energy of the incident photon and *k* is the experimentally measured

 

(3)

Figure 6 shows the absorption spectra α(*E*) of the same films, obtained by the relation:

substrate with a preliminarily deposited aluminum film.

0,5

1,0

' **, "**

1,5

2,0

2,5

4 4 ( ) *<sup>E</sup> E kk*

respectively.

the similar values of *c*-Si.

extinction coefficient.

energies lower than 2 eV is easily seen in Fig. 5 (curves *3* and *3* ').

The permittivity spectra of *nc*-Si films were calculated from the measured frequency dependences of the capacitance of corresponding samples and their impedances, Z(ν) = Z′ - iZ′′, Z(ν) = U(ν) / I(ν),

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 419

(*T* = 297 K) was 9×10–10 Ω–1 m–1 and was used to calculate σAC(ν). The dependence σAC(ν) is

Fig. 8a. (*1*, *2*) Frequency dependences of ε' and ε'', obtained from impedance spectra. Cole– Cole approximation of ε' - (*3*) and ε'' spectra (*4*) without and (*5*) with consideration of the

5

<sup>100</sup> <sup>101</sup> <sup>10</sup><sup>2</sup> <sup>10</sup><sup>3</sup> <sup>104</sup> <sup>10</sup><sup>5</sup> <sup>10</sup><sup>6</sup> <sup>0</sup>

Frequency (Hz)

1,5 3

Fig. 8b. (*1*) Dependence ε''(ε') for the *nc*-Si film. Cole–Cole approximation (*2*) without and (*3*)

3,5 4,0 4,5 5,0 5,5 6,0 0,0

'

1

2

This figure suggests that σAC(ν) can be well approximated by the power law dependence

with consideration of the contribution of free carriers.

0,5

1,0

1

', "

4

4

5

6

3

2

1

"

shown in Fig. 9 on a log scale.

contribution of free carriers.

with an exponent of 0.74.

where *U*(ν) is the potential difference at sample electrodes and *I*(ν) is the current flowing through the sample.

In what follows, we will analyze the dielectric properties of the Al–*nc*-Si–Al sandwich system in which the *n*-Si layer was precipitated from the sol with unetched nanoparticles. The thickness of this film was 2 μm; the geometrical capacitance of this system was *C*0 = 1.15 × 10–10 F. The dielectric dispersion of this film is typical of other films obtained in a similar way from similar *nc*-Si particles.

Figure 7 shows the frequency dependence of the capacitance of this system. The capacitance was measured in parallel connection. The figure also shows the spectrum of the real component ε'(ν) of the film permittivity, calculated from the relation ε' = *C*(ν)/*C*0.

Fig. 7. Frequency dependence of the *nc*-Si film capacitance. The dashed curve is the approximation by function (3) (see text).

The ε'(ν) and ε''(ν) spectra of *nc*-Si films were also determined from the frequency dependence the film impedance by the expression

$$\text{i.e.} = \text{e}' - i\text{e}'' = \frac{1}{i2\pi\text{vC}\_0 Z(\text{v})} \tag{4}$$

Figure 8.a shows the dependences ε'(ν) and ε''(ν) calculated by the above method for the film under study. A comparison of the values of ε'(ν) obtained from *C*(ν) and *Z*(ν) measurements shows good quantitative and qualitative agreement of the values calculated in two different ways; in both cases, in the frequency range of 10 ≤ ν ≤ 106 Hz, the value of ε'(ν) is within 6– 3.4 and decreases with frequency.

#### **2.1.2.4 AC conductivity of films I**

The ac conductivity of *nc*-Si films was determined by the known relation

$$
\sigma\_{\rm AC}(\mathbf{v}) \cdot \sigma(\mathbf{0}) = \varepsilon\_0 \cdot \mathbf{\varepsilon}''(\mathbf{v}) \cdot 2\mathbf{n} \mathbf{v}
$$

where σ(0) is the dark conductivity of films in a dc electric field and ε0 = 8.85 × 10–12 F/m is the permittivity of free space. The value of σ(0) of the film under study at room temperature

where *U*(ν) is the potential difference at sample electrodes and *I*(ν) is the current flowing

In what follows, we will analyze the dielectric properties of the Al–*nc*-Si–Al sandwich system in which the *n*-Si layer was precipitated from the sol with unetched nanoparticles. The thickness of this film was 2 μm; the geometrical capacitance of this system was *C*0 = 1.15 × 10–10 F. The dielectric dispersion of this film is typical of other films obtained in a similar

Figure 7 shows the frequency dependence of the capacitance of this system. The capacitance was measured in parallel connection. The figure also shows the spectrum of the real

component ε'(ν) of the film permittivity, calculated from the relation ε' = *C*(ν)/*C*0.

Fig. 7. Frequency dependence of the *nc*-Si film capacitance. The dashed curve is the

<sup>101</sup> <sup>102</sup> <sup>103</sup> <sup>104</sup> <sup>105</sup> <sup>106</sup> 3,5x10-10

*i*

The ac conductivity of *nc*-Si films was determined by the known relation

The ε'(ν) and ε''(ν) spectra of *nc*-Si films were also determined from the frequency

Frequency (Hz)

Figure 8.a shows the dependences ε'(ν) and ε''(ν) calculated by the above method for the film under study. A comparison of the values of ε'(ν) obtained from *C*(ν) and *Z*(ν) measurements shows good quantitative and qualitative agreement of the values calculated in two different ways; in both cases, in the frequency range of 10 ≤ ν ≤ 106 Hz, the value of ε'(ν) is within 6–

σАС(ν) - σ(0) = ε0·ε″(ν)·2πν where σ(0) is the dark conductivity of films in a dc electric field and ε0 = 8.85 × 10–12 F/m is the permittivity of free space. The value of σ(0) of the film under study at room temperature

0 1 2 ()

(4)

3,2 3,4 3,6 3,8 4,0 4,2 4,4 4,6 4,8 5,0

'

*i CZ*

through the sample.

way from similar *nc*-Si particles.

approximation by function (3) (see text).

Capacity ( F)

3.4 and decreases with frequency. **2.1.2.4 AC conductivity of films I** 

dependence the film impedance by the expression

4,0x10-10

4,5x10-10

5,0x10-10

5,5x10-10

(*T* = 297 K) was 9×10–10 Ω–1 m–1 and was used to calculate σAC(ν). The dependence σAC(ν) is shown in Fig. 9 on a log scale.

Fig. 8a. (*1*, *2*) Frequency dependences of ε' and ε'', obtained from impedance spectra. Cole– Cole approximation of ε' - (*3*) and ε'' spectra (*4*) without and (*5*) with consideration of the contribution of free carriers.

Fig. 8b. (*1*) Dependence ε''(ε') for the *nc*-Si film. Cole–Cole approximation (*2*) without and (*3*) with consideration of the contribution of free carriers.

This figure suggests that σAC(ν) can be well approximated by the power law dependence with an exponent of 0.74.

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 421

like structures of the films II and III with Mg or Al electrodes were heated to a temperature

The values of ε'and ε'' of films I and II in the frequency range below 104 Hz are quite close to each other. The main difference between the permittivity's spectra of these films observed in

In this frequencies region permittivity spectra of the films II reveal sharp decrease in ε' while the dielectric losses of ε'' has a form of enough narrow peak (see Figure 10). Such behavior of the spectrum is typical for the Debye dipole relaxation process, and will be discussed

Fig. 10. The frequency dependence of ε 'and ε'' for: Film I: - (1 and 1′), Film II - (2, 2′),

The ε (ω) spectra of the films III, similar to those of the films II, but for the films III decreasing of ε 'is observed in the frequency of large 104Hz. The frequency at which a maximum of dielectric loss ε'' observed in films III, is νmax ≈ 9,7 · 103 Hz, while for films II, this frequency is 7,5·104 Hz (see Figure 10). At frequencies ν ≤ 104 Hz the magnitude of ε' of films III reveal a sharp increase with decreasing frequency of the external electric field and

100 10<sup>1</sup> 102 10<sup>3</sup> 104 105 10<sup>6</sup>

1

Frequency (Hz)

In contrast to the film I conductivity of the films II and III may be approximated by a power law σ(ω) ~ ωs on the frequency of the alternating electric field only in a very limited range of

of 1400 C and held at that temperature for 30 minutes.

**2.2.2.1 Dielectric dispersion of the films II** 

the frequency range higher of 105 Hz

**2.2.2 Experimental results** 

later.

Film III - (3, 3').

**2.2.2.2 Dielectric dispersion of the films III** 

0

5

10

15

',

"

3'

2'

1'

2

3

20

25

30

35

**2.2.2.3 AC conductivity of the films II and III** 

greatly exceeds the corresponding values of the films I and II.

Fig. 9. (*1*) Frequency dependence of the ac conductivity of the *nc*-Si film; (*2*) dependence σac(ν) defined by the DCA model (see text) using experimentally measured ε*s*, ε∞, and σ(0).

#### **2.2 Films deposited from aged nc-Si sols (Films II) and from aged nc-Si sols with tetraaniline (Films III)**

#### **2.2.1 Samples**

The previous sections have presented experimental results of a study of thin films obtained from nanoparticles synthesized by one week prior to their deposition on the substrate. As already mentioned silicon nanoparticles could be no precipitation of sols for a long time. By the time of this writing, the silicon nanoparticles used for the deposition of films analyzed in the previous sections, were in sols over two years and in the next section we will report on the results of studies of the properties of the films deposited on substrates of these sols. It should be noted here that the film deposited on a substrate not as a result of centrifugation of sols, and with the spin coating method. Also in the following sections we will analyze the dielectric properties of films deposited from a 2-year nc-Si sols, in which the conductive tetramer – tetraaniline was added (Wang & MacDiarmid, 2002).

Because pure tetraaniline has low conductivity, for its increase the tetra aniline doped with p-toluensulfonic acid (CH3(C6H4)SO3H). Briefly the process of doping was as follows. A solution of tetraaniline and dimethyl sulfoxide (DMSO) as a solvent mixed with a DMSO solution of para-toluenesulfonic acid, so that the resulting solution in the molar ratio of tetra aniline and acid was 1.5. At the end of doping the color of resulting solution became green. The conductivity of the film which was deposited on a substrate of resulting tetraaniline solution was at room temperature 10-4 Ohm-1m-1. The resulting solution of tetraaniline in DMSO was added to the sol of silicon nanoparticles in ethanol in a mass ratio 1:10 before deposition of film on substrates.

As we have already reported, the films deposited on a substrate of silicon nanoparticles in a week after their synthesis we call the film**s** I; films, obtained from the same nanoparticles, but two years after their synthesis (aged nanoparticles) - films II and films with aged nanoparticles and addition of tetraaniline - films III. Before the measurement the sandwich like structures of the films II and III with Mg or Al electrodes were heated to a temperature of 1400 C and held at that temperature for 30 minutes.

#### **2.2.2 Experimental results**

420 Smart Nanoparticles Technology

Fig. 9. (*1*) Frequency dependence of the ac conductivity of the *nc*-Si film; (*2*) dependence σac(ν) defined by the DCA model (see text) using experimentally measured ε*s*, ε∞, and σ(0).

102 10<sup>3</sup> 10<sup>4</sup> 105 10<sup>6</sup>

1

2

Frequency, Hz

**2.2 Films deposited from aged nc-Si sols (Films II) and from aged nc-Si sols with** 

tetramer – tetraaniline was added (Wang & MacDiarmid, 2002).

The previous sections have presented experimental results of a study of thin films obtained from nanoparticles synthesized by one week prior to their deposition on the substrate. As already mentioned silicon nanoparticles could be no precipitation of sols for a long time. By the time of this writing, the silicon nanoparticles used for the deposition of films analyzed in the previous sections, were in sols over two years and in the next section we will report on the results of studies of the properties of the films deposited on substrates of these sols. It should be noted here that the film deposited on a substrate not as a result of centrifugation of sols, and with the spin coating method. Also in the following sections we will analyze the dielectric properties of films deposited from a 2-year nc-Si sols, in which the conductive

Because pure tetraaniline has low conductivity, for its increase the tetra aniline doped with p-toluensulfonic acid (CH3(C6H4)SO3H). Briefly the process of doping was as follows. A solution of tetraaniline and dimethyl sulfoxide (DMSO) as a solvent mixed with a DMSO solution of para-toluenesulfonic acid, so that the resulting solution in the molar ratio of tetra aniline and acid was 1.5. At the end of doping the color of resulting solution became green. The conductivity of the film which was deposited on a substrate of resulting tetraaniline solution was at room temperature 10-4 Ohm-1m-1. The resulting solution of tetraaniline in DMSO was added to the sol of silicon nanoparticles in ethanol in a mass ratio 1:10 before

As we have already reported, the films deposited on a substrate of silicon nanoparticles in a week after their synthesis we call the film**s** I; films, obtained from the same nanoparticles, but two years after their synthesis (aged nanoparticles) - films II and films with aged nanoparticles and addition of tetraaniline - films III. Before the measurement the sandwich

**tetraaniline (Films III)** 

10-9

10-8

AC- (0)

(Ohm-1m-1)

10-7

10-6

deposition of film on substrates.

**2.2.1 Samples** 

## **2.2.2.1 Dielectric dispersion of the films II**

The values of ε'and ε'' of films I and II in the frequency range below 104 Hz are quite close to each other. The main difference between the permittivity's spectra of these films observed in the frequency range higher of 105 Hz

In this frequencies region permittivity spectra of the films II reveal sharp decrease in ε' while the dielectric losses of ε'' has a form of enough narrow peak (see Figure 10). Such behavior of the spectrum is typical for the Debye dipole relaxation process, and will be discussed later.

Fig. 10. The frequency dependence of ε 'and ε'' for: Film I: - (1 and 1′), Film II - (2, 2′), Film III - (3, 3').

## **2.2.2.2 Dielectric dispersion of the films III**

The ε (ω) spectra of the films III, similar to those of the films II, but for the films III decreasing of ε 'is observed in the frequency of large 104Hz. The frequency at which a maximum of dielectric loss ε'' observed in films III, is νmax ≈ 9,7 · 103 Hz, while for films II, this frequency is 7,5·104 Hz (see Figure 10). At frequencies ν ≤ 104 Hz the magnitude of ε' of films III reveal a sharp increase with decreasing frequency of the external electric field and greatly exceeds the corresponding values of the films I and II.

#### **2.2.2.3 AC conductivity of the films II and III**

In contrast to the film I conductivity of the films II and III may be approximated by a power law σ(ω) ~ ωs on the frequency of the alternating electric field only in a very limited range of

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 423

other words, the oxidized crystalline silicon nanoparticle with a size smaller than 10 nm should exhibit amorphous properties to an appreciable extent. We have confirmed this statement previously based on an analysis of Raman spectra of *nc*-Si thin films (see section 2.A.2.1 and also Dorofeev at al., *2009*). The second cause of a decrease in the permittivity is

To estimate the relation between crystalline and amorphous film components and their porosity, we use the Bruggeman EMA model. In the EMA approximation, the effective permittivity of the inhomogeneous medium consisting of spherical microobjects with permittivities ε1, ε2, …,ε*N* – 1, immersed into a medium with ε*N* (ε*N* ≡ εe) is determined from

0

*N i i f* 

1

(5)

<sup>1</sup>

 1

 

2

is the degree of medium volume filling with an element with permittivity ε*<sup>i</sup>* and *Vi* is the

Initially, to determine ε*<sup>e</sup>* of the films under study, we assumed that the medium is two-phase and consists of purely crystalline silicon nanoparticles and the air gaps. In this case, Eq. (5) was reduced to a sum of two terms; knowing the dispersion relation of crystalline silicon, it was required to determine *f*1 and *f*2 so that approximating dispersion profiles would be identical to experimental ε'(ν) and ε''(ν). However, it was impossible to achieve satisfactory

Since the oxidation state of nanoparticles is unknown, we assumed that each particle in the two phase Bruggeman model behaves on average as a SiO*x* medium (rather than as crystalline silicon), where 0 ≤*x* ≤ 2 was a fitting parameter, as well as *f*1 and *f*2. The ε'(ν) and ε''(ν) spectra for SiO*<sup>x</sup>* in the entire range 0 ≤ *x* ≤ 2 were taken from (Zuter, 1980), in which it was supposed that SiO*<sup>x</sup>* is a mixture of Si–Si*y*O4 – *<sup>y</sup>* tetrahedra; the random parameter takes values from 0 to 4 (random binding model (Hubner, 1980)). Using these spectra, it became possible to achieve good approximation of the experimental dependences ε'(ν) and ε''(ν) at *x*  = 1 and *f*1 = *f*2 = 0.5. The approximating EMA spectra for these parameters are shown in Fig. 5 by dashed curves. Thus, it was shown that the *nc*-Si films under study on average behave as media consisting of SiO with a porosity of 0.5. Here we note already mentioned study (Pickering, 1984) in which the ε'(ν) and ε''(ν) spectra were measured and which are qualitatively and quantitatively rather similar to the spectra analyzed in the present study. The absorption spectra of *nc*-Si films calculated from ellipsometric data are quite typical. As seen in Fig. 6, the film absorption at incident photon energies below 3 eV is stronger than that of *c*-Si; at higher energies, it is significantly lower. Such an absorption behavior shows that the SiO*x* shell with high density of states of defects near to the phase interface with the crystalline core mainly contributes to absorption for low energy photons; photons with

*i e*

air gaps between nanoparticles, which appear during film formation.

*N*

*i i i e f* 

the equation

where:

1

*i i N*

*<sup>V</sup> <sup>f</sup>*

 

*i i*

volume occupied by this element.

approximation at no values of *f*1 and *f*2.

*V* 

frequencies. So for films II, this area is 1 ≤ ν ≤ 4·102 Hz in which the exponent is 0.66, and for films III conductivity satisfactorily approximated by a power law with exponent s = 0,63 in the frequency range 5 ≤ ν ≤ 5·102 Hz.

For both types of films, a significant increase of the growth rate of the conductivity is observed at frequencies exceeding 2 · 103 Hz, however, the conductivity of the films II and III begins very weakly dependent on frequency of external electric field (see Figure 11) at frequencies larger of 105 and 3 · 104 Hz respectively.

The conductivity of films III containing tetraaniline exceeds the conductivity of the films II in the frequency range 1 ≤ ν ≤ 3·104 Hz ,while at higher frequencies observed the opposite picture in which the conductivity of the films II is higher then that of film**s** III (see the same figure).

Fig. 11. Frequency dependence of AC conductivity of: films I - (1), film II - (2) and film III - (3)

## **2.3 Discussion**

#### **2.3.1 Ellipsometry of films I**

Analysis of ellipsometric spectra shows that the value of ε' of the *nc*-Si films under study varies in the range of 2.1–1.1 in the energy range of 2–4.4 eV or in the frequency range of 5×1014 – 1×1015 Hz of the electromagnetic field, respectively, which is significantly below the values typical of *c*-Si in this range. In our opinion, there are two causes resulting in such low ε' and ε''. One is that *nc*-Si particles contacted with atmospheric oxygen for some time during film preparation; therefore, their surface was coated with a SiO*x* + SiO2 layer (0 ≤ *x* ≤ 2). Silicon nanoparticles oxidation was studied by Schuppler at al. (Schuppler at al., 1995), in that study the SiO*<sup>x</sup>* layer thickness on their surface was determined as a function of the nanoparticle diameter. It was shown that the SiO*<sup>x</sup>* + SiO2 layer thickness in the nanoparticle diameter range of 10–3 nm is ~1 nm. However, this means that the ratio of the volume of the crystalline silicon core to the volume of the SiO*x* amorphous shell is from 100 to 40%. In other words, the oxidized crystalline silicon nanoparticle with a size smaller than 10 nm should exhibit amorphous properties to an appreciable extent. We have confirmed this statement previously based on an analysis of Raman spectra of *nc*-Si thin films (see section 2.A.2.1 and also Dorofeev at al., *2009*). The second cause of a decrease in the permittivity is air gaps between nanoparticles, which appear during film formation.

To estimate the relation between crystalline and amorphous film components and their porosity, we use the Bruggeman EMA model. In the EMA approximation, the effective permittivity of the inhomogeneous medium consisting of spherical microobjects with permittivities ε1, ε2, …,ε*N* – 1, immersed into a medium with ε*N* (ε*N* ≡ εe) is determined from the equation

$$\sum\_{i=1}^{N} f\_i \frac{\left(\varepsilon\_i - \varepsilon\_\varepsilon\right)}{\left(\varepsilon\_i + 2\varepsilon\_\varepsilon\right)} = 0 \quad \sum\_{i=1}^{N} f\_i = 1 \tag{5}$$

where: 1 *i i N i i <sup>V</sup> <sup>f</sup> V* 

422 Smart Nanoparticles Technology

frequencies. So for films II, this area is 1 ≤ ν ≤ 4·102 Hz in which the exponent is 0.66, and for films III conductivity satisfactorily approximated by a power law with exponent s = 0,63 in

For both types of films, a significant increase of the growth rate of the conductivity is observed at frequencies exceeding 2 · 103 Hz, however, the conductivity of the films II and III begins very weakly dependent on frequency of external electric field (see Figure 11) at

The conductivity of films III containing tetraaniline exceeds the conductivity of the films II in the frequency range 1 ≤ ν ≤ 3·104 Hz ,while at higher frequencies observed the opposite picture in which the conductivity of the films II is higher then that of film**s** III (see the same

Fig. 11. Frequency dependence of AC conductivity of: films I - (1), film II - (2) and

Analysis of ellipsometric spectra shows that the value of ε' of the *nc*-Si films under study varies in the range of 2.1–1.1 in the energy range of 2–4.4 eV or in the frequency range of 5×1014 – 1×1015 Hz of the electromagnetic field, respectively, which is significantly below the values typical of *c*-Si in this range. In our opinion, there are two causes resulting in such low ε' and ε''. One is that *nc*-Si particles contacted with atmospheric oxygen for some time during film preparation; therefore, their surface was coated with a SiO*x* + SiO2 layer (0 ≤ *x* ≤ 2). Silicon nanoparticles oxidation was studied by Schuppler at al. (Schuppler at al., 1995), in that study the SiO*<sup>x</sup>* layer thickness on their surface was determined as a function of the nanoparticle diameter. It was shown that the SiO*<sup>x</sup>* + SiO2 layer thickness in the nanoparticle diameter range of 10–3 nm is ~1 nm. However, this means that the ratio of the volume of the crystalline silicon core to the volume of the SiO*x* amorphous shell is from 100 to 40%. In

100 10<sup>1</sup> 10<sup>2</sup> 103 104 10<sup>5</sup> 10<sup>6</sup>

Frequency (Hz)

the frequency range 5 ≤ ν ≤ 5·102 Hz.

figure).

film III - (3)

**2.3 Discussion** 

**2.3.1 Ellipsometry of films I** 

frequencies larger of 105 and 3 · 104 Hz respectively.

10-10

10-9

10-8

Conductivity (Ohm



m

)

3

1

2

10-7

10-6

10-5

is the degree of medium volume filling with an element with permittivity ε*<sup>i</sup>* and *Vi* is the volume occupied by this element.

Initially, to determine ε*<sup>e</sup>* of the films under study, we assumed that the medium is two-phase and consists of purely crystalline silicon nanoparticles and the air gaps. In this case, Eq. (5) was reduced to a sum of two terms; knowing the dispersion relation of crystalline silicon, it was required to determine *f*1 and *f*2 so that approximating dispersion profiles would be identical to experimental ε'(ν) and ε''(ν). However, it was impossible to achieve satisfactory approximation at no values of *f*1 and *f*2.

Since the oxidation state of nanoparticles is unknown, we assumed that each particle in the two phase Bruggeman model behaves on average as a SiO*x* medium (rather than as crystalline silicon), where 0 ≤*x* ≤ 2 was a fitting parameter, as well as *f*1 and *f*2. The ε'(ν) and ε''(ν) spectra for SiO*<sup>x</sup>* in the entire range 0 ≤ *x* ≤ 2 were taken from (Zuter, 1980), in which it was supposed that SiO*<sup>x</sup>* is a mixture of Si–Si*y*O4 – *<sup>y</sup>* tetrahedra; the random parameter takes values from 0 to 4 (random binding model (Hubner, 1980)). Using these spectra, it became possible to achieve good approximation of the experimental dependences ε'(ν) and ε''(ν) at *x*  = 1 and *f*1 = *f*2 = 0.5. The approximating EMA spectra for these parameters are shown in Fig. 5 by dashed curves. Thus, it was shown that the *nc*-Si films under study on average behave as media consisting of SiO with a porosity of 0.5. Here we note already mentioned study (Pickering, 1984) in which the ε'(ν) and ε''(ν) spectra were measured and which are qualitatively and quantitatively rather similar to the spectra analyzed in the present study.

The absorption spectra of *nc*-Si films calculated from ellipsometric data are quite typical. As seen in Fig. 6, the film absorption at incident photon energies below 3 eV is stronger than that of *c*-Si; at higher energies, it is significantly lower. Such an absorption behavior shows that the SiO*x* shell with high density of states of defects near to the phase interface with the crystalline core mainly contributes to absorption for low energy photons; photons with

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 425

The ε'(ν) and ε''(ν) frequency spectra obtained by measuring the *nc*-Si film impedance are shown in Fig. 8. The semi empirical Cole–Cole relation ( Cole, K. S. & Cole, R. H., 1941;

> <sup>1</sup> 1 *s <sup>h</sup> i*

where ε<sup>s</sup> and ε∞ are the static and optical permittivities determined above, ω = 2πν is the

As is known, the Cole–Cole relation is valid when a material simultaneously contains several types of dipoles each with a specific relaxation time. Therefore, the quantity τ entering Eq. (7) is the relaxation time averaged over the ensemble of dipole groups

The approximating Cole–Cole curves are shown in Fig. 8.a by dashed curves. We can see that ε'(ν) is very well approximated in the entire measured frequency range; for ε''(ν), the Cole–Cole dependence exhibits good agreement only in the frequency range of 2 ×102 ≤ ν ≤ 106 Hz. The values ε*s* = 10.8, ε∞ = 3.43, τ=6 × 10–2 s, and *h* = 0.7 correspond to the found approximation. It should be noted here that the value of ε∞ is close to the values of ε'

A comparison of the values of ε<sup>s</sup> and ε∞ corresponding to the Cole–Cole approximation with similar values determined from capacitance measurements shows the closeness of their numerical values. The value of 1 – *h* is also very close to the exponent β in formula (6). Furthermore, if we consider that *A* in formula (6) is the relaxation time multiplied by 2π, then τ = *A*/2π = 6.4 × 10–2 s, which is also close to the average dipole relaxation time

The static permittivity ε*<sup>s</sup>* = 10.8 determined from the Cole–Cole relation is slightly larger than the similar value found from Eq. (6); however, it is also smaller than ε*<sup>s</sup>* = 12

In our opinion, there are two causes resulting in a decrease in ε*<sup>s</sup>* for the *nc*-Si film in comparison with ε*<sup>s</sup>* of *c*-Si. The first cause is associated with air voids in the film body; the second cause is that the size distribution of nanoparticles composing the film includes a large fraction of particles with sizes smaller than 10 nm (see the Fig. 1). In (Tsu at al., 1997), the permittivity of silicon nanoparticles was calculated as a function of their size. According to these results, the static permittivity decreases as the particle diameter becomes smaller than 10 nm; for particles 10 nm in diameter, the permittivity is from 11.2 to 10.1, depending

In Fig. 8.a, in the frequency region ν ≤ 2 × 102 Hz, we can see a notable disagreement between the Cole–Cole approximating function and the experimental dependence ε''(ν). This disagreement is caused by the fact that the Cole–Cole relation that describes dipole moment relaxation in dielectrics does not take into account the presence of free electric charges. However, free charges exist in the *nc*-Si film under study, which is indicated by the nonzero dc conductivity, which, as noted above, is σ(0) = 9 ×10–10 Ω–1 m–1 at temperature *T* = 297 K.

0≤h≤1 (7)

Moliton, 2007) appeared to be a good approximation for these spectra,

 

cyclic frequency, and τ is the dipole relaxation time.

determined in the optical region by the ellipsometry method.

corresponding to the Cole–Cole approximation.

characteristic of crystalline silicon.

on the used calculation model.

contained by the *nc*-Si film under study.

**2.3.3 Dielectric relaxation in films I** 

energies above 3 eV are mostly absorbed by crystalline cores of nanoparticles with a wider band gap than that of *c*-Si due to quantum confinement.

#### **2.3.2 Frequency dependence of the capacitance of films I**

There are several models of the interpretation of the results of measurements of the ac conductivity of materials. For semiconductors, the model of (Goswami,A. & Goswami,A.P. 1973) is a good approximation, according to which a conductive material is a composition of a capacitor with capacitance *C*1 and a resistor with conductance *G*1 (*G*1 = 1/*R*) connected in parallel. Furthermore, to take into account the effect of supplying contacts, a resistor with conductance *G*2 (*G*2 = 1/*r*) is connected in series with this group. According to this model, *C*<sup>1</sup> and *G*1 are independent of the frequency of the applied ac electric field; however, *G*<sup>1</sup> depends on the conductive material temperature.

If the sample capacitance is measured in the mode of in parallel connected *Cp*, the measured value is related to *C*1, *G*1, and *G*2 as

$$\mathcal{C}\_p = \frac{\mathcal{C}\_1 \mathcal{G}\_2^2}{\left(\mathcal{G}\_1 + \mathcal{G}\_2\right)^2 + \left(2\pi\nu\mathcal{C}\_1\right)^2}$$

We can see from this equality that the measured *nc*-Si film capacitance should satisfy the condition *Cp* ~ ν–2 while satisfying the conditions of the model of(27Goswami,A. & Goswami,A.P. 1973). However, it was impossible to approximate the experimental curve for *Cnc*-Si shown in Fig. 7 by such power law dependence. Such a fact suggests that *C*1 and *G*<sup>1</sup> should depend on frequency. Indeed, under experimental conditions, *G*2 >> *G*1 and *G*2 >>ν*C*1, hence, *Cp* ≈ *C*1.

Therefore, for approximation, we used the following semi empirical function:

$$\mathcal{C}\_{nc-Si}(\nu) = \mathcal{C}\_{\alpha} + \frac{\mathcal{C}}{1 + \left(A\nu\right)^{\beta}} \tag{6}$$

It follows from formula (6) that Cnc-Si→С∞, at ν→∞ and Cnc-Si = С∞ + С ≡С(0) at ν = 0.

Thus, the quantity С∞ entering expression (6) is the film capacitance at an "infinitely high frequency" and С(0) = С∞ + С is the film static capacitance. The dimension of the fitting parameter *A* in the formula is time; the fitting parameter β defines the power law dependence of *Cnc*-Si on the applied ac field frequency. Function (6) appeared to be a very good approximation of the experimental dependence *Cnc*-Si(ν) at the following coefficients: С∞= 3.9 ×10–10 F, *C*(0) =11.8×10–10 F, *A* = 0.5, and β = 0.32.

The film capacitance is related to the real component of its permittivity by the relation Cnc-Si(ν) = ε′nc-Si(ν)·С0. As noted above, *C*0 = 1.15 × 10–10 F for the film under study; the static and optical permittivities ε*<sup>s</sup>* = ε(0) = 10.3 and ε∞ = 3.4 correspond to the determined capacitances *C*(0) and *C*∞.

The static permittivity of the film under study, which is 10.3, is significantly lower than the permittivity of crystalline silicon, which, as is known, is ~ 12. This result will be discussed below.

## **2.3.3 Dielectric relaxation in films I**

424 Smart Nanoparticles Technology

energies above 3 eV are mostly absorbed by crystalline cores of nanoparticles with a wider

There are several models of the interpretation of the results of measurements of the ac conductivity of materials. For semiconductors, the model of (Goswami,A. & Goswami,A.P. 1973) is a good approximation, according to which a conductive material is a composition of a capacitor with capacitance *C*1 and a resistor with conductance *G*1 (*G*1 = 1/*R*) connected in parallel. Furthermore, to take into account the effect of supplying contacts, a resistor with conductance *G*2 (*G*2 = 1/*r*) is connected in series with this group. According to this model, *C*<sup>1</sup> and *G*1 are independent of the frequency of the applied ac electric field; however, *G*<sup>1</sup>

If the sample capacitance is measured in the mode of in parallel connected *Cp*, the measured

 ( ) 1

Thus, the quantity С∞ entering expression (6) is the film capacitance at an "infinitely high frequency" and С(0) = С∞ + С is the film static capacitance. The dimension of the fitting parameter *A* in the formula is time; the fitting parameter β defines the power law dependence of *Cnc*-Si on the applied ac field frequency. Function (6) appeared to be a very good approximation of the experimental dependence *Cnc*-Si(ν) at the following coefficients:

The film capacitance is related to the real component of its permittivity by the relation Cnc-Si(ν) = ε′nc-Si(ν)·С0. As noted above, *C*0 = 1.15 × 10–10 F for the film under study; the static and optical permittivities ε*<sup>s</sup>* = ε(0) = 10.3 and ε∞ = 3.4 correspond to the determined

The static permittivity of the film under study, which is 10.3, is significantly lower than the permittivity of crystalline silicon, which, as is known, is ~ 12. This result will be discussed

 (6)

*<sup>C</sup> C C <sup>A</sup>*

*GG C*

12 1 <sup>2</sup> *<sup>p</sup>*

We can see from this equality that the measured *nc*-Si film capacitance should satisfy the condition *Cp* ~ ν–2 while satisfying the conditions of the model of(27Goswami,A. & Goswami,A.P. 1973). However, it was impossible to approximate the experimental curve for *Cnc*-Si shown in Fig. 7 by such power law dependence. Such a fact suggests that *C*1 and *G*<sup>1</sup> should depend on frequency. Indeed, under experimental conditions, *G*2 >> *G*1 and

*C G <sup>C</sup>*

Therefore, for approximation, we used the following semi empirical function:

It follows from formula (6) that Cnc-Si→С∞, at ν→∞ and Cnc-Si = С∞ + С ≡С(0) at ν = 0.

*nc Si*

С∞= 3.9 ×10–10 F, *C*(0) =11.8×10–10 F, *A* = 0.5, and β = 0.32.

2 1 2 2 2

band gap than that of *c*-Si due to quantum confinement.

depends on the conductive material temperature.

value is related to *C*1, *G*1, and *G*2 as

*G*2 >>ν*C*1, hence, *Cp* ≈ *C*1.

capacitances *C*(0) and *C*∞.

below.

**2.3.2 Frequency dependence of the capacitance of films I** 

The ε'(ν) and ε''(ν) frequency spectra obtained by measuring the *nc*-Si film impedance are shown in Fig. 8. The semi empirical Cole–Cole relation ( Cole, K. S. & Cole, R. H., 1941; Moliton, 2007) appeared to be a good approximation for these spectra,

$$
\omega = \varepsilon\_{\alpha} + \frac{\varepsilon\_{s} - \varepsilon\_{\alpha}}{1 + \left( i \alpha \tau \right)^{1 - h}} \text{ 0\lesssim h\le 1} \tag{7}
$$

where ε<sup>s</sup> and ε∞ are the static and optical permittivities determined above, ω = 2πν is the cyclic frequency, and τ is the dipole relaxation time.

As is known, the Cole–Cole relation is valid when a material simultaneously contains several types of dipoles each with a specific relaxation time. Therefore, the quantity τ entering Eq. (7) is the relaxation time averaged over the ensemble of dipole groups contained by the *nc*-Si film under study.

The approximating Cole–Cole curves are shown in Fig. 8.a by dashed curves. We can see that ε'(ν) is very well approximated in the entire measured frequency range; for ε''(ν), the Cole–Cole dependence exhibits good agreement only in the frequency range of 2 ×102 ≤ ν ≤ 106 Hz. The values ε*s* = 10.8, ε∞ = 3.43, τ=6 × 10–2 s, and *h* = 0.7 correspond to the found approximation. It should be noted here that the value of ε∞ is close to the values of ε' determined in the optical region by the ellipsometry method.

A comparison of the values of ε<sup>s</sup> and ε∞ corresponding to the Cole–Cole approximation with similar values determined from capacitance measurements shows the closeness of their numerical values. The value of 1 – *h* is also very close to the exponent β in formula (6). Furthermore, if we consider that *A* in formula (6) is the relaxation time multiplied by 2π, then τ = *A*/2π = 6.4 × 10–2 s, which is also close to the average dipole relaxation time corresponding to the Cole–Cole approximation.

The static permittivity ε*<sup>s</sup>* = 10.8 determined from the Cole–Cole relation is slightly larger than the similar value found from Eq. (6); however, it is also smaller than ε*<sup>s</sup>* = 12 characteristic of crystalline silicon.

In our opinion, there are two causes resulting in a decrease in ε*<sup>s</sup>* for the *nc*-Si film in comparison with ε*<sup>s</sup>* of *c*-Si. The first cause is associated with air voids in the film body; the second cause is that the size distribution of nanoparticles composing the film includes a large fraction of particles with sizes smaller than 10 nm (see the Fig. 1). In (Tsu at al., 1997), the permittivity of silicon nanoparticles was calculated as a function of their size. According to these results, the static permittivity decreases as the particle diameter becomes smaller than 10 nm; for particles 10 nm in diameter, the permittivity is from 11.2 to 10.1, depending on the used calculation model.

In Fig. 8.a, in the frequency region ν ≤ 2 × 102 Hz, we can see a notable disagreement between the Cole–Cole approximating function and the experimental dependence ε''(ν). This disagreement is caused by the fact that the Cole–Cole relation that describes dipole moment relaxation in dielectrics does not take into account the presence of free electric charges. However, free charges exist in the *nc*-Si film under study, which is indicated by the nonzero dc conductivity, which, as noted above, is σ(0) = 9 ×10–10 Ω–1 m–1 at temperature *T* = 297 K.

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 427

*s q* 

where *q* = 4 or 5, depending on the theoretical model, and νph ≈ 1012 Hz is the phonon

It follows from relation (9) that *s* should decrease with frequency. However, such behavior of *s* contradicts our experimental data and a large number of other experimental data (Dyre

Currently, it has been sufficiently reliably determined that a large role in conduction processes in unordered solids is played by percolation processes with the result that electric transport occurs along trajectories with the lowest resistance (percolation trajectories) (Hunt, 2001; Isichenko, 1992). Conductive properties of percolation trajectories are controlled by the

In highly unordered solids, percolation trajectories at small scales exhibit a fractal structure with the result that their fractal dimension *df* appears larger than the topological one *D* (e.g., the fractal and topological dimensions of the Brownian particle trajectory is *df* = 2 and *D* = 1)

In this regard, we note theoretical studies (Dyre & Schrøder, 2000; Schrøder & Dyre, 2002; Schrøder & Dyre, 2008) in which the diffusion cluster approximation (DCA) model is formulated. As these papers, it is argued that the so-called diffusion clusters with fractal dimensions of 1.1–1.7 make the largest contribution to the ac conductivity in the percolation mode. This statement means that the fractal structure of such clusters is simpler than the structure of multiply connected percolation clusters formed above the percolation threshold in conductive materials (backbone clusters), the fractal dimension of which is 1.7 (Isichenko, 1992). Simultaneously, the structure of diffusion clusters is more branched than the network of singly connected clusters and breaking of each results in disappearance of the current flowing through it (*redbonds*). The fractal dimension of *redbonds* clusters is 1.1 (Isichenko,

In these papers, the universal dependence of the dimensionless complex conductivity

() () (0) *AC <sup>i</sup>* 

 

<sup>0</sup> <sup>2</sup> (0) *<sup>s</sup>* 

> *<sup>i</sup>*

 

*f d*

*ph*

(9)

(10)

<sup>1</sup> 1 ln

structure of (percolation) clusters composing the shell of solids.

frequency.

& Schrøder, 2000).

(Isichenko, 1992).

1992).

on the dimensionless frequency

was derived. This dependence is given by

<sup>2</sup> ln

According to studies by Barton, Nakajima, and Namikawa (Barton 1966; Nakajima, 1972; Namikawa, 1975), the frequency ν*<sup>m</sup>* corresponding to the dispersion maximum for ε''(ν) is related to σ(0) as σ(0) = *p*(ε*<sup>s</sup>* –ε∞)·ε02πν*m*, where the numerical coefficient *p* is approximately equal to unity. We can see in Fig. 8.a that the Cole–Cole approximating function reaches a maximum at the frequency ν*<sup>m</sup>* = 2.5 Hz, and this value is in good agreement with the experimental value of σ(0) when using the Barton–Nakajima–Namikawa formula.

To take into account the conductivity associates with free electric charges, relation (4) should be written as

$$
\varepsilon = \varepsilon\_{\alpha} + \frac{\varepsilon\_{s} - \varepsilon\_{\alpha}}{1 + \left(i\alpha\tau\right)^{1-h}} + \frac{\sigma(0)}{\varepsilon\_{0}\alpha} \tag{8}
$$

The approximation of the ε''(ν) spectrum of the film under study is shown by the dashed curve in Fig. 8.a (curve *5*), from which it is obvious that function (8) is a good approach of the experimental dependence ε''(ν).

The effect of free electric charges on dielectric properties of the *nc*-Si film rather clearly appears in the Nyquist plot in which ε'' for each frequency is shown as a function of ε' (see Fig. 8.b).

It follows from the Cole–Cole approximation (see curve *2* in Fig. 8.b) that the ε''(ε') should be shaped as a part of a semicircle whose center is below the horizontal axis ε''. The intersection of this circle with the ε' axis at ω = 0 and ω → ∞ yields the values of ε*<sup>s</sup>* and ε∞.

Figure 8.b shows only the semicircle part corresponding to the measured frequency range; therefore, the value ε*<sup>s</sup>* = 10.8 is out of sight of the figure; the intersection of the semicircle with the ε' axis at ω → ∞ is clearly seen and corresponds to ε∞ = 3.4. The same figure shows the approximation corresponding to function (8) (curve *3*), similar to the approximation shown in Fig. 8.a.

### **2.3.4 AC conductivity of films I**

To determine the nature of electric charge transport in *nc*-Si films, the frequency dependence of the conductivity σAC(ν), σAC(ν) – σ(0) = ε0·2πν·ε″(ν), was studied.

The σac(ν)–σ(0) plot on a log scale for the film analyzed in this paper is shown in Fig. 10. We can see that σAC(ν) in the entire measured frequency range is well approximated by the power law function: σac(ν) = σ(0) + *A*ν*<sup>s</sup>* with *s* = 0.74. Such σAC(ν) behavior means that the electric transport in the film has the hopping mechanism, which in turn is a manifestation of the structure disorder in that film region over which charge transport occurs.

Currently, there are several theoretical models describing hopping conductivity in unordered solids. All these models yield the power law dependence of the ac conductivity on the ac electric field frequency:σ(ν) ~ ν*s*. However, the numerical values of the exponent *s*  differ. For example, in the models (Austin & Mott, 1969; Hunt, 2001) according to which the conduction results from electric charge tunneling through energy barriers separating close localized states, the parameter *s* is given by

$$s = 1 + q \times \ln^{-1} \left(\frac{\nu}{\nu\_{ph}}\right) \tag{9}$$

where *q* = 4 or 5, depending on the theoretical model, and νph ≈ 1012 Hz is the phonon frequency.

It follows from relation (9) that *s* should decrease with frequency. However, such behavior of *s* contradicts our experimental data and a large number of other experimental data (Dyre & Schrøder, 2000).

Currently, it has been sufficiently reliably determined that a large role in conduction processes in unordered solids is played by percolation processes with the result that electric transport occurs along trajectories with the lowest resistance (percolation trajectories) (Hunt, 2001; Isichenko, 1992). Conductive properties of percolation trajectories are controlled by the structure of (percolation) clusters composing the shell of solids.

In highly unordered solids, percolation trajectories at small scales exhibit a fractal structure with the result that their fractal dimension *df* appears larger than the topological one *D* (e.g., the fractal and topological dimensions of the Brownian particle trajectory is *df* = 2 and *D* = 1) (Isichenko, 1992).

In this regard, we note theoretical studies (Dyre & Schrøder, 2000; Schrøder & Dyre, 2002; Schrøder & Dyre, 2008) in which the diffusion cluster approximation (DCA) model is formulated. As these papers, it is argued that the so-called diffusion clusters with fractal dimensions of 1.1–1.7 make the largest contribution to the ac conductivity in the percolation mode. This statement means that the fractal structure of such clusters is simpler than the structure of multiply connected percolation clusters formed above the percolation threshold in conductive materials (backbone clusters), the fractal dimension of which is 1.7 (Isichenko, 1992). Simultaneously, the structure of diffusion clusters is more branched than the network of singly connected clusters and breaking of each results in disappearance of the current flowing through it (*redbonds*). The fractal dimension of *redbonds* clusters is 1.1 (Isichenko, 1992).

In these papers, the universal dependence of the dimensionless complex conductivity

$$
\tilde{\sigma} = \frac{\sigma\_{A\mathbb{C}}(\nu) + i\sigma''(\nu)}{\sigma(0)}
$$

on the dimensionless frequency

426 Smart Nanoparticles Technology

According to studies by Barton, Nakajima, and Namikawa (Barton 1966; Nakajima, 1972; Namikawa, 1975), the frequency ν*<sup>m</sup>* corresponding to the dispersion maximum for ε''(ν) is related to σ(0) as σ(0) = *p*(ε*<sup>s</sup>* –ε∞)·ε02πν*m*, where the numerical coefficient *p* is approximately equal to unity. We can see in Fig. 8.a that the Cole–Cole approximating function reaches a maximum at the frequency ν*<sup>m</sup>* = 2.5 Hz, and this value is in good agreement with the

To take into account the conductivity associates with free electric charges, relation (4) should

The approximation of the ε''(ν) spectrum of the film under study is shown by the dashed curve in Fig. 8.a (curve *5*), from which it is obvious that function (8) is a good approach of

The effect of free electric charges on dielectric properties of the *nc*-Si film rather clearly appears in the Nyquist plot in which ε'' for each frequency is shown as a function of ε' (see

It follows from the Cole–Cole approximation (see curve *2* in Fig. 8.b) that the ε''(ε') should be shaped as a part of a semicircle whose center is below the horizontal axis ε''. The intersection

Figure 8.b shows only the semicircle part corresponding to the measured frequency range; therefore, the value ε*<sup>s</sup>* = 10.8 is out of sight of the figure; the intersection of the semicircle with the ε' axis at ω → ∞ is clearly seen and corresponds to ε∞ = 3.4. The same figure shows the approximation corresponding to function (8) (curve *3*), similar to the approximation

To determine the nature of electric charge transport in *nc*-Si films, the frequency dependence

The σac(ν)–σ(0) plot on a log scale for the film analyzed in this paper is shown in Fig. 10. We can see that σAC(ν) in the entire measured frequency range is well approximated by the power law function: σac(ν) = σ(0) + *A*ν*<sup>s</sup>* with *s* = 0.74. Such σAC(ν) behavior means that the electric transport in the film has the hopping mechanism, which in turn is a manifestation of

Currently, there are several theoretical models describing hopping conductivity in unordered solids. All these models yield the power law dependence of the ac conductivity on the ac electric field frequency:σ(ν) ~ ν*s*. However, the numerical values of the exponent *s*  differ. For example, in the models (Austin & Mott, 1969; Hunt, 2001) according to which the conduction results from electric charge tunneling through energy barriers separating close

of this circle with the ε' axis at ω = 0 and ω → ∞ yields the values of ε*<sup>s</sup>* and ε∞.

of the conductivity σAC(ν), σAC(ν) – σ(0) = ε0·2πν·ε″(ν), was studied.

the structure disorder in that film region over which charge transport occurs.

0 (0)

(8)

 

experimental value of σ(0) when using the Barton–Nakajima–Namikawa formula.

1 *s <sup>h</sup> i* 

<sup>1</sup>

the experimental dependence ε''(ν).

 

be written as

Fig. 8.b).

shown in Fig. 8.a.

**2.3.4 AC conductivity of films I** 

localized states, the parameter *s* is given by

$$
\tilde{\phi} = \frac{\varepsilon\_0 \left(\varepsilon\_s - \varepsilon\_\phi\right)}{\sigma(0)} 2\pi\nu
$$

was derived. This dependence is given by

$$\ln \tilde{\sigma} = \left(\frac{\mathrm{i}\tilde{a}\tilde{o}}{\tilde{\sigma}}\right)^{\frac{d\_f}{2}} \tag{10}$$

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 429

Such a scheme allows implementation of proton transport near the glass surface. Returning to nc-Si films, we note that particles used to apply films represent hydrogenized nanocrystalline silicon. However, when exposing these particles to atmospheric air, a SiOx shell (0 ≤ x ≤ 2) is formed on their surface. In (Du at al., 2003; Cao at al., 2007), the kinetics of the interaction of H2O molecules with SiO2 chain structures was calculated. It was shown that H2O molecules very efficiently break Si–O–Si bonds during the interaction with SiO2 surface groups with the formation of Si–O–H groups. The subsequent interaction of H2O molecules and Si–O–H groups yields H3O+ ions, which, having high mobility, can appreciably contribute to the proton transport along the SiO2

In addition to the above process, the collective proton conductivity caused by associated Si– O–H groups, i.e., groups linked by hydrogen bond, as shown in Fig. 12.a (Glasser, 1975).

Fig. 12. Diagrams illustrating the mechanism of the collective proton conductivity, caused by (a) associated Si–O–H groups and (b) the interaction of water molecules with hydroxyl

a b

Si O H

O H

H

Si

Si Si

O H

O H

5,4А<sup>0</sup>

H

2,8А<sup>0</sup>

O H

H

Si

O H

The collective proton conductivity is also possible during the interaction of water molecules with hydroxyl groups, which results in the surface structure shown in Fig. 12.b. Since the О···Н─О group length is within 2.5–2.9 Å (Leite at al., 1998) and the angle between H–O–H bonds is ~104°, there is good spatial alignment between the element of this surface structure and the crystalline silicon lattice constant which, as is known,

As applied to the nc-Si films analyzed in this paper, there is direct proof of the existence of such structures. Previously, in the investigations of IR transmission spectra of thin wafers (with thickness ≈50 μm) made by pressing (P~109 Pa) from nc-Si powders similar to those used in this study, it was shown that the spectra contain a broad intense band with a maximum at ~3420 cm–1 (see Fig. 13 and Kononov at al., 2005). In papers (Wovchko at al., 1995; Stuart, 2004) this band is attributed to O–H vibrations in hydrogen bound hydroxyl groups. It was also shown that heating of nc-Si particles to 400°C causes an appreciably decrease in the intensity of the band near 3420 cm–1 and an increase in the intensity of the narrow band with a maximum near 3750 cm–1, which is identified with

groups. Arrows indicate the direction of positive charge transport.

Si

O

H

Arrows in the diagram indicate the direction of positive charge transport.

H

Si

O

chain.

H

Si

Si

O

H

O

is 5.4 Å.

The fractal dimension *df* in formula (10) is a fitting parameter. Processing of a large number of experimental dependences in (Schrøder & Dyre, 2002; Schrøder & Dyre, 2008) showed that the best agreement in the frequency region ν > 1 Hz is achieved at *df* = 1.35.

We compared the experimental dependence σAC (ν) obtained in the present study with the values defined by formula (10). Here it should be noted that complex valued equation (10) has no analytical solution and should be solved numerically.

However, in the low frequency region ω → 0, Eq. (10) can be written as 1 2 *f d i* ; accordingly (Kononov at al., 2011):

$$
\sigma\_{A\mathbb{C}}(\nu) - \sigma(0) = \sigma(0)^{\binom{1-\frac{d\_f}{2}}{2}} \cos\left(\frac{\pi d\_f}{4}\right) (2\pi \varepsilon\_0 A \varepsilon)^{\frac{d\_f}{2}} \frac{d\_f}{\nu^{\frac{d\_f}{2}}} \tag{11}
$$

where Δε = ε*<sup>s</sup>* – ε∞.

Substitution of experimentally determined values of ε*s*, ε∞, σ(0), and *s* ≡ *df*/2 = 0.74 into formula (11) gives the approximating dependence for σac(ν) (see Fig. 9) corresponding to the DCA model. We can see that the calculated dependence rather well approximates the experimental curve σac(ν) in the entire measured frequency range. At the same time, the calculated dependence yields values of σAC larger than the experimental ones by a factor of ~1.5. We attribute such disagreement to possible errors when determining the numerical values of ε*s*, ε∞, and σ(0).

#### **2.3.5 Proton conductivity of films I**

One of the possible causes that can result in σ(0) measurement errors for nc-Si films is the dependence of σ(0) on the ambient air humidity. We qualitatively determines the following systematic feature: the higher the laboratory air humidity, the higher (at a constant temperature) the conductivity σ(0) of films similar to the film analyzed in this paper. On the contrary, if the film is preliminarily heated at a temperature of ~200°C for a time longer than 15 min and then it is cooled to its initial temperature, the film conductivity will decrease almost by two orders of magnitude. Thus the presence of water in an atmosphere surrounding the film changes its conductive properties significantly. In (Nogami & Abe, 1997; Nogami at al., 1998) a similar phenomenon was observed in the study of the ionic conductivity in fused silica glasses. It was shown that, in the presence of Si–O–H bonds on the glass surfaces, H2O molecules form complexes with them, confined hydrogen bonds. These complexes can dissociate forming free H3O+ ions and bound Si–O– groups according to the scheme:

$$\text{Si-O-H}\cdots\text{OH}\_2 \rightarrow \text{Si-O}\cdot + \text{H}^\*\text{.}\text{H}\_2\text{O}$$

Here, dots denote the hydrogen bond between H and O atoms. In this case, the dissociated proton H+ can be trapped by a neighboring H2O molecule,

$$\text{H}\_2\text{O:}\text{H}\_2\text{O}\_{\text{(l)}};\text{H}^\* + \text{H}\_2\text{O}\_{\text{(2)}} \rightarrow \text{H}\_2\text{O}\_{\text{(l)}} + \text{H}^\* + \text{H}\_2\text{O}\_{\text{(2)}} \rightarrow \text{H}\_2\text{O}\_{\text{(1)}} + \text{H}^\*;\text{H}\_2\text{O}\_{\text{(2)}} \text{ etc.} \text{}$$

The fractal dimension *df* in formula (10) is a fitting parameter. Processing of a large number of experimental dependences in (Schrøder & Dyre, 2002; Schrøder & Dyre, 2008) showed

We compared the experimental dependence σAC (ν) obtained in the present study with the values defined by formula (10). Here it should be noted that complex valued equation (10)

However, in the low frequency region ω → 0, Eq. (10) can be written as 1 2

<sup>2</sup> <sup>2</sup> <sup>2</sup> <sup>0</sup> ( ) (0) (0) cos 2 <sup>4</sup>

Substitution of experimentally determined values of ε*s*, ε∞, σ(0), and *s* ≡ *df*/2 = 0.74 into formula (11) gives the approximating dependence for σac(ν) (see Fig. 9) corresponding to the DCA model. We can see that the calculated dependence rather well approximates the experimental curve σac(ν) in the entire measured frequency range. At the same time, the calculated dependence yields values of σAC larger than the experimental ones by a factor of ~1.5. We attribute such disagreement to possible errors when determining the numerical

One of the possible causes that can result in σ(0) measurement errors for nc-Si films is the dependence of σ(0) on the ambient air humidity. We qualitatively determines the following systematic feature: the higher the laboratory air humidity, the higher (at a constant temperature) the conductivity σ(0) of films similar to the film analyzed in this paper. On the contrary, if the film is preliminarily heated at a temperature of ~200°C for a time longer than 15 min and then it is cooled to its initial temperature, the film conductivity will decrease almost by two orders of magnitude. Thus the presence of water in an atmosphere surrounding the film changes its conductive properties significantly. In (Nogami & Abe, 1997; Nogami at al., 1998) a similar phenomenon was observed in the study of the ionic conductivity in fused silica glasses. It was shown that, in the presence of Si–O–H bonds on the glass surfaces, H2O molecules form complexes with them, confined hydrogen bonds. These complexes can dissociate forming free H3O+ ions and bound Si–O– groups according

Si-O-H···OH2→ Si-O-

proton H+ can be trapped by a neighboring H2O molecule,

Here, dots denote the hydrogen bond between H and O atoms. In this case, the dissociated

H2O: H2O(1):H+ + H2O(2)→ H2O(1) + H+ + H2O(2)→ H2O(1) + H+: H2O(2) etc.

+ H+: H2O

*<sup>f</sup> <sup>f</sup> <sup>f</sup> <sup>d</sup> <sup>d</sup> <sup>d</sup> f*

 

*d*

 

1

  *f d*

 *i* ;

(11)

that the best agreement in the frequency region ν > 1 Hz is achieved at *df* = 1.35.

has no analytical solution and should be solved numerically.

 

accordingly (Kononov at al., 2011):

where Δε = ε*<sup>s</sup>* – ε∞.

values of ε*s*, ε∞, and σ(0).

to the scheme:

**2.3.5 Proton conductivity of films I** 

*AC*

 Such a scheme allows implementation of proton transport near the glass surface. Returning to nc-Si films, we note that particles used to apply films represent hydrogenized nanocrystalline silicon. However, when exposing these particles to atmospheric air, a SiOx shell (0 ≤ x ≤ 2) is formed on their surface. In (Du at al., 2003; Cao at al., 2007), the kinetics of the interaction of H2O molecules with SiO2 chain structures was calculated. It was shown that H2O molecules very efficiently break Si–O–Si bonds during the interaction with SiO2 surface groups with the formation of Si–O–H groups. The subsequent interaction of H2O molecules and Si–O–H groups yields H3O+ ions, which, having high mobility, can appreciably contribute to the proton transport along the SiO2 chain.

In addition to the above process, the collective proton conductivity caused by associated Si– O–H groups, i.e., groups linked by hydrogen bond, as shown in Fig. 12.a (Glasser, 1975). Arrows in the diagram indicate the direction of positive charge transport.

Fig. 12. Diagrams illustrating the mechanism of the collective proton conductivity, caused by (a) associated Si–O–H groups and (b) the interaction of water molecules with hydroxyl groups. Arrows indicate the direction of positive charge transport.

The collective proton conductivity is also possible during the interaction of water molecules with hydroxyl groups, which results in the surface structure shown in Fig. 12.b. Since the О···Н─О group length is within 2.5–2.9 Å (Leite at al., 1998) and the angle between H–O–H bonds is ~104°, there is good spatial alignment between the element of this surface structure and the crystalline silicon lattice constant which, as is known, is 5.4 Å.

As applied to the nc-Si films analyzed in this paper, there is direct proof of the existence of such structures. Previously, in the investigations of IR transmission spectra of thin wafers (with thickness ≈50 μm) made by pressing (P~109 Pa) from nc-Si powders similar to those used in this study, it was shown that the spectra contain a broad intense band with a maximum at ~3420 cm–1 (see Fig. 13 and Kononov at al., 2005). In papers (Wovchko at al., 1995; Stuart, 2004) this band is attributed to O–H vibrations in hydrogen bound hydroxyl groups. It was also shown that heating of nc-Si particles to 400°C causes an appreciably decrease in the intensity of the band near 3420 cm–1 and an increase in the intensity of the narrow band with a maximum near 3750 cm–1, which is identified with

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 431

Fig. 14. Spectra of the real (a) and imaginary (b) components of permittivity film II. Shortdotted line shows the approximation of the Debye. Dotted line shows the approximation of the Cole-Cole. The dash-dotted line shows the approximation of free charges. The dashed

a b

0,0

0,5

1,0

"

1,5

2,0

2,5

σDC, (Ohm·m)- 1

measurements of the films resistance and from the Barton–Nakajima–Namikawa formula.

These values for films I, II and III are shown in the table 1. The table 1 also gives values of σ(0) received from direct measurements of the films resistance at constant current at T = 297K, and those which obtained from the Barton–Nakajima–Namikawa formula. From table 1 it can be seen that the values of the static dielectric constant of films III are about 67, significantly higher than similar values of the films I and II, which are close to the values characteristic of crystalline silicon. However, the value of ε<sup>0</sup> ≈ 67 is much lower quantities ε0 ~ 103 typical for composites consisting of nanoparticles of tin dioxide and polyaniline

The authors of this work attributed so high ε0 to an anomalously strong polarization of nanoparticle of SnO2 which caused by inhomogeneity of the conductivity of its surface and core. However, the value of ε0≈67 which have been measured by us, is quite close to the values of the static dielectric constant of tetraaniline with different degrees of doping it with hydrochloric acid (Bianchi at al., 1999) and which, depending on the degree of doping lies in

The presence in equation (12) two different laws of approximation indicates that there are two different dipole relaxation process associated with the various structural components of

I 10,8 3,4 0,74 1,4·10-9 9·10-10 10-9 0,06 - II 11,5 4 0,66 4·10-11 3,5·10-11 9·10-11 0,72 2,12·10-6 III 66,9 4,9 0,5 9·10-11 3,5·10-9 2·10-9 0,27 1,75·10-5 Table 1. Fit parameters for the two dielectric relaxation lows of the films investigated in this

study. σDC and σB(0) - the conductivites at constant current received from direct

σB(0),

(Ohm·m)-1 <sup>τ</sup>1, <sup>s</sup> <sup>τ</sup>2, s

100 10<sup>1</sup> 102 10<sup>3</sup> 104 10<sup>5</sup> 106

Frequency (Hz)

line shows the complete approximation of the spectra.

100 101 10<sup>2</sup> 10<sup>3</sup> 104 105 106

Frequency (Hz)

which have been reported in (Kousik at al., 2007)

the range 35 - 80.

(Ohm·m)-1

№ <sup>ε</sup><sup>0</sup> ε∞ h σ(0),

'

O–H vibrations in the isolated Si–O–H group ( Kononov at al., 2005). Similar spectra are shown in Figure 13. Such behavior of the intensities of bands at 3420 and 3750 cm–1 means that associated Si–O–H groups become isolated upon heating of nc-Si particles. Accordingly, heating should decrease the proton conductivity associated with these groups.

Thus the dependence of the conductivity σ(0) of the *nc*-Si films under study on the ambient air humidity and the thermal behavior of the absorption bands associated with Si–O–H groups allows the conclusion to be drawn that the proton conductivity makes the main contribution to the dark dc conductivity of *nc*-Si films.

Fig. 13. Infrared transmittance spectra of: (*1*) - thin wafer from *nc-*Si particles prepared at a pressure of 5 × 108 Pa at 200C, (2) - the same *nc-*Si wafer but annealed at 400°C for 30 min.

#### **2.3.6 Double dielectric relaxation in the films II and III**

Earlier, we noted that the spectra of the ε'(ν) and ε"(ν) of the films II and III near a frequency ≈ 104 Hz reveal the structure arising in the Debye dipole relaxation. Following this observation for the numerical approximation of the experimental spectra, we used not only semi-empirical law of Cole-Cole, but the law of Debye dipole relaxation. Thus, all experimental spectra were approximated by the following relation:

$$\varepsilon = \frac{\varepsilon\_s - \varepsilon\_\alpha}{1 + \left(i\alpha\tau\_1\right)^{1-h}} + \frac{\varepsilon\_\alpha}{1 + \left(i\alpha\tau\_2\right)^2} + \frac{\sigma(0)}{\varepsilon\_0\alpha} \tag{12}$$

Here τ1 and τ2 is the relaxation times of dipole moments in the various structural components of the films. With the help of equation (12) was able to accurately approximate the dielectric spectra of the films studied; example of such an approximation for film II is shown in Figure 14.

Furthermore the approximation (12) allowed us to determine the static (ε0), high-frequency (ε∞) dielectric constants (ν ~ 105 Hz), the conductivity of the films at constant current σ (0), and relaxation times τ1 and τ2.

O–H vibrations in the isolated Si–O–H group ( Kononov at al., 2005). Similar spectra are shown in Figure 13. Such behavior of the intensities of bands at 3420 and 3750 cm–1 means that associated Si–O–H groups become isolated upon heating of nc-Si particles. Accordingly, heating should decrease the proton conductivity associated with these

Thus the dependence of the conductivity σ(0) of the *nc*-Si films under study on the ambient air humidity and the thermal behavior of the absorption bands associated with Si–O–H groups allows the conclusion to be drawn that the proton conductivity makes the main

Fig. 13. Infrared transmittance spectra of: (*1*) - thin wafer from *nc-*Si particles prepared at a pressure of 5 × 108 Pa at 200C, (2) - the same *nc-*Si wafer but annealed at 400°C for 30 min.

2000 2500 3000 3500 4000

Wavenumber, cm-1

Earlier, we noted that the spectra of the ε'(ν) and ε"(ν) of the films II and III near a frequency ≈ 104 Hz reveal the structure arising in the Debye dipole relaxation. Following this observation for the numerical approximation of the experimental spectra, we used not only semi-empirical law of Cole-Cole, but the law of Debye dipole relaxation. Thus, all

> 1 2 0 1 2

Here τ1 and τ2 is the relaxation times of dipole moments in the various structural components of the films. With the help of equation (12) was able to accurately approximate the dielectric spectra of the films studied; example of such an approximation for film II is

Furthermore the approximation (12) allowed us to determine the static (ε0), high-frequency (ε∞) dielectric constants (ν ~ 105 Hz), the conductivity of the films at constant current σ (0),

*<sup>h</sup> i i* 

1 1

 (0)

3750 cm-1

3420 cm-1

2

1

(12)

 

> 

contribution to the dark dc conductivity of *nc*-Si films.

Transmittance, arb. units

**2.3.6 Double dielectric relaxation in the films II and III** 

experimental spectra were approximated by the following relation:

*s*

 

groups.

shown in Figure 14.

and relaxation times τ1 and τ2.

Fig. 14. Spectra of the real (a) and imaginary (b) components of permittivity film II. Shortdotted line shows the approximation of the Debye. Dotted line shows the approximation of the Cole-Cole. The dash-dotted line shows the approximation of free charges. The dashed line shows the complete approximation of the spectra.


Table 1. Fit parameters for the two dielectric relaxation lows of the films investigated in this study. σDC and σB(0) - the conductivites at constant current received from direct measurements of the films resistance and from the Barton–Nakajima–Namikawa formula.

These values for films I, II and III are shown in the table 1. The table 1 also gives values of σ(0) received from direct measurements of the films resistance at constant current at T = 297K, and those which obtained from the Barton–Nakajima–Namikawa formula. From table 1 it can be seen that the values of the static dielectric constant of films III are about 67, significantly higher than similar values of the films I and II, which are close to the values characteristic of crystalline silicon. However, the value of ε<sup>0</sup> ≈ 67 is much lower quantities ε0 ~ 103 typical for composites consisting of nanoparticles of tin dioxide and polyaniline which have been reported in (Kousik at al., 2007)

The authors of this work attributed so high ε0 to an anomalously strong polarization of nanoparticle of SnO2 which caused by inhomogeneity of the conductivity of its surface and core. However, the value of ε0≈67 which have been measured by us, is quite close to the values of the static dielectric constant of tetraaniline with different degrees of doping it with hydrochloric acid (Bianchi at al., 1999) and which, depending on the degree of doping lies in the range 35 - 80.

The presence in equation (12) two different laws of approximation indicates that there are two different dipole relaxation process associated with the various structural components of

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 433

The grains of silicon nanoparticles constituting the films II and III are similar to each other, so this difference frequency νm can be attributed only to differences in the strength of interaction between the dipoles on the surface of the nanoparticles in these films. In other words, the presence of tetraaniline complexes on the surface of silicon nanoparticles leads to a weakening of the interaction between the dipoles are formed on the surface at the

Dependence of the conductivity of the films I, II and III of the frequency of the applied electric field is shown in Figure 11. This figure shows that the conductivity of films I with

 σ (ω) = σ (0) + Aωs. (13) In the entire range of measured frequencies, the exponent s = 0,74 equal to the value h which

Conductivity of the films II describe such an equation is possible only in very limited region,

For low-frequency component of the conductivity of the films II as well as for the film**s** I, the value of s coincides with that of h, shown in Table 1. For films of III this statement is incorrect. Indeed, as noted in Section B.2 conductivity of the films III is well approximated by a power law exponent with s = 0,63 only in small range of frequencies 5 ≤ ν ≤ 5·102 Hz. As can be seen from Table 1, this value differs significantly from the values of

The coincidence of the values of s and h for a film I is explained as follows circumstance. Spectrum ε''(ω) of the film over the entire range of measured frequencies is approximated by

*A A*

 <sup>1</sup> 1 *h A* 

As can be seen from Table 1 for the film I τ1 = 0,06 s, hence equation (13) is valid for it, at frequencies ν ≥ 10 Hz. A similar analysis is applicable also to the low frequency component of the film II. For film II τ1 = 0,72 s, therefore, the dependence (13) will be observed if ν ≥ 1 Hz. This fact is shown in Figure 16, where the conductivity of the films II and III is

1 2 1 1 1 1 <sup>1</sup> <sup>1</sup>

*h h h*

,

*h*

1

namely in the frequency range ν ≤ 103Hz (let's call it a low-frequency component).

obtained from the approximation of the Cole-Cole and given in table 1.

h = 0,5 obtained from the approximation of the Cole-Cole.

 

1 1

*h*

*B B*

 

<sup>1</sup> <sup>1</sup>

approximated by the sum of σ (0) and two distributions of Cole-Cole and Debye.

and hence the following relation is valid for the conductivity σ(ω) - σ(0) = ε0·ω ·ε′′~ ωh

the Cole-Cole distribution which has the form:

Where A and B is constants and B≤2

If ωτ1>> 1, this equation takes the form:

polarization of the particle.

good accuracy obey the law:

**2.3.7 AC conductivity of the films II and III** 

the studied films II and III. Very clear in understanding this phenomenon is a plot of ε'' vs ε '(Nyquist Plot), shown in Figure 15.

In the inset of Fig. 15 we can see that the dependence of ε'' vs of ε' for film III consists of two semicircles, which can be termed as high- and low- frequency components. The film II has a similar structure while the graph ε''(ε') of the film I consists of only one semicircle (which is a low-frequency component) and low-frequency tail defined by the presence of free charges. Nanoparticles of silicon used for deposition of films II and III were in ethanol for two years after their synthesis, i.e., they were subjected to natural oxidation significantly longer than the nanoparticles of which consist film I. Therefore we can assume that oxidation of their surface is significantly higher than that of nanoparticles films I.

The previous sections have shown that the optical and electrical properties of films I greatly influenced by the surface of the nanoparticles from which these films are composed. It was found that the average properties of the surface similar to those of SiO and the component ε (ω) is determined by the Cole-Cole law related to the dipole relaxation in SiOx shell of silicon nanoparticles.

Fig. 15. The graph of dependence ε'' vs ε' for: film I - (1), film II - (2) and film III - (3) The inset shows an expanded plot ε''(ε ') for film III.

Since during the aging process of silicon nanoparticles the SiO2 shell must increase, the appearance of high-frequency components of the Debye spectra ε (ω) of the films II and III gives reason to assume that the source of this component is the structure of SiO2 with a narrow distribution of the dipole, which was formed on the surface of nanoparticles in two years of their presence in ethanol.

The fact that the Debye component of the spectrum ε (ω) as well as component Cole-Cole connected with the surface of the nanoparticles is confirmed by the fact noted earlier that the maxima of the Debye peak in the spectra of ε''(ω) of the films II and III correspond to different frequencies νm.

The grains of silicon nanoparticles constituting the films II and III are similar to each other, so this difference frequency νm can be attributed only to differences in the strength of interaction between the dipoles on the surface of the nanoparticles in these films. In other words, the presence of tetraaniline complexes on the surface of silicon nanoparticles leads to a weakening of the interaction between the dipoles are formed on the surface at the polarization of the particle.

## **2.3.7 AC conductivity of the films II and III**

432 Smart Nanoparticles Technology

the studied films II and III. Very clear in understanding this phenomenon is a plot of ε'' vs

In the inset of Fig. 15 we can see that the dependence of ε'' vs of ε' for film III consists of two semicircles, which can be termed as high- and low- frequency components. The film II has a similar structure while the graph ε''(ε') of the film I consists of only one semicircle (which is a low-frequency component) and low-frequency tail defined by the presence of free charges. Nanoparticles of silicon used for deposition of films II and III were in ethanol for two years after their synthesis, i.e., they were subjected to natural oxidation significantly longer than the nanoparticles of which consist film I. Therefore we can assume that oxidation of their

The previous sections have shown that the optical and electrical properties of films I greatly influenced by the surface of the nanoparticles from which these films are composed. It was found that the average properties of the surface similar to those of SiO and the component ε (ω) is determined by the Cole-Cole law related to the dipole relaxation in SiOx shell of silicon

Fig. 15. The graph of dependence ε'' vs ε' for: film I - (1), film II - (2) and film III - (3)

Since during the aging process of silicon nanoparticles the SiO2 shell must increase, the appearance of high-frequency components of the Debye spectra ε (ω) of the films II and III gives reason to assume that the source of this component is the structure of SiO2 with a narrow distribution of the dipole, which was formed on the surface of nanoparticles in two

0 2 4 6 8 10 12

1

0 10 20 30

'

'

2

3

The fact that the Debye component of the spectrum ε (ω) as well as component Cole-Cole connected with the surface of the nanoparticles is confirmed by the fact noted earlier that the maxima of the Debye peak in the spectra of ε''(ω) of the films II and III correspond to

The inset shows an expanded plot ε''(ε ') for film III.

0

1

2

3

0

5

10

"

15

"

4

5

6

years of their presence in ethanol.

different frequencies νm.

ε '(Nyquist Plot), shown in Figure 15.

nanoparticles.

surface is significantly higher than that of nanoparticles films I.

Dependence of the conductivity of the films I, II and III of the frequency of the applied electric field is shown in Figure 11. This figure shows that the conductivity of films I with good accuracy obey the law:

$$\mathbf{o} \ (\mathbf{o}) \equiv \mathbf{o} \ (0) + \mathbf{A} \mathbf{o} \mathbf{o} \tag{13}$$

In the entire range of measured frequencies, the exponent s = 0,74 equal to the value h which obtained from the approximation of the Cole-Cole and given in table 1.

Conductivity of the films II describe such an equation is possible only in very limited region, namely in the frequency range ν ≤ 103Hz (let's call it a low-frequency component).

For low-frequency component of the conductivity of the films II as well as for the film**s** I, the value of s coincides with that of h, shown in Table 1. For films of III this statement is incorrect. Indeed, as noted in Section B.2 conductivity of the films III is well approximated by a power law exponent with s = 0,63 only in small range of frequencies 5 ≤ ν ≤ 5·102 Hz. As can be seen from Table 1, this value differs significantly from the values of h = 0,5 obtained from the approximation of the Cole-Cole.

The coincidence of the values of s and h for a film I is explained as follows circumstance. Spectrum ε''(ω) of the film over the entire range of measured frequencies is approximated by the Cole-Cole distribution which has the form:

$$\varepsilon'' = \frac{A\left(o\sigma\tau\_1\right)^{1-h}}{1 + B\left(o\sigma\tau\_1\right)^{1-h} + \left(o\sigma\tau\_1\right)^{2\left(1-h\right)}} = \left(\frac{A}{B + \frac{1}{\left(o\sigma\tau\_1\right)^{1-h}} + \left(o\sigma\tau\_1\right)^{1-h}}\right)$$

Where A and B is constants and B≤2

If ωτ1>> 1, this equation takes the form: <sup>1</sup> 1 *h A* ,

and hence the following relation is valid for the conductivity σ(ω) - σ(0) = ε0·ω ·ε′′~ ωh

As can be seen from Table 1 for the film I τ1 = 0,06 s, hence equation (13) is valid for it, at frequencies ν ≥ 10 Hz. A similar analysis is applicable also to the low frequency component of the film II. For film II τ1 = 0,72 s, therefore, the dependence (13) will be observed if ν ≥ 1 Hz. This fact is shown in Figure 16, where the conductivity of the films II and III is approximated by the sum of σ (0) and two distributions of Cole-Cole and Debye.

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 435

Dielectric and transport properties of thin films obtained by deposition of silicon nanoparticles from ethanol sols on a glass, quartz, and aluminum substrates were measured by optical ellipsometry and impedance spectroscopy methods. The real and imaginary permittivities of *nc*-Si films were measured in frequency ranges of 5 × 1014–1015 and 10–106 Hz. It was found that the permittivity spectra depend on the time which has elapsed since

Only one type of dipole relaxation, which can be described by semi-empirical Cole-Cole equation, exists in films prepared from sols with silicon nanoparticles, synthesized a week before their deposition on a substrate (film I). In films prepared from sols containing aged nanoparticles (film II) there is a double-dipole relaxation, which is revealed in the fact that for the approximation of the experimental spectra of these films not only Cole-Cole relation but the law of Debye dipole relaxation should be used. A similar confirmation is valid also for the films deposited from the sols with aged nanoparticles in which tetra aniline was

In the measured frequency ranges, ε' and ε'' vary within 2.1–1.1, 3.4–6.2 and 0.25–0.75, 0.08– 1.8, respectively. From the EMA analysis of the spectra, it was concluded that the *nc*-Si film in light reflection processes can on average be considered as a two component medium

It was shown that the complex dielectric dispersion of films in the frequency range of 10 – 2×106 Hz is well approximated by the semiempirical Cole–Cole relation, taking into account

An analysis of the frequency dependences of the ac conductivity of the studied films allowed the conclusion to be drawn that the ac conduction process is well described by the

The dependence of the dark conductivity of films on the ambient air humidity and the temperature dependence of absorption bands related to associated Si–O–H groups allows the conclusion to be drawn that the conductivity at frequencies lower than 2 ×102 Hz is controlled by proton transport through hydrogen bound hydroxyl groups on the surface of

Using Cole-Cole and Debye relations for approximation of experimental spectra ε (ω) the values of static permittivity ε0 of films I, II and III have been found. For films I and II quantities ε0 close to the values characteristic of crystalline silicon. For films of III ε0≈ 67, i.e. greatly exceeds ε0 for c-Si. Such a high value ε0 we attribute to increasing polarization of the silicon nanoparticles when the tetraaniline complexes are attached to

AC conductivity of the films II and III in the whole frequency range of 1-106 Hz can not be approximated by a power law, which is characteristic of the conductivity of the films I. We show that such deviation from the dependence σAS ~ ωs is associated with a doubledielecrtic relaxation typical for films II and III and with the presence in the spectra ε "(ω) of

the synthesis of nanoparticles until their deposition on the substrate.

consisting of SiO and air gaps with a porosity of 50%.

cluster diffusion approximation model.

silicon nanoparticles.

their surface.

these films Debye components.

the effect of free charges controlling the dark dc conductivity of films.

**3. Conclusion** 

added (film III).

From this figure it is clear that if the ε''(ω) spectrum of the films II describes only the distribution of the Cole-Cole, they would obey the conductivity relation (13) throughout the frequency range 1 ≤ ν ≤ 106 Hz as well as the conductivity of the films I.

For the film III observed more complicated situation, its spectrum is distorted with respect to relation (13), not only at high frequencies ν≥103Hz, but also at frequencies ν ≤ 10 Hz (see Figure 16, b). According to the vast majority of experimental data, the frequency dependence of the conductivity of disordered media has kind of plateau (low-frequency plateaus) at low frequencies and is a power in excess of a certain critical frequency.

Fig. 16. The frequency dependence of AC conductivity of the films II (a) and III (b), as well as its approximation by: the Debye law - (1), the relation of Cole - Cole - (2) and the total approximation, which takes into account the dc conductivity - (3). (4) - power dependence with an exponent equal to the value of h at the Cole-Cole relation.

For films of III observes the opposite situation, instead, the appearance of a plateau at low frequencies, the conductivity σ (ω) begins to decrease more quickly with decreasing frequency of the external electric field. The reason for the absence of such low frequency plateau may be the existence of significant resistance at the interface of the film-electrode.

Comparison of σ (0), σDC and σB (0) from Table 1 shows their good agreement for film I. For films II are in good agreement the values σ (0) and σDC but somewhat too high the value of σ<sup>B</sup> (0) with respect to them. For films III good agreement is observed for the values σDC and σB (0) but σ (0) is less than these quantities is about 20 times. The fact that σDCI more than 25 times higher then σDCII (see Table1) confirms our earlier assumption that the degree of surface oxidation of silicon nanoparticles of films II is significantly higher than that in films I.

At frequencies νs1 ≥ 1·105Hz for films II and νs2 ≥ 3 · 104Hz for films III conductivity begins to depend very weakly on the frequency of an external electric field. This behavior is usually associated with the manifestation of the nature of hopping conduction (Barsoukov & Macdonald, 2002), and the frequency νс determined by the height of the barriers between potential wells, which are involved in the hopping transport of charge carriers. Because νs1> νs2, we can conclude that the presence of tetraaniline on the surface of silicon nanoparticles lowers the barriers separating localized states.

## **3. Conclusion**

434 Smart Nanoparticles Technology

From this figure it is clear that if the ε''(ω) spectrum of the films II describes only the distribution of the Cole-Cole, they would obey the conductivity relation (13) throughout the

For the film III observed more complicated situation, its spectrum is distorted with respect to relation (13), not only at high frequencies ν≥103Hz, but also at frequencies ν ≤ 10 Hz (see Figure 16, b). According to the vast majority of experimental data, the frequency dependence of the conductivity of disordered media has kind of plateau (low-frequency

Fig. 16. The frequency dependence of AC conductivity of the films II (a) and III (b), as well as its approximation by: the Debye law - (1), the relation of Cole - Cole - (2) and the total approximation, which takes into account the dc conductivity - (3). (4) - power dependence

a b

10-10

10-9

10-8

Conductivity (Ohm\*m)


**4**

**2**

**3**

10-7

10-6

10-5

10-1 100 101 10<sup>2</sup> 103 104 105 106

**1**

Frequency (Hz)

For films of III observes the opposite situation, instead, the appearance of a plateau at low frequencies, the conductivity σ (ω) begins to decrease more quickly with decreasing frequency of the external electric field. The reason for the absence of such low frequency plateau may be the existence of significant resistance at the interface of the film-electrode.

Comparison of σ (0), σDC and σB (0) from Table 1 shows their good agreement for film I. For films II are in good agreement the values σ (0) and σDC but somewhat too high the value of σ<sup>B</sup> (0) with respect to them. For films III good agreement is observed for the values σDC and σB (0) but σ (0) is less than these quantities is about 20 times. The fact that σDCI more than 25 times higher then σDCII (see Table1) confirms our earlier assumption that the degree of surface

At frequencies νs1 ≥ 1·105Hz for films II and νs2 ≥ 3 · 104Hz for films III conductivity begins to depend very weakly on the frequency of an external electric field. This behavior is usually associated with the manifestation of the nature of hopping conduction (Barsoukov & Macdonald, 2002), and the frequency νс determined by the height of the barriers between potential wells, which are involved in the hopping transport of charge carriers. Because νs1> νs2, we can conclude that the presence of tetraaniline on the surface of silicon nanoparticles

oxidation of silicon nanoparticles of films II is significantly higher than that in films I.

with an exponent equal to the value of h at the Cole-Cole relation.

10-1 100 101 102 103 104 105 106

**1**

Frequency (Hz)

10-10 10-9 10-8 10-7 10-6 10-5

Conductivity (Ohm\*m)-1

**3**

lowers the barriers separating localized states.

plateaus) at low frequencies and is a power in excess of a certain critical frequency.

frequency range 1 ≤ ν ≤ 106 Hz as well as the conductivity of the films I.

**2**

Dielectric and transport properties of thin films obtained by deposition of silicon nanoparticles from ethanol sols on a glass, quartz, and aluminum substrates were measured by optical ellipsometry and impedance spectroscopy methods. The real and imaginary permittivities of *nc*-Si films were measured in frequency ranges of 5 × 1014–1015 and 10–106 Hz. It was found that the permittivity spectra depend on the time which has elapsed since the synthesis of nanoparticles until their deposition on the substrate.

Only one type of dipole relaxation, which can be described by semi-empirical Cole-Cole equation, exists in films prepared from sols with silicon nanoparticles, synthesized a week before their deposition on a substrate (film I). In films prepared from sols containing aged nanoparticles (film II) there is a double-dipole relaxation, which is revealed in the fact that for the approximation of the experimental spectra of these films not only Cole-Cole relation but the law of Debye dipole relaxation should be used. A similar confirmation is valid also for the films deposited from the sols with aged nanoparticles in which tetra aniline was added (film III).

In the measured frequency ranges, ε' and ε'' vary within 2.1–1.1, 3.4–6.2 and 0.25–0.75, 0.08– 1.8, respectively. From the EMA analysis of the spectra, it was concluded that the *nc*-Si film in light reflection processes can on average be considered as a two component medium consisting of SiO and air gaps with a porosity of 50%.

It was shown that the complex dielectric dispersion of films in the frequency range of 10 – 2×106 Hz is well approximated by the semiempirical Cole–Cole relation, taking into account the effect of free charges controlling the dark dc conductivity of films.

An analysis of the frequency dependences of the ac conductivity of the studied films allowed the conclusion to be drawn that the ac conduction process is well described by the cluster diffusion approximation model.

The dependence of the dark conductivity of films on the ambient air humidity and the temperature dependence of absorption bands related to associated Si–O–H groups allows the conclusion to be drawn that the conductivity at frequencies lower than 2 ×102 Hz is controlled by proton transport through hydrogen bound hydroxyl groups on the surface of silicon nanoparticles.

Using Cole-Cole and Debye relations for approximation of experimental spectra ε (ω) the values of static permittivity ε0 of films I, II and III have been found. For films I and II quantities ε0 close to the values characteristic of crystalline silicon. For films of III ε0≈ 67, i.e. greatly exceeds ε0 for c-Si. Such a high value ε0 we attribute to increasing polarization of the silicon nanoparticles when the tetraaniline complexes are attached to their surface.

AC conductivity of the films II and III in the whole frequency range of 1-106 Hz can not be approximated by a power law, which is characteristic of the conductivity of the films I. We show that such deviation from the dependence σAS ~ ωs is associated with a doubledielecrtic relaxation typical for films II and III and with the presence in the spectra ε "(ω) of these films Debye components.

Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 437

[13] Cao, Chao; He, Yao; Torras, J.; Deumens, E.; Trickey, S. B. & Cheng, Hai-Ping. (2007)

*Chemical Physics,* Vol. 126, №21, (June 2007) p.p. 211101(1-3), ISSN 0021-9606 [14] Cole, K. S. & Cole, R. H. (1941). Dispersion and Absorption in Dielectrics. *Journal of Chemical Physics,* Vol. 9, №, (February 1941) p.p. 341-351, ISSN 0021-9606 [15] Conte, G.; Feliciangeli, M. C.; & Rossi, M. C. (2006) Impedance of nanometer sized

[16] Dorofeev, S. G.; Kononov, N. N.; Ishchenko, A. A.; Vasil'ev, R. B.; Goldschtrakh, M. A.;

[17] Du, Mao-Hua; Kolchin, A. & Chenga, Hai-Ping. (2003). Water–silica surface

[18] Dyre, J.C. & Schrøder, T. B. (2000). Universality of ac conduction in disordered solids. *Reviews of Modern Physics*, Vol.72, №3, (July 2000), p.p. 873 – 892, ISSN 0034-6861. [19] Ehbrecht, M.; Ferkel, H.; Huisken, F.; Holz, L.; Polivanov, Yu.N.; Smirnov, V.V.;

[20] Glasser, L. (1975) Proton Conduction and Injection in Solids. *Chemical Reviews*, Vol.75,

[21] Goswami, A. & Goswami, A.P. (1973). Dielectric and optical properties of ZnS films.

[22] Hubner, K. (1980). Chemical Bond and Related Properties of SiO2. *Physica Status Solidi*

[23] Hunt, A.G. (2001). Ac hopping conduction: perspective from percolation theory.

[24] Isichenko, M. B. (1992) Percolation, statistical topography, and transport in random

[25] Jurbergs, D.; Rogojina, E.; Mongolini, L. & Kortshagen, U. (2006). Silicon nanocrystalls

[26] Kakinuma, H.; Mohri, M.; Sakamoto, M. & Tsuruoka T. (1991). Sructural properties of

[27] Kononov, N. N.; Kuz'min, G. P.; Orlov, A. N.; Surkov, A. A. and Tikhonevich, O. V.

*Philosophical Magazine* B Vol. 64, №9, (2001), p.p. 875-913, ISSN 1364-2812

media. *Reviews of Modern Physics*, Vol. 64, №4, (October 1992), p.p.961 – 1043, ISSN

with ensemble quantum yields exceeding 60%. *Applied Physycs Letters,* Vol. 88,

polycrystalline silicon films prepared at low temperature by chemical vapor deposition. *Journal of Applied Physics*, Vol.70, (December 1991), p.p. 7374 - 7381,

(2005). Optical and Electrical Properties of Thin Wafers Fabricated from Nanocrystalline Silicon Powder. *Rus. Semiconductors,* Vol. 39, No. 7, (November

9, (November 1995), p.p. 5302-5305, ISSN 0021-8979

*Thin Solid Films* Vol. 16, (January 1973), p.p. 175 – 185

№23, (June 2006) 233116(1-3), ISSN 0003-6951.

ISSN0003-6951

ISSN 1063-7826.

(2003) ISSN 0021-9606.

№1, (January 1974), p.p. 21 – 65.

(a) Vol. 61, (May 1980), p.p. 665-673

2005)*,* pp. 835–839, ISSN 1063-7826

print/ISSN 1463-6417 online

0034-6861.

ISSN 0021-8979

Fracture, water dissociation, and proton conduction in SiO2 nanochains. *Journal of* 

silicon structures. *Applied Physics Letters,* Vol. 89, № 2, (July 2006), p.p.022118(1-3),

Zaitseva, K. V.; Koltashev, V. V.; Plotnichenko, V. G. and O. V. Tikhonevich. (2009). Optical and Structural Properties of Thin Films Precipitated from the Sol of Silicon Nanoparticles. *Rus. Semiconductors,* Vol. 43, No. 11, (April 2009), pp. 1420–1427.

interactions: A combined quantum-classical molecular dynamic study of energetics and reaction pathways. *Journal of Chemical Physics*, Vol. 119, №131, p.p.6418 – 6422

Stelmakh, O.M. & Schmidt R. (1995) Deposition and analysis of silicon clusters generated by laser-induced gas phase reaction *Journal of Applied Physics,* Vol.78, №

## **4. Acknowledgment**

We sincerely thank Dr. Helen Yagudayev, the senior researcher of the Shemyakin - Ovchinnicov Institute of Bioorganic Chemistry of RAS, for providing us the conductive tetraaniline solutions.

We also thank our colleagues prof. Plotnichenko V.G., prof. Kuz'min G.P., prof. Ischenko A.A., dr. Koltashev V.V., researcher Tikhonevich O.V. for the fruitful cooperation in investigation of the properties of nano-sized silicon.

## **5. References**


We sincerely thank Dr. Helen Yagudayev, the senior researcher of the Shemyakin - Ovchinnicov Institute of Bioorganic Chemistry of RAS, for providing us the conductive

We also thank our colleagues prof. Plotnichenko V.G., prof. Kuz'min G.P., prof. Ischenko A.A., dr. Koltashev V.V., researcher Tikhonevich O.V. for the fruitful cooperation in

[1] Anopchenko,A.; Marconi, A.; Moser, E.; Prezioso, S.; Wang; M., Pavesi; L., Pucker, G. &

[2] Aspens, D. E. & Studna, A. A. (1983) Dielectric functions and optical parameters of Si,

[3] Austin, I. G. & Mott, N. F. (1069). Polarons in crystalline and non-crystalline materials.

[4] Axelrod, E.; Givant, A.; Shappir, J.; Feldman, Y. & Sa'ar. A. (2002) Dielectric relaxation

[5] Azzam, R.M.A. & Bashara N.M. (1977) *Ellipsometry and polarized light*, North-Holland publishing company, ISBN 1704050000 , Amsterdam, New York, Oxford [6] Barsoukov, E. & Macdonald, J. R. (2005) *Impedance Spectroscopy. Theory, Experiment, and* 

[8] Ben-Chorin, M.; Möller, F.; Koch, F.; Schirmacher, W. & Eberhard, M. (1995) Hopping

[9] Bianchi, R.F.; Leal Ferreira, G.F.; Lepienski, C.M. & Faria, R.M. (1999). Alternating

[10] D.A.G. Bruggeman. (1935). Berechung verschiedener physikalisher konstanten von heterogenen substanzen. *Annalen der Physik* (Leipzig), Vol. 24, (1935), pp. 636-664 [11] Brus, L.E.; Szajowski, P.F.; Wilson, W. L.; Harris, T. D.; Schuppler, S. & Citrin. P. H.

[12] Campbell, I.H. & Faushet P.M. (1986) The effect of microcrystalline size and shape on

A*dvances in physics*, Vol.18, №71, (January 1969), pp. 41-102

Bellutti. P. J. (2009) Low-voltage onset of electroluminescence in nanocrystalline-Si/SiO2 multilayers *Journal of Applied Physics,* Vol.106, (2009), p.p. 033104, ISSN

Ge, Gap, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV, *Physical Review* B, Vol.

and transport in porous silicon *Physical Review* B, Vol. 65, №16, (April 2002) , p.p.

*Applications*, Second Edition, A John Wiley & Sons, Inc., Publication, New Jersey,

transport on a fractal: ac conductivity of porous silicon *Physical Review* B, Vol. 51,

electrical conductivity of polyaniline. *Journal of Chemical Physics*, Vol.110,№9,

(1995) Electronic Spectroscopy and Photophysics of Si Nanocrystals: Relationship to Bulk c-Si and Porous Si. *Journal of American Chemical Society,* Vol. 117, (1995) pp.

the one phonon Raman spectra of crystalline semiconductors. Solid State Communications. Vol. 58, №10 (February 1986), p.p.739-741, ISSN 0038-1098

**4. Acknowledgment** 

tetraaniline solutions.

**5. References** 

0021-8979

2915-2922

investigation of the properties of nano-sized silicon.

27,№2, (January 1983), p.p.985 - 1009

USA and Canada ISBN: 0-471-64749-7 [7] J. L. Barton, (1966). *Verres Réfract*. Vol. 20, p.p. 328 (1966).

№4, (January 1995) , p.p. 2199(1-15) , ISSN 0163-1829

(March 1999), p.p. 4602-4607, ISSN 0021-9606

165429(1-7) ,ISSN 0163-1829


Dielectric and Transport Properties of Thin Films Deposited from Sols with Silicon Nanoparticles 439

[42] Puzder, A.; Williamson, A.J.; Grossman, J.C. & Galli G. (2002). Surface Chemistry of

[43] Richter, H.; Wang, Z. & Ley L. (1981). The one phonon Raman spectrum in

[44] Saadane, O.; Lebib, S.; Kharchenko, A.V.; Longeaud, C. & R. Roca I Cabarrocas. (2003)

[45] Schrøder, T. B. & Dyre. J. C. (2002). Computer simulations of the random barrier model. *Physical Chemistry and Chemical Physics*, Vol.4, (June 2002), p.p. 3173–3178 [46] Schrøder, T. B. & Dyre J. C.(2008). AC Hopping Conduction at Extreme Disorder Takes

[47] Schuppler, S.; Friedman, S.L.; Marcus, M.A.; Adler, D.L.; Xie, Y. H.; Ross, F.M.; Chabal,

[48] Stuart B. (2004). *Infrared Spectroscopy: Fundamentals and Applications*, John Wiley & Sons,

[49] Eds. by Tompkins, G. H. & Irene, E.A. (2005). *Handbook of ellipsometry*. p.p. 282-289.

[50] De la Torre, J.; Bremond, G.; Lemiti, M.; Guillot , G.; Mur, P. & Buffet. N. (2006) Silicon

[51] Tsang, J.C.; Tischler, M.A. & Collins R.T. (1992). Raman scattering from H and O

[52] Tsu, R.; Shen, H. & Dutta M. (1992). Correlation of Raman and photoluminescence

[53] Tsu, R.; Babić, D. & Ioriatti, L. Jr. (1997). Simple model for the dielectric constant of

[54] Tsu, R. (2000) Phenomena in silicon nanostructure devices. *Applied Physics* A Vol.71,

[55] Urbach, B.; Axelrod, E. & Sa'ar A. (2007). Correlation between transport, dielectric, and

[56] Voutsas, A.T.; Hatalis, M.K.; Boyce, J. & Chiang A. (1995). Raman spectroscopy of

(September 2000) p.p.391–402, DOI 10.1007/s003390000552

Vol. 75, №20, (May 2007) , p.p. 205330(11) , ISSN 1098-0121

*Physics*, Vol. 93, №11, (June 2003), p.p.9371 – 9379, ISSN 0021-8979

0031-9007

p.p.625-629, ISSN 0038-1098

p.p.025901(1-4), ISSN 0031-9007

4910-4925, ISSN 1098-0121

Ltd., ISBN 0-470-85427-8

430, ISSN 0928-4931

2281, ISSN 0003-6951

112-114, ISSN 0003-6951

p.p.1327 – 1329, ISSN 0021-8979

(Springer-Verlag GmbH & Co. KG)

Silicon Nanoclusters. *Physical Review Letters*, Vol. 88, (2002), p.p.097401(1-4), ISSN

microcrystalline silicon. *Solid State Communications*, Vol.39, №5, (May 1981),

Structural, opical and electronic properties of hydrogenated polymorphous silicon films deposited from silane-hydrogen and silane-helium mixtures. *Journal of Applied* 

Place on the Percolating Cluster *Physical Review Letters,* Vol.101, (July 2008)

Y.J.; Harris, T.D.; Brus, L.E.; Brown, W.L.; Chaban, E.E.; Szajowski, P.E.; Christman, S.B. & Citrin, P.H. (1995). Size, shape and composition of luminescent species in oxidized Si nanocrystals and H-passivated porous Si. *Physical Review* B, Vol.52, p.p.

William Andrew publishing, Springer-Verlag GmbH & Co. KG. New York, Heidelberg. ISBN: 0-8155-1499-9 (William Andrew, Inc.), ISBN: 3-540-22293-6

nanostructured layers for improvement of silicon solar cells efficiency: A promising perspective. Materials Science and Engineering C Vol. 26, (January 2006), p.p. 427–

terminated porous Si. *Applied Physics Letters*, Vol.60, №18, (May 1992) p.p. 2279-

spectra of porous silicon. *Applied Physics Letters,* Vol.60, №1, (January1992), p.p.

nanoscale silicon particle. *Journal Applied Physics,* Vol. 82, № 3, (August 1997),

optical properties of oxidized and nonoxidized porous silicon *Physical Review* B,

amorphous and microcrystalline silicon films deposited by low-pressure chemical


[28] Kononov, N. N.; Dorofeev, S. G.; Ishenko, A. A.; Mironov, R. A.; Plotnichenko, V. G. &

[29] Kovalev, D.; Polisski, G.; Ben-Chorin, M.; Diener, J. & Koch F. (1996) The temperature

[30] Kousik, D. & De, S.K. (2007). Double dielectric relaxations in SnO2 nanoparticles

[32] Leite, V. B. P.; Cavalli, A. & Oliveira, O. N. Jr. (1998) Hydrogen-bond control of

[33] Luppi, M. & Ossicini S. (2005). Ab initio study on oxidized silicon clusters and silicon

[34] Ma, Zhixun; Liao, Xianbo; Kong, Guanglin & Chu, Junhao (2000) Raman scattering of

[35] Min, R .B. & Wagner, S. (2002), Nanocrystalline silicon thin-film transistors with 50-nm-

[36] Moliton, A. (2007) *Applied Electromagnetism and Materials*, Ch.1, p.8. Springer Science

*[37]* Nakajima, T. (1971) *Annual Report, Conference on Electric Insulation and Dielectric Phenomena* (Washington, D.C., National Academy of Sciences, 1972), p. 168. [38] Namikawa. H. (1975).Characterization of the diffusion process in oxide glasses based on

[39] Nogami, M. & Abe, Y. (1997). Evidence of water-cooperative proton conduction in silica

[40] Nogami, M.; Nagao, R. & Wong, C. (1998). Proton Conduction in Porous Silica Glasses

[41] Pickering, C.; Beale, M. I. J.; Robbins, D. J.; Pearson, P. J. & Greef. R. (1984). Optical

Rev. B V.71, (January 2005), p.p. 035340(1-15), ISSN 1098-0121

2007), p.p. 084110 -1,084110 -7, ISSN 0021-8979 print | 1089-7550 online [31] Kuz'min, G.P.; Karasev, M.E.; Khokhlov, E.M. Kononov, N.N.; Korovin, S.B.;

Vol.80, №10, (November 1996) , p.p.5978 -5983, ISSN 0021-8979

(August 2011), pp. 1038–1048. ISSN 1063-7826

Vol.10, №4, (April 2000) p.p. 939-945

1998), p.p. 6835 – 6839, ISSN 1063-651X

543 (DOI) 10.1007/s003390100927

and Business Media. ISBN-10: 0-387-38062-0

414-420

1829

5772-5775, S1089-5647

p.p.6535-6552, ISSN 0022-3719

E. M. Dianov. (2011). Dielectric and Transport Properties of Thin Films Precipitated from Sols with Silicon Nanoparticles *Rus. Semiconductors,* 2011, Vol. 45, No. 8,

dependence of the absorption coefficient of porous silicon *Journal of Applied Physics*,

dispersed in conducting polymer. *Journal of Applied Physics,* Vol.102,*.*№ 8, ( October

Plotnichenko, V.G.; Polyakov, S.N.; Pustovoy, V.I. & Tikhonevich O.V. (2000). Nanosize Silicon Powders: The Structure and Optical Properties. *Rus. Laser Physics*

structure and conductivity of Langmuir films. *Physical. Review* E, Vol. 57, №6, (June

nanocrystals embedded in SiO2: Beyond the quantum confinement effect. Phys.

nanocrystalline silicon embedded in SiO2. *Science in China* A, Vol.43, (2000), p.p.

thick deposited channel layer, 10 cm2 V−1s−1 electron mobility and 108 on*/*off current ratio *Applied Physics A Materials Science &Processing*, Vol. 74, (August 2001), p.p.541–

the correlation between electric conduction and dielectric relaxation. Journal of Non-Crystalline Solids, Vol.18, №2, (September 1975), p.p.173-195, ISSN 0022-3093.

glasses. *Physical Review* B, Vol. 55, №18, (May 1997), p.p.12108 - 12112, ISSN 0163-

with High Water Content. *Journal of Physical Chemistry* B, Vol. 102, (July 1998), p.p.

studies of the structure of porous silicon films formed in p-type degenerate and non- degenerate silicon. *Journal Physics* C: *Solid State Physics*, Vol.17, (August 1984)


**20** 

*Slovakia* 

**Self-Assembly of Nanoparticles** 

The research field of nanoparticle synthesis and related nanoparticle applied sciences have been steadily growing in the past two decades. The chemical synthesis of nanoparticles was improved up to the point that the organic and inorganic nanoparticle colloids are produced with a low size dispersion and with a well defined nanoparticle shape in large quantities. A stunning feature of a drying nanoparticle colloidal solution is the ability to create selfassembled arrays of nanoparticles. The self-assembled nanoparticle arrays mimic the natural crystals. The size of perfectly ordered domains is limited by the size dispersion of nanoparticles. Consequently the defects in the self-assembled structure are obvious and unavoidable. Despite these defects, the self-assembled nanoparticle arrays represent a new class of nanostructures built on "bottom-up" technological approach to fabrication. The traditional way of "top-down" fabrication technology primarily based on nano-lithography is complex, including many technological steps, time consuming and expensive. The main advantage is the tight control of all parameters governing the final nanostructures. On the other hand, the emerging fabrication technologies based on the self-assembled nanoparticles are fast, less complex and more price competitive. An extensive research is now focused on a deeper understanding of processes that control the self-assembly. New routes for directed or stimulated self-assembly are studied to achieve a tighter control than readily available in the spontaneous self-assembly. In this chapter we will discuss the spontaneous nanoparticle self-assembly with emphasis on characterization of nanoparticle arrays at various stages of the self-assembly process. The main diagnostic technique used throughout this chapter will be the grazing-incidence small-angle X-ray scattering (GISAXS) that represents a reliable and simple monitor of nanoparticle arrangement. The theoretical background of GISAXS and required instrumentation are described in Section 2. The most flexible surface to study the nanoparticle self-assembly processes is the liquid surface. The Section 3. reviews the latest results of studies combing the GISAXS technique with Langmuir nanoparticle layers on the water subphase. Almost all relevant nanoparticle applications rely on self-assembled arrays on solid surfaces. The Section 4 describes in detail the possibilities of nanoparticle transfer from liquid onto solid surfaces. The post-processing of self-assembled nanoparticle

arrays and their applications are reviewed in the last Section 5.

**1. Introduction** 

**at Solid and Liquid Surfaces** 

Peter Siffalovic, Eva Majkova, Matej Jergel, Karol Vegso, Martin Weis and Stefan Luby *Institute of Physics, Slovak Academy of Sciences* 

vapor deposition *Journal of Applied Physics,* Vol.78, №12, (December 1995), p.p. 6999-7005, ISSN 0021-8979


## **Self-Assembly of Nanoparticles at Solid and Liquid Surfaces**

Peter Siffalovic, Eva Majkova, Matej Jergel, Karol Vegso, Martin Weis and Stefan Luby *Institute of Physics, Slovak Academy of Sciences Slovakia* 

## **1. Introduction**

440 Smart Nanoparticles Technology

[57] Wang, K.; Chen, H. & Shen, W.Z. (2003). AC electrical properties of nanocrystalline silicon thin films. *Physica* B, Vol. 336, (April 2003), p.p. 369-378, ISSN 0921-4526 [58] Wang, W. & MacDiarmid, A. (2002), New synthesis of phenil/phenil end-capped

[59] Wovchko, E. A.; Camp, J. C.; Glass, J. A. Jr. & Yates, J. T. Jr. (1995). Active sites on SiO2:

[60] G. Zuter.(1980) Dielectric and Optical Properties of SiOx. *Physica Status Solidi* (a) Vol. 59,

6999-7005, ISSN 0021-8979

(April 1980), p.p. K109 –K113

p.p. 199-205, ISSN

0743-7463

vapor deposition *Journal of Applied Physics,* Vol.78, №12, (December 1995), p.p.

tetraaniline in the leucoemeraldine oxidation states. *Synthetic metals,* Vol. (2002) 129,

role in CH30H decomposition. Langmuir Vol.11, №7, (1995), p.p.2592-2599, ISSN

The research field of nanoparticle synthesis and related nanoparticle applied sciences have been steadily growing in the past two decades. The chemical synthesis of nanoparticles was improved up to the point that the organic and inorganic nanoparticle colloids are produced with a low size dispersion and with a well defined nanoparticle shape in large quantities. A stunning feature of a drying nanoparticle colloidal solution is the ability to create selfassembled arrays of nanoparticles. The self-assembled nanoparticle arrays mimic the natural crystals. The size of perfectly ordered domains is limited by the size dispersion of nanoparticles. Consequently the defects in the self-assembled structure are obvious and unavoidable. Despite these defects, the self-assembled nanoparticle arrays represent a new class of nanostructures built on "bottom-up" technological approach to fabrication. The traditional way of "top-down" fabrication technology primarily based on nano-lithography is complex, including many technological steps, time consuming and expensive. The main advantage is the tight control of all parameters governing the final nanostructures. On the other hand, the emerging fabrication technologies based on the self-assembled nanoparticles are fast, less complex and more price competitive. An extensive research is now focused on a deeper understanding of processes that control the self-assembly. New routes for directed or stimulated self-assembly are studied to achieve a tighter control than readily available in the spontaneous self-assembly. In this chapter we will discuss the spontaneous nanoparticle self-assembly with emphasis on characterization of nanoparticle arrays at various stages of the self-assembly process. The main diagnostic technique used throughout this chapter will be the grazing-incidence small-angle X-ray scattering (GISAXS) that represents a reliable and simple monitor of nanoparticle arrangement. The theoretical background of GISAXS and required instrumentation are described in Section 2. The most flexible surface to study the nanoparticle self-assembly processes is the liquid surface. The Section 3. reviews the latest results of studies combing the GISAXS technique with Langmuir nanoparticle layers on the water subphase. Almost all relevant nanoparticle applications rely on self-assembled arrays on solid surfaces. The Section 4 describes in detail the possibilities of nanoparticle transfer from liquid onto solid surfaces. The post-processing of self-assembled nanoparticle arrays and their applications are reviewed in the last Section 5.

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 443

where *N* is the total number of nanoparticles, *<sup>i</sup> F (q )* is the form-factor of the *i*th nanoparticle

For the nanoparticles immobilized at interfaces we have to include the refraction/reflection phenomena at the interfaces and the associated multiple scattering events. This is treated in detail within the framework of the distorted-wave Born approximation (DWBA) which introduces a modified form-factor for each nanoparticle confined near the interface (Holý, Pietsch et al. 1999). A detailed survey of the DWBA theory can be found in the following reference (Renaud, Lazzari et al. 2009). A typical DWBA effect is the presence of the Yoneda enhancement at the critical exit angle in the GISAXS patterns (Yoneda 1963). In many cases we can avoid the DWBA multiple scattering terms by recording the GISAXS pattern at the incident angle several times larger than the critical angle for the total X-ray reflection of the supporting substrate (Daillant and Gibaud 2009). If we assume that the nanoparticles can be described by an average form-factor <sup>2</sup> *F(q )* than the eq. (2) in BA can be rearranged as

*ir* defines the position of the *i*th nanoparticle. Within the simple Born (kinematic) approximation (BA) the nanoparticle form-factor is simply given by the Fourier transform of

*i(r)* as follows (Glatter and Kratky 1982)

*<sup>i</sup> F (q) (r ).exp(iq.r )dr <sup>i</sup>* (3)

<sup>2</sup> *<sup>I</sup>*() () *<sup>q</sup> N F <sup>q</sup> <sup>S</sup> <sup>q</sup>* (4)

*r* centered at

*<sup>S</sup> <sup>q</sup>* represent the nanoparticle interference function. The nanoparticle

*P r* defined in real space (Lazzari 2009). The pair correlation function is

interference function is the reciprocal space equivalent of the nanoparticle pair correlation

an arbitrarily selected nanoparticle. This function is directly accessible from the TEM/SEM

The GISAXS experimental technique was confined for a long time to synchrotron facilities as the scattering cross-section is generally very low. Each synchrotron ring has a dedicated SAXS beamline that can support conventional GISAXS setup. The Fig. 2 shows the typical GISAXS scheme of the BW4 beamline at the DORIS III ring at HASYLAB, Hamburg (Stribeck 2007). The front-end of the experimental setup is a wiggler that generates the X-ray radiation. The crystal monochromator is used to select a single wavelength typically at 0.139 nm. The radiation is further conditioned with slits and two cylindrical mirrors to focus the radiation in both directions at the detector plane. The additional beryllium X-ray lenses can be attached to focus the radiation at the sample

The distance between the sample and detector can vary between 3 m and 13 m that allows flexibility in the accessible range of the reciprocal space. The two-dimensional (2D) X-ray CCD detector is used to record the X-ray radiation scattered by the sample. The primary and

proportional to the probability of finding a nanoparticle at the position vector

and

follows

Here the

function

micrographs.

position (Roth, Döhrmann et al. 2006).

specularly reflected beams are suppressed by the beamstops.

the nanoparticle density function

## **2. SAXS/GISAXS techniques and their employment for nanoparticle research**

The transmission (TEM) and scanning (SEM) electron microscopy provide information on the nanoparticle shape, average size and size distribution. However, this information is usually obtained after numerical evaluation of real space micrographs from limited data sets. Alternative approach is based on the angle-resolved analysis of scattered X-rays or neutrons from the nanoparticles and their assemblies. In this chapter we will employ the small-angle X-ray scattering (SAXS) (Guinier and Fournet 1955) for the nanoparticle colloidal solutions. For nanoparticles immobilized at interfaces, a related technique so-called grazing-incidence small-angle X-ray scattering (GISAXS) is used that has been recently reviewed (Renaud, Lazzari et al. 2009). A general scheme of the GISAXS experiment is shown in Fig. 1.

Fig. 1. The GISAXS measurement geometry

The collimated X-ray beam defined by *<sup>i</sup> k* is incident under a small grazing angle on the sample surface. The scattered radiation is recorded by a two dimensional X-ray detector. Each point at the detector plane receives the scattered radiation given by a set of two angles (*f*, *f*) that corresponds to a unique scattering vector *q* in the reciprocal space. The relationship between the scattering vector in reciprocal space and the scattering angles in the real space is given by the following equations (Müller-Buschbaum 2009)

$$\begin{aligned} q\_{\chi} &= \frac{2\pi}{\lambda} \Big[ \cos(2\Theta\_f) \cos(\alpha\_f) - \cos(\alpha\_i) \Big] \\ q\_{\psi} &= \frac{2\pi}{\lambda} \Big[ \sin(2\Theta\_f) \cos(\alpha\_f) \Big] \\ q\_z &= \frac{2\pi}{\lambda} \Big[ \sin(\alpha\_f) + \sin(\alpha\_i) \Big] \end{aligned} \tag{1}$$

The SAXS/GISAXS signal is given by constructive interferences of X-ray waves partially scattered on individual nanoparticles. The total scattered intensity (also called the scattering cross-section) at specific *q* vector in the reciprocal space is given as (Feigin, Svergun et al. 1987)

$$I(\vec{q}) = \sum\_{i=1}^{N} \sum\_{j=1}^{N} F^i(\vec{q}).F^{j,\*}(\vec{q}).exp\left[i\vec{q}.(\vec{r\_i} - \vec{r\_j})\right] \tag{2}$$

where *N* is the total number of nanoparticles, *<sup>i</sup> F (q )* is the form-factor of the *i*th nanoparticle and *ir* defines the position of the *i*th nanoparticle. Within the simple Born (kinematic) approximation (BA) the nanoparticle form-factor is simply given by the Fourier transform of the nanoparticle density function *i(r)* as follows (Glatter and Kratky 1982)

$$F^{\vec{i}}(\vec{q}) = \int \mathfrak{p}\_i(\vec{r}) .exp(\vec{i}\vec{q}.\vec{r})d\vec{r} \tag{3}$$

For the nanoparticles immobilized at interfaces we have to include the refraction/reflection phenomena at the interfaces and the associated multiple scattering events. This is treated in detail within the framework of the distorted-wave Born approximation (DWBA) which introduces a modified form-factor for each nanoparticle confined near the interface (Holý, Pietsch et al. 1999). A detailed survey of the DWBA theory can be found in the following reference (Renaud, Lazzari et al. 2009). A typical DWBA effect is the presence of the Yoneda enhancement at the critical exit angle in the GISAXS patterns (Yoneda 1963). In many cases we can avoid the DWBA multiple scattering terms by recording the GISAXS pattern at the incident angle several times larger than the critical angle for the total X-ray reflection of the supporting substrate (Daillant and Gibaud 2009). If we assume that the nanoparticles can be described by an average form-factor <sup>2</sup> *F(q )* than the eq. (2) in BA can be rearranged as

follows

442 Smart Nanoparticles Technology

**2. SAXS/GISAXS techniques and their employment for nanoparticle research**  The transmission (TEM) and scanning (SEM) electron microscopy provide information on the nanoparticle shape, average size and size distribution. However, this information is usually obtained after numerical evaluation of real space micrographs from limited data sets. Alternative approach is based on the angle-resolved analysis of scattered X-rays or neutrons from the nanoparticles and their assemblies. In this chapter we will employ the small-angle X-ray scattering (SAXS) (Guinier and Fournet 1955) for the nanoparticle colloidal solutions. For nanoparticles immobilized at interfaces, a related technique so-called grazing-incidence small-angle X-ray scattering (GISAXS) is used that has been recently reviewed (Renaud, Lazzari et al. 2009). A general scheme of the GISAXS experiment is

sample surface. The scattered radiation is recorded by a two dimensional X-ray detector. Each point at the detector plane receives the scattered radiation given by a set of two angles

relationship between the scattering vector in reciprocal space and the scattering angles in

*x ff i*

The SAXS/GISAXS signal is given by constructive interferences of X-ray waves partially scattered on individual nanoparticles. The total scattered intensity (also called the scattering

> *N N*

*<sup>i</sup> j,\* i j*

*q* vector in the reciprocal space is given as (Feigin, Svergun et al.

*I q F (q).F (q).exp iq.(r r )* (2)

*q cos( )cos( ) cos( )*

 

*f*) that corresponds to a unique scattering vector

2

1 1

*i j*

the real space is given by the following equations (Müller-Buschbaum 2009)

<sup>2</sup> <sup>2</sup>

<sup>2</sup> <sup>2</sup>

*y ff*

*q sin( )cos( )*

 

 

*z fi*

*q sin( ) sin( )*

*<sup>i</sup> k* is incident under a small grazing angle on the

*q* in the reciprocal space. The

(1)

shown in Fig. 1.

(*f*, 

1987)

cross-section) at specific

Fig. 1. The GISAXS measurement geometry The collimated X-ray beam defined by

$$I(\vec{q}) = N \left\langle \left| F(\vec{q}) \right|^2 \right\rangle S\left(\vec{q}\right) \tag{4}$$

Here the *<sup>S</sup> <sup>q</sup>* represent the nanoparticle interference function. The nanoparticle interference function is the reciprocal space equivalent of the nanoparticle pair correlation function *P r* defined in real space (Lazzari 2009). The pair correlation function is proportional to the probability of finding a nanoparticle at the position vector *r* centered at an arbitrarily selected nanoparticle. This function is directly accessible from the TEM/SEM micrographs.

The GISAXS experimental technique was confined for a long time to synchrotron facilities as the scattering cross-section is generally very low. Each synchrotron ring has a dedicated SAXS beamline that can support conventional GISAXS setup. The Fig. 2 shows the typical GISAXS scheme of the BW4 beamline at the DORIS III ring at HASYLAB, Hamburg (Stribeck 2007). The front-end of the experimental setup is a wiggler that generates the X-ray radiation. The crystal monochromator is used to select a single wavelength typically at 0.139 nm. The radiation is further conditioned with slits and two cylindrical mirrors to focus the radiation in both directions at the detector plane. The additional beryllium X-ray lenses can be attached to focus the radiation at the sample position (Roth, Döhrmann et al. 2006).

The distance between the sample and detector can vary between 3 m and 13 m that allows flexibility in the accessible range of the reciprocal space. The two-dimensional (2D) X-ray CCD detector is used to record the X-ray radiation scattered by the sample. The primary and specularly reflected beams are suppressed by the beamstops.

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 445

Fig. 4. a) The SEM micrograph of Fe-O self-assembled nanoparticles. Measured (b) and simulated (c) GISAXS pattern of self-assembled nanoparticles. d) The extracted line-cut from

The auxiliary knife-edge blade is used to reduce the parasitic air-scattering. The additional vacuum flight-tube can be inserted between the sample and the X-ray detector to reduce the air scattering and absorption. The detector used is a fast acquisition CMOS based 2D X-ray

To illustrate the capability of the GISAXS technique to characterize the self-assembled nanoparticle monolayers we use an example of iron oxide nanoparticles (Siffalovic, Majkova et al. 2007). The Fig. 4a shows the SEM image of a self-assembled array of iron oxide nanoparticles. The inset of Fig. 4a shows the Fourier transform of SEM micrograph with partially smeared-out spots corresponding to the hexagonal arrangement. The smearing-out is due to mutually misaligned nanoparticle domains originating from finite nanoparticle size dispersion which is in sharp contrast to natural atomic crystals. The Fig. 4a and 4b show the measured and simulated GISAXS pattern, respectively. The characteristic side maxima located at the <sup>1</sup> 0 82 *q . nm <sup>y</sup>* are the "finger prints" of the self-assembly in the nanoparticle array. In the first approximation, the mean interparticle separation can be estimated from

the measured GISAXS pattern along with the simulation.

detector of PILATUS detector family (Kraft, Bergamaschi et al. 2009).

Fig. 2. The sketch of the experimental GISAXS geometry at BW4 beamline, HASYLAB

Fig. 3. a) The scheme of the laboratory GISAXS setup and (b) the photograph of its realization at Institute of Physics SAS.

The latest advances in the low-power X-ray generators and the efficient X-ray optics opened a new era of laboratory equipments suitable for GISAXS measurements (Michaelsen, Wiesmann et al. 2002). Nowadays already several companies (Bruker AXS, Anton Paar, Hecus XRS, Rigaku) supply complete X-ray solutions supporting GISAXS measurement modes for solid-state samples. The Fig. 3a and Fig. 3b show the laboratory setup scheme and the photograph of a home-built GISAXS instrumentation developed at the Institute of Physics SAS, respectively (Siffalovic, Vegso et al. 2010). This setup supports GISAXS measurements on solid as well as liquid surfaces. The core of the experimental apparatus is a compact low-power (30 W) X-ray source (Cu-K) equipped with a loosely focusing X-ray Montel optics (Wiesmann, Graf et al. 2009). The source can be freely rotated and translated in the vertical direction. This is important for the precise adjustment of the incident angle in the GISAXS measurements at liquid surfaces. The unwanted scattered radiation is eliminated by laser-beam precisely cut tungsten pinholes. The sample is fixed on a goniometer that allows precise height and tilt adjustments.

Fig. 2. The sketch of the experimental GISAXS geometry at BW4 beamline, HASYLAB

Fig. 3. a) The scheme of the laboratory GISAXS setup and (b) the photograph of its

The latest advances in the low-power X-ray generators and the efficient X-ray optics opened a new era of laboratory equipments suitable for GISAXS measurements (Michaelsen, Wiesmann et al. 2002). Nowadays already several companies (Bruker AXS, Anton Paar, Hecus XRS, Rigaku) supply complete X-ray solutions supporting GISAXS measurement modes for solid-state samples. The Fig. 3a and Fig. 3b show the laboratory setup scheme and the photograph of a home-built GISAXS instrumentation developed at the Institute of Physics SAS, respectively (Siffalovic, Vegso et al. 2010). This setup supports GISAXS measurements on solid as well as liquid surfaces. The core of the experimental apparatus is a compact low-power (30 W) X-ray source (Cu-K) equipped with a loosely focusing X-ray Montel optics (Wiesmann, Graf et al. 2009). The source can be freely rotated and translated in the vertical direction. This is important for the precise adjustment of the incident angle in the GISAXS measurements at liquid surfaces. The unwanted scattered radiation is eliminated by laser-beam precisely cut tungsten pinholes. The sample is fixed on a

realization at Institute of Physics SAS.

goniometer that allows precise height and tilt adjustments.

Fig. 4. a) The SEM micrograph of Fe-O self-assembled nanoparticles. Measured (b) and simulated (c) GISAXS pattern of self-assembled nanoparticles. d) The extracted line-cut from the measured GISAXS pattern along with the simulation.

The auxiliary knife-edge blade is used to reduce the parasitic air-scattering. The additional vacuum flight-tube can be inserted between the sample and the X-ray detector to reduce the air scattering and absorption. The detector used is a fast acquisition CMOS based 2D X-ray detector of PILATUS detector family (Kraft, Bergamaschi et al. 2009).

To illustrate the capability of the GISAXS technique to characterize the self-assembled nanoparticle monolayers we use an example of iron oxide nanoparticles (Siffalovic, Majkova et al. 2007). The Fig. 4a shows the SEM image of a self-assembled array of iron oxide nanoparticles. The inset of Fig. 4a shows the Fourier transform of SEM micrograph with partially smeared-out spots corresponding to the hexagonal arrangement. The smearing-out is due to mutually misaligned nanoparticle domains originating from finite nanoparticle size dispersion which is in sharp contrast to natural atomic crystals. The Fig. 4a and 4b show the measured and simulated GISAXS pattern, respectively. The characteristic side maxima located at the <sup>1</sup> 0 82 *q . nm <sup>y</sup>* are the "finger prints" of the self-assembly in the nanoparticle array. In the first approximation, the mean interparticle separation can be estimated from

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 447

drying colloidal solution at solid surfaces (Siffalovic, Majkova et al. 2007). We used the focused X-ray beam to map the nanoparticle self-assembly at arbitrary selected position

Fig. 5. The GISAXS pattern recorded from a drying colloidal Fe-O nanoparticle drop at three different stages: a) directly after drop casting, b) intermediate phase. c) dried colloidal drop.

The Fig. 5a shows the GISAXS pattern directly after application of a colloidal Fe-O nanoparticle solution onto silicon substrate. The GISAXS pattern does not show any maxima typical for self-assembled nanoparticle layers. The visible scattering in the GISAXS pattern is characteristic for a diluted nanoparticle solution and can be described by the nanoparticle form-factor. The Fig. 5b shows the intermediate state when the X-ray beam partially passes through the colloidal drop surface. The scattering streaks originating from interfaces also called "detector scans" are visible. The first one can be attributed to the scattering from the substrate surface and the second one originates from the colloidal drop surface. The angle between the two detector streaks directly maps the angle between the normal of substrate surface and the normal of the probed colloidal drop surface. The side maxima belong to the already dried self-assembled areas. The Fig. 5c shows the final GISAXS pattern after the colloidal solution is completely evaporated. The interparticle distance of final nanoparticle

The spatially static GISAXS technique can track the nanoparticle assembly only in one selected probing volume within the evaporating colloidal drop. In order to monitor various probe volumes inside the colloidal nanoparticle drop during the self-assembly process we introduced a scanning GISAXS technique. The scanning GISAXS method is based on the fast vertical or horizontal scanning of the evaporating colloidal drop by the probing X-ray beam (Siffalovic, Majkova et al. 2008). The sketch of the scanning GISAXS technique is shown in Fig. 6a. The colloidal drop composed of iron oxide nanoparticles dispersed in toluene was applied onto silicon substrate located on a vertically scanning goniometer. As the evaporating drop was gradually scanned across the incoming X-ray beam we continuously recorded X-ray scattering from three different drop zones. In the zone Z0 the X-ray beam passed above the evaporating drop. These data were used for the background correction. In the zone Z1 we recorded exclusively the X-ray scattering originating from the drying drop surface and drop interior. In the zone Z2 we additionally detected the X-ray scattering coming from the substrate surface. The Fig. 6b shows the line cuts extracted from the GISAXS frames taken in zone Z1 corresponding to the three different stages of the colloidal drop evaporation process: 1.) directly after drop casting, 2.) intermediate state, and 3.) final state characterized by the complete solvent evaporation. It is important to notice that the

assembly are clearly manifested in the GISAXS pattern by the side maxima.

within the colloidal drop. The Fig. 5 shows the three typical GISAXS patterns.

the side maximum position in the reciprocal space as 2 77 *<sup>y</sup> q . nm* . This simple estimation is valid only for a slowly varying nanoparticle form-factors within the kinematic BA. A precise fitting of the measured GISAXS data using the full DWBA theory can provide further information on the nanoparticle size and size dispersion as well as their correlation length (Lazzari 2002). The Fig. 4d shows a line cut extracted from the measured GISAXS pattern with the corresponding fit. The fitted nanoparticle diameter was 6.1±0.6 nm and the lateral correlation length in the nanoparticle array was 87 nm. It has to be noted that colloidal nanoparticles are covered by a surfactant shell to avoid their spontaneous agglomeration in colloidal suspensions. In the case of Fe-O nanoparticles discussed above, oleic acid and oleylamine were used. A GISAXS pattern fitting provides basic information on the metallic-like nanoparticle core size while the organic shell is rather invisible for Xrays. On the other hand, the positions of the side maxima in the GISAXS pattern are always connected with the interparticle distance which is affected by the surfactant shell. This example clearly demonstrates the ability of GISAXS technique to extract main nanoparticle parameters in the self-assembled arrays. The main advantage is that the GISAXS technique does not require any specific sample environment conditions such as vacuum nor special sample preparation. On the other hand it can be applied even in very aggressive environments such as UV/ozone reactor (Siffalovic, Chitu et al. 2010). Moreover, a rapid GISAXS data acquisition in millisecond range can be used for a real-time in-situ probing of nanoparticle reactions and self-assembly processes (Siffalovic, Majkova et al. 2008).

## **3. Nanoparticle self-assembly at liquid/air interfaces**

In the last ten years we have seen a tremendous progress in the colloidal nanoparticle chemistry (Feldheim 2002; Nagarajan 2008; Niederberger and Pinna 2009). The refined chemical synthesis routes can produce large quantities of highly monodisperse nanoparticles in colloidal solutions with the size dispersion below 10 % (Park, An et al. 2004). The low nanoparticle dispersion is the "holy grail" of the large-scale nanoparticle selfassembly (Pileni 2005). Being able to prepare nanoparticles with zero size dispersion, we could fabricate genuine artificial nanoparticle crystals competing with natural ones in terms of the structure perfection and long-range order. However the finite nanoparticle size dispersion permits only a limited extent of ordering in nanoparticle self-assembled arrays. A typical model for description of the real nanoparticle assemblies is the paracrystal model (Hosemann and Bagchi 1962; Guinier 1963). Here a paracrystal order parameter summed up with the mean interparticle distance defines degree of the array perfection.

The colloidal nanoparticle solutions can be applied on a solid substrate directly or in two steps, utilizing liquid surface for self-assembly with a subsequent transfer onto a solid substrate. Drop casting followed by solvent evaporation is an example of the former method (Chushkin, Ulmeanu et al. 2003) that proved to be successful e.g. for preparation of largearea self-assembled arrays of noble metal nanoparticles with the diameter of a few tens nm. In addition to the nanoparticle size, surfactant type affects the self-assembly as well. For smaller nanoparticles, such as those presented in this chapter with the diameter below 10 nm, a direct application of the colloidal nanoparticle solutions on solid substrate produces only locally well assembled regions but is not suitable for large-area nanoparticle depositions. Here, the latter above mentioned method is promising as it will be shown later. The GISAXS technique can be employed to track the nanoparticle assemblies in rapidly

the side maximum position in the reciprocal space as 2 77 *<sup>y</sup> q . nm* . This simple estimation is valid only for a slowly varying nanoparticle form-factors within the kinematic BA. A precise fitting of the measured GISAXS data using the full DWBA theory can provide further information on the nanoparticle size and size dispersion as well as their correlation length (Lazzari 2002). The Fig. 4d shows a line cut extracted from the measured GISAXS pattern with the corresponding fit. The fitted nanoparticle diameter was 6.1±0.6 nm and the lateral correlation length in the nanoparticle array was 87 nm. It has to be noted that colloidal nanoparticles are covered by a surfactant shell to avoid their spontaneous agglomeration in colloidal suspensions. In the case of Fe-O nanoparticles discussed above, oleic acid and oleylamine were used. A GISAXS pattern fitting provides basic information on the metallic-like nanoparticle core size while the organic shell is rather invisible for Xrays. On the other hand, the positions of the side maxima in the GISAXS pattern are always connected with the interparticle distance which is affected by the surfactant shell. This example clearly demonstrates the ability of GISAXS technique to extract main nanoparticle parameters in the self-assembled arrays. The main advantage is that the GISAXS technique does not require any specific sample environment conditions such as vacuum nor special sample preparation. On the other hand it can be applied even in very aggressive environments such as UV/ozone reactor (Siffalovic, Chitu et al. 2010). Moreover, a rapid GISAXS data acquisition in millisecond range can be used for a real-time in-situ probing of

nanoparticle reactions and self-assembly processes (Siffalovic, Majkova et al. 2008).

with the mean interparticle distance defines degree of the array perfection.

In the last ten years we have seen a tremendous progress in the colloidal nanoparticle chemistry (Feldheim 2002; Nagarajan 2008; Niederberger and Pinna 2009). The refined chemical synthesis routes can produce large quantities of highly monodisperse nanoparticles in colloidal solutions with the size dispersion below 10 % (Park, An et al. 2004). The low nanoparticle dispersion is the "holy grail" of the large-scale nanoparticle selfassembly (Pileni 2005). Being able to prepare nanoparticles with zero size dispersion, we could fabricate genuine artificial nanoparticle crystals competing with natural ones in terms of the structure perfection and long-range order. However the finite nanoparticle size dispersion permits only a limited extent of ordering in nanoparticle self-assembled arrays. A typical model for description of the real nanoparticle assemblies is the paracrystal model (Hosemann and Bagchi 1962; Guinier 1963). Here a paracrystal order parameter summed up

The colloidal nanoparticle solutions can be applied on a solid substrate directly or in two steps, utilizing liquid surface for self-assembly with a subsequent transfer onto a solid substrate. Drop casting followed by solvent evaporation is an example of the former method (Chushkin, Ulmeanu et al. 2003) that proved to be successful e.g. for preparation of largearea self-assembled arrays of noble metal nanoparticles with the diameter of a few tens nm. In addition to the nanoparticle size, surfactant type affects the self-assembly as well. For smaller nanoparticles, such as those presented in this chapter with the diameter below 10 nm, a direct application of the colloidal nanoparticle solutions on solid substrate produces only locally well assembled regions but is not suitable for large-area nanoparticle depositions. Here, the latter above mentioned method is promising as it will be shown later. The GISAXS technique can be employed to track the nanoparticle assemblies in rapidly

**3. Nanoparticle self-assembly at liquid/air interfaces** 

drying colloidal solution at solid surfaces (Siffalovic, Majkova et al. 2007). We used the focused X-ray beam to map the nanoparticle self-assembly at arbitrary selected position within the colloidal drop. The Fig. 5 shows the three typical GISAXS patterns.

Fig. 5. The GISAXS pattern recorded from a drying colloidal Fe-O nanoparticle drop at three different stages: a) directly after drop casting, b) intermediate phase. c) dried colloidal drop.

The Fig. 5a shows the GISAXS pattern directly after application of a colloidal Fe-O nanoparticle solution onto silicon substrate. The GISAXS pattern does not show any maxima typical for self-assembled nanoparticle layers. The visible scattering in the GISAXS pattern is characteristic for a diluted nanoparticle solution and can be described by the nanoparticle form-factor. The Fig. 5b shows the intermediate state when the X-ray beam partially passes through the colloidal drop surface. The scattering streaks originating from interfaces also called "detector scans" are visible. The first one can be attributed to the scattering from the substrate surface and the second one originates from the colloidal drop surface. The angle between the two detector streaks directly maps the angle between the normal of substrate surface and the normal of the probed colloidal drop surface. The side maxima belong to the already dried self-assembled areas. The Fig. 5c shows the final GISAXS pattern after the colloidal solution is completely evaporated. The interparticle distance of final nanoparticle assembly are clearly manifested in the GISAXS pattern by the side maxima.

The spatially static GISAXS technique can track the nanoparticle assembly only in one selected probing volume within the evaporating colloidal drop. In order to monitor various probe volumes inside the colloidal nanoparticle drop during the self-assembly process we introduced a scanning GISAXS technique. The scanning GISAXS method is based on the fast vertical or horizontal scanning of the evaporating colloidal drop by the probing X-ray beam (Siffalovic, Majkova et al. 2008). The sketch of the scanning GISAXS technique is shown in Fig. 6a. The colloidal drop composed of iron oxide nanoparticles dispersed in toluene was applied onto silicon substrate located on a vertically scanning goniometer. As the evaporating drop was gradually scanned across the incoming X-ray beam we continuously recorded X-ray scattering from three different drop zones. In the zone Z0 the X-ray beam passed above the evaporating drop. These data were used for the background correction. In the zone Z1 we recorded exclusively the X-ray scattering originating from the drying drop surface and drop interior. In the zone Z2 we additionally detected the X-ray scattering coming from the substrate surface. The Fig. 6b shows the line cuts extracted from the GISAXS frames taken in zone Z1 corresponding to the three different stages of the colloidal drop evaporation process: 1.) directly after drop casting, 2.) intermediate state, and 3.) final state characterized by the complete solvent evaporation. It is important to notice that the

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 449

Fig. 7. The GISAXS patterns of self-assembled Ag nanoparticle Lagmuir films at surface

The surface pressure of 16 mN/m corresponds to a closed nanoparticle monolayer on the water surface. The interference function produces two symmetrical side maxima at <sup>1</sup> 0 87 *q . nm <sup>y</sup>* (truncation rods) corresponding to the average interparticle distance of 7.2 nm. The higher order side maxima are absent due to the short exposition time. The twodimensional nanoparticle monolayer has a constant interference function in the *<sup>z</sup> q* direction where the modulation visible on the truncation rods is produced solely by the nanoparticle form-factor (Holý, Pietsch et al. 1999). At the surface pressure of 26 mN/m, the second nanoparticle layer forms and changes the observed GISAXS pattern (Vegso, Siffalovic et al. 2011). The newly formed nanoparticle vertical correlation perpendicular to the Langmuir film plane results in the modulation of the observed truncation rod depicted by the dashed white line in Fig. 7b. It can be shown that the modulation along the truncation rod is associated with the second nanoparticle layer laterally shifted in analogy with the "AB stacking" in solid state crystals (Kittel 2005). The presence of the second layer can be verified also by distinct second order maxima in Fig. 7b. The presented GISAXS results show the possibility to study not only the lateral but also the vertical nanoparticle correlations in 3D nanoparticle assemblies that is due to the ability of GISAXS to inspect non-destructively buried layers and interfaces. This useful feature of the GISAXS technique to study the buried vertical correlations of interfaces was already applied in studies of multilayered thin films

Recently we have performed in-situ real-time studies of compression and decompression of Ag nanoparticle Langmuir films. We were interested in the correlation between the macroscopic elastic properties of nanoparticle layers and microscopic layer parameters like the interparticle distance. As a convenient measure of macroscopic elastic properties we use

*E A*

*T*

(1)

*A* 

Here is the measured surface pressure of the nanoparticle layer with the area *A* at a constant subphase temperature *T*. The Fig. 8 shows the evaluated side maximum position along the *<sup>y</sup> q* direction in the GISAXS reciprocal space map similar to the one shown in

pressure a) 16 mN/m and b) 26 mN/m.

(Salditt, Metzger et al. 1994; Siffalovic, Jergel et al. 2011).

Fig. 7a.

the surface elastic modulus defined as (Barnes, Gentle et al. 2005)

experimental data for all three evaporation stages can be fitted solely using the nanoparticle form-factor function. According to the eq. (4) the interference function is constant in this case, i.e. <sup>1</sup> *S q* .

Fig. 6. a) The scheme of the GISAXS scanning technique. b) The GISAXS pattern line cuts at the critical exit angle for the three different stages of the colloidal Fe-O nanoparticle drop evaporation.

This means that the nanoparticles do not create self-assembled domains at the evaporating drop surface or in its volume at any time that suggests the origin of the nanoparticle selfassembly to be located at the three-phase boundary as predicted for a drying drop of dispersed particles (Deegan, Bakajin et al. 1997). The scanning GISAXS technique clearly demonstrates the ability to track the nanoparticle self-assembly process in real-time with millisecond time resolution.

As mentioned above, colloidal nanoparticles are usually terminated by surfactant molecules to avoid spontaneous agglomeration in colloidal suspensions. The nanoparticles with hydrophobic termination allow self-assembly at liquid/air interfaces and formation of Langmuir films in the form of simple 2D systems (Ulman 1991). Controlling the surface pressure by changing the nanoparticle layer area and the temperature of the subphase, we can produce large-area and homogenous self-assembled nanoparticle layers. The electron microscopy techniques including SEM, TEM or scanning probe techniques (AFM, STM) cannot be utilized to monitor the nanoparticle self-assembly at liquid/air interface. The visible/UV optical microscopy and Brewster angle microscopy are limited in resolution due to diffraction limit (Born and Wolf 1999). For a certain kind of metal and metal oxide nanoparticles exhibiting plasmonic properties (Au, Ag, Al, Cu) the interparticle distance can be indirectly monitored by the energy shift in localized surface plasmon resonance due to the dipole-dipole coupling of excited plasmons in the self-assembled nanoparticle arrays (Rycenga, Cobley et al. 2011). On the other hand the GISAXS technique can be employed to directly monitor the interparticle distance in self-assembled arrays directly in the Langmuir trough. The laboratory GISAXS setup shown in Fig. 3 was used to record the GISAXS patterns of Ag nanoparticles (6.2±0.7 nm) directly in the Langmuir trough. The GISAXS patterns of self-assembled Ag nanoparticles with oleic acid as surfactant at the surface pressures of 16 mN/m and 26 mN/m are shown in Fig. 7a and Fig. 7b, respectively.

experimental data for all three evaporation stages can be fitted solely using the nanoparticle form-factor function. According to the eq. (4) the interference function is constant in this

Fig. 6. a) The scheme of the GISAXS scanning technique. b) The GISAXS pattern line cuts at the critical exit angle for the three different stages of the colloidal Fe-O nanoparticle drop

This means that the nanoparticles do not create self-assembled domains at the evaporating drop surface or in its volume at any time that suggests the origin of the nanoparticle selfassembly to be located at the three-phase boundary as predicted for a drying drop of dispersed particles (Deegan, Bakajin et al. 1997). The scanning GISAXS technique clearly demonstrates the ability to track the nanoparticle self-assembly process in real-time with

As mentioned above, colloidal nanoparticles are usually terminated by surfactant molecules to avoid spontaneous agglomeration in colloidal suspensions. The nanoparticles with hydrophobic termination allow self-assembly at liquid/air interfaces and formation of Langmuir films in the form of simple 2D systems (Ulman 1991). Controlling the surface pressure by changing the nanoparticle layer area and the temperature of the subphase, we can produce large-area and homogenous self-assembled nanoparticle layers. The electron microscopy techniques including SEM, TEM or scanning probe techniques (AFM, STM) cannot be utilized to monitor the nanoparticle self-assembly at liquid/air interface. The visible/UV optical microscopy and Brewster angle microscopy are limited in resolution due to diffraction limit (Born and Wolf 1999). For a certain kind of metal and metal oxide nanoparticles exhibiting plasmonic properties (Au, Ag, Al, Cu) the interparticle distance can be indirectly monitored by the energy shift in localized surface plasmon resonance due to the dipole-dipole coupling of excited plasmons in the self-assembled nanoparticle arrays (Rycenga, Cobley et al. 2011). On the other hand the GISAXS technique can be employed to directly monitor the interparticle distance in self-assembled arrays directly in the Langmuir trough. The laboratory GISAXS setup shown in Fig. 3 was used to record the GISAXS patterns of Ag nanoparticles (6.2±0.7 nm) directly in the Langmuir trough. The GISAXS patterns of self-assembled Ag nanoparticles with oleic acid as surfactant at the surface

pressures of 16 mN/m and 26 mN/m are shown in Fig. 7a and Fig. 7b, respectively.

case, i.e. <sup>1</sup> *S q* .

evaporation.

millisecond time resolution.

Fig. 7. The GISAXS patterns of self-assembled Ag nanoparticle Lagmuir films at surface pressure a) 16 mN/m and b) 26 mN/m.

The surface pressure of 16 mN/m corresponds to a closed nanoparticle monolayer on the water surface. The interference function produces two symmetrical side maxima at <sup>1</sup> 0 87 *q . nm <sup>y</sup>* (truncation rods) corresponding to the average interparticle distance of 7.2 nm. The higher order side maxima are absent due to the short exposition time. The twodimensional nanoparticle monolayer has a constant interference function in the *<sup>z</sup> q* direction where the modulation visible on the truncation rods is produced solely by the nanoparticle form-factor (Holý, Pietsch et al. 1999). At the surface pressure of 26 mN/m, the second nanoparticle layer forms and changes the observed GISAXS pattern (Vegso, Siffalovic et al. 2011). The newly formed nanoparticle vertical correlation perpendicular to the Langmuir film plane results in the modulation of the observed truncation rod depicted by the dashed white line in Fig. 7b. It can be shown that the modulation along the truncation rod is associated with the second nanoparticle layer laterally shifted in analogy with the "AB stacking" in solid state crystals (Kittel 2005). The presence of the second layer can be verified also by distinct second order maxima in Fig. 7b. The presented GISAXS results show the possibility to study not only the lateral but also the vertical nanoparticle correlations in 3D nanoparticle assemblies that is due to the ability of GISAXS to inspect non-destructively buried layers and interfaces. This useful feature of the GISAXS technique to study the buried vertical correlations of interfaces was already applied in studies of multilayered thin films (Salditt, Metzger et al. 1994; Siffalovic, Jergel et al. 2011).

Recently we have performed in-situ real-time studies of compression and decompression of Ag nanoparticle Langmuir films. We were interested in the correlation between the macroscopic elastic properties of nanoparticle layers and microscopic layer parameters like the interparticle distance. As a convenient measure of macroscopic elastic properties we use the surface elastic modulus defined as (Barnes, Gentle et al. 2005)

$$E = -A \left(\frac{\partial \mathcal{H}}{\partial \mathcal{A}}\right)\_T \tag{1}$$

Here is the measured surface pressure of the nanoparticle layer with the area *A* at a constant subphase temperature *T*. The Fig. 8 shows the evaluated side maximum position along the *<sup>y</sup> q* direction in the GISAXS reciprocal space map similar to the one shown in Fig. 7a.

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 451

In the previous section we discussed the formation of nanoparticle monolayers at water/air interface. The Langmuir film represented by self-assembled nanoparticle monolayer seems to be the most promising candidate for the homogenous deposition of large-area nanoparticle arrays. The two important questions are remaining. The first one is: "What is the suitable surface pressure for deposition and how to monitor it?" The second one is: "How to transfer the Langmuir film onto solid substrate with a minimum damage of the

The first question was partially addressed in the previous section. We have shown the GISAXS technique gives a precise tool to monitor the monolayer formation at nanoscale. In Fig. 8 we showed the evolution of the interparticle distance with increasing surface pressure and we related formation of the second nanoparticle layer to a sudden drop in the observed surface elastic modulus. Additionally, we can track the evolution of the interference function in the *<sup>z</sup> q* direction. We showed that the interference along the *<sup>z</sup> q* axis is a constant function for the nanoparticle monolayer. A new vertical correlation between the two layers may appear with the monolayer collapse accompanying the formation of the second nanoparticle layer as discussed in the previous section. This transition is manifested in the modulation of the X-ray scattered intensity along the truncation rod. The Fig. 7b shows the GISAXS pattern of the nanoparticle multilayer with a new peak formed along the first truncation rod (marked with dashed white line). For the nanoparticle monolayer, the intensity is at maximum at the critical exit angle, i.e. at the Yoneda peak. The formation of

**4. Transfer of self-assembled layers from liquid onto solid surfaces** 

self-assembled layer?" In this section we try to give answers to them.

the second layer shifts the maximum intensity upward in the *<sup>z</sup> q* direction.

Fig. 9. The integral intensity of the first Bragg peak along the first truncation rod

function of the layer area.

corresponding to the formation of a vertically correlated Ag nanoparticle multilayer as a

The Fig. 9 shows the integral intensity of the newly formed Bragg peak along the first truncation rod corresponding to the vertically correlated nanoparticles as a function of the surface area. The GISAXS measurement clearly shows that the decrease in the elastic

Fig. 8. The evaluated GISAXS peak maximum position and the surface elastic modulus of the Ag nanoparticle layer at water/air interface as a function of the layer area.

After spreading the nanoparticle solution onto the water subphase, the nanoparticles assemble into small clusters with hexagonal ordering that has been identified by independent ex situ experiments (to be published). Increasing the surface pressure by reducing the layer area results in the formation of a continuous monolayer without a change of the interparticle distance. This compression stage is characterized by a constant elastic modulus as the isolated nanoparticle clusters are joining into larger entities. At surface area of approximately 250 cm2 we observe an increase in the elastic modulus peaking at the area of 180 cm2. This stage can be associated with the densification of the nanoparticle layer accompanied by the nanoparticle rearrangements along the individual cluster boundaries and cluster coalescence. At the maximum of surface elastic modulus we observe also a slight compaction of the nanoparticle layer at nanoscale indicated by the change of the interparticle distance. This phase ends up with a compact nanoparticle layer. A further compression of the nanoparticle layer results in the formation of a second nanoparticle layer that induces a sudden drop in the elastic modulus and significant release of the mean interparticle distance. The nanoparticles forming the second layer create vacancies in the first one that is accompanied by deterioration of the order in the first nanoparticle layer. In this case the paracrystal model of the nanoparticle layer predicts a shift of the maximum to lower *<sup>y</sup> q* values in the reciprocal space (Lazzari 2009) that was confirmed by this experimental observation. After the decompression the interparticle distance in the nanoparticle layer does not relax to the initial value. It has to be noted that the second layer formation and tendency to form 3D ordered nanoparticle assemblies was demonstrated here for Ag nanoparticles with oleic acid as surfactant, however, other types of metallic nanoparticles with other type of surfactant may behave differently. This example shows the benefit of GISAXS technique to precisely monitor microscopic parameters of the nanoparticle assemblies prior to the deposition onto solid substrates that will be discussed in the following section.

Fig. 8. The evaluated GISAXS peak maximum position and the surface elastic modulus of

After spreading the nanoparticle solution onto the water subphase, the nanoparticles assemble into small clusters with hexagonal ordering that has been identified by independent ex situ experiments (to be published). Increasing the surface pressure by reducing the layer area results in the formation of a continuous monolayer without a change of the interparticle distance. This compression stage is characterized by a constant elastic modulus as the isolated nanoparticle clusters are joining into larger entities. At surface area of approximately 250 cm2 we observe an increase in the elastic modulus peaking at the area of 180 cm2. This stage can be associated with the densification of the nanoparticle layer accompanied by the nanoparticle rearrangements along the individual cluster boundaries and cluster coalescence. At the maximum of surface elastic modulus we observe also a slight compaction of the nanoparticle layer at nanoscale indicated by the change of the interparticle distance. This phase ends up with a compact nanoparticle layer. A further compression of the nanoparticle layer results in the formation of a second nanoparticle layer that induces a sudden drop in the elastic modulus and significant release of the mean interparticle distance. The nanoparticles forming the second layer create vacancies in the first one that is accompanied by deterioration of the order in the first nanoparticle layer. In this case the paracrystal model of the nanoparticle layer predicts a shift of the maximum to lower *<sup>y</sup> q* values in the reciprocal space (Lazzari 2009) that was confirmed by this experimental observation. After the decompression the interparticle distance in the nanoparticle layer does not relax to the initial value. It has to be noted that the second layer formation and tendency to form 3D ordered nanoparticle assemblies was demonstrated here for Ag nanoparticles with oleic acid as surfactant, however, other types of metallic nanoparticles with other type of surfactant may behave differently. This example shows the benefit of GISAXS technique to precisely monitor microscopic parameters of the nanoparticle assemblies prior to the deposition onto solid substrates that will be discussed

the Ag nanoparticle layer at water/air interface as a function of the layer area.

in the following section.

## **4. Transfer of self-assembled layers from liquid onto solid surfaces**

In the previous section we discussed the formation of nanoparticle monolayers at water/air interface. The Langmuir film represented by self-assembled nanoparticle monolayer seems to be the most promising candidate for the homogenous deposition of large-area nanoparticle arrays. The two important questions are remaining. The first one is: "What is the suitable surface pressure for deposition and how to monitor it?" The second one is: "How to transfer the Langmuir film onto solid substrate with a minimum damage of the self-assembled layer?" In this section we try to give answers to them.

The first question was partially addressed in the previous section. We have shown the GISAXS technique gives a precise tool to monitor the monolayer formation at nanoscale. In Fig. 8 we showed the evolution of the interparticle distance with increasing surface pressure and we related formation of the second nanoparticle layer to a sudden drop in the observed surface elastic modulus. Additionally, we can track the evolution of the interference function in the *<sup>z</sup> q* direction. We showed that the interference along the *<sup>z</sup> q* axis is a constant function for the nanoparticle monolayer. A new vertical correlation between the two layers may appear with the monolayer collapse accompanying the formation of the second nanoparticle layer as discussed in the previous section. This transition is manifested in the modulation of the X-ray scattered intensity along the truncation rod. The Fig. 7b shows the GISAXS pattern of the nanoparticle multilayer with a new peak formed along the first truncation rod (marked with dashed white line). For the nanoparticle monolayer, the intensity is at maximum at the critical exit angle, i.e. at the Yoneda peak. The formation of the second layer shifts the maximum intensity upward in the *<sup>z</sup> q* direction.

Fig. 9. The integral intensity of the first Bragg peak along the first truncation rod corresponding to the formation of a vertically correlated Ag nanoparticle multilayer as a function of the layer area.

The Fig. 9 shows the integral intensity of the newly formed Bragg peak along the first truncation rod corresponding to the vertically correlated nanoparticles as a function of the surface area. The GISAXS measurement clearly shows that the decrease in the elastic

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 453

compression and decompression cycle is obvious and supports the interpretation of the GISAXS measurements. The Fig. 10 shows selected BAM images during the compression and expansion cycles. However we have recorded a full series of BAM images at 15 second time intervals during the compression cycle. Based on the BAM images we can calculate the average nanoparticle surface coverage based on the ratio between the bright areas that can be attributed to the nanoparticle layer and the black areas corresponding to the water

Fig. 11. The nanoparticle surface coverage based on BAM measurement along with the surface elastic modulus as a function of the Ag nanoparticle layer area during compression.

We have to keep in mind that the calculation is correct only at microscale as the nanoscale vacancies are invisible due to the BAM diffraction limit. The Fig. 11 shows the calculated nanoparticle surface coverage as a function of the film area. The graph shows also the calculated elastic modulus based on the measured nanoparticle layer surface pressure. The nanoparticle surface coverage reaches its maximum value of 100% short before the maximum in the film elastic modulus appears during the compression cycle. This is in a very good correlation with the GISAXS measurement that relates the nanoparticle monolayer collapse to the maximum in elastic modulus. The BAM measurements underestimate the nanometer-sized vacancies in the forming monolayer. This is the reason that the BAM indicate formation of nanoparticle monolayer already before the monolayer collapse. An alternative would be the imaging ellipsometry being able to track the nanoparticle layer formation at microscale more quantitatively than the BAM technique

In order to understand the formation of nanoparticle monolayer at nanoscale we deposited the nanoparticle layers on silicon substrates. The probes were deposited at different surface pressures by simply immersing the substrate into the nanoparticle covered water subphase. The selected areas of nanoparticle layers were studied by the non-contact atomic force microscopy (AFM) rather than the scanning electron microscopy as the latter one cannot

subphase.

(Roth and et al. 2011).

provide the information on the layer height.

modulus is associated with the formation of the second nanoparticle layer. Moreover we observe a hysteretic behavior during the Langmuir film decompression associated with the irreversibility of the expanded nanoparticle layer that is also documented by the interparticle distance behavior shown in Fig. 8. After opening the barriers the nanoparticle layer does not relax into a monolayer but fragments into small islands still exhibiting a certain amount of nanoparticles in the second layer (see also further). The GISAXS measurements confirmed the assumption that the fully closed nanoparticle monolayer forms short before the monolayer collapse evidenced by a maximum in surface elastic modulus.

Fig. 10. The BAM images taken at surface areas a) 500 cm2, b) 293 cm2 and c) 122 cm2 taken during the Ag nanoparticle layer compression and BAM images at surface areas d) 139 cm2, e) 302 cm2 and f) 501 cm2 taken during the nanoparticle layer expansion.

The Brewster angle microscopy (BAM) provides further evidence of the nanoparticle monolayer formation at microscale (Henon and Meunier 1991). The laser based BAM provides much better contrast between the nanoparticle monolayer and water subphase than the conventional normal incident microscopy. The Fig. 10a)-10c) show three images taken during the nanoparticle layer compression and Fig. 10d)-10f show three images taken during the nanoparticle layer decompression. The nanoparticle layer was composed of surfactant terminated Ag nanoparticles with a core size of 6.2±0.7 nm. The nanoparticle surfactant was oleic acid. The nanoparticle layer shows vacant areas in Fig. 10a). Decreasing the film area, we close the vacancies and a compact nanoparticle monolayer forms as shown in Fig. 10c). The subsequent expansion of the nanoparticle layer is accompanied by the generation of millimeters long cracks across the nanoparticle layer as shown in Fig. 10d). A further increase of the area available for the nanoparticle expansion leads to the disruption of nanoparticle layer into micrometer large needle-like clusters as shown in Fig. 10e) and Fig. 10f). The hysteretic behavior of the nanoparticle layer at microscale during the

modulus is associated with the formation of the second nanoparticle layer. Moreover we observe a hysteretic behavior during the Langmuir film decompression associated with the irreversibility of the expanded nanoparticle layer that is also documented by the interparticle distance behavior shown in Fig. 8. After opening the barriers the nanoparticle layer does not relax into a monolayer but fragments into small islands still exhibiting a certain amount of nanoparticles in the second layer (see also further). The GISAXS measurements confirmed the assumption that the fully closed nanoparticle monolayer forms short before the monolayer collapse evidenced by a maximum in surface elastic

Fig. 10. The BAM images taken at surface areas a) 500 cm2, b) 293 cm2 and c) 122 cm2 taken during the Ag nanoparticle layer compression and BAM images at surface areas d) 139 cm2,

The Brewster angle microscopy (BAM) provides further evidence of the nanoparticle monolayer formation at microscale (Henon and Meunier 1991). The laser based BAM provides much better contrast between the nanoparticle monolayer and water subphase than the conventional normal incident microscopy. The Fig. 10a)-10c) show three images taken during the nanoparticle layer compression and Fig. 10d)-10f show three images taken during the nanoparticle layer decompression. The nanoparticle layer was composed of surfactant terminated Ag nanoparticles with a core size of 6.2±0.7 nm. The nanoparticle surfactant was oleic acid. The nanoparticle layer shows vacant areas in Fig. 10a). Decreasing the film area, we close the vacancies and a compact nanoparticle monolayer forms as shown in Fig. 10c). The subsequent expansion of the nanoparticle layer is accompanied by the generation of millimeters long cracks across the nanoparticle layer as shown in Fig. 10d). A further increase of the area available for the nanoparticle expansion leads to the disruption of nanoparticle layer into micrometer large needle-like clusters as shown in Fig. 10e) and Fig. 10f). The hysteretic behavior of the nanoparticle layer at microscale during the

e) 302 cm2 and f) 501 cm2 taken during the nanoparticle layer expansion.

modulus.

compression and decompression cycle is obvious and supports the interpretation of the GISAXS measurements. The Fig. 10 shows selected BAM images during the compression and expansion cycles. However we have recorded a full series of BAM images at 15 second time intervals during the compression cycle. Based on the BAM images we can calculate the average nanoparticle surface coverage based on the ratio between the bright areas that can be attributed to the nanoparticle layer and the black areas corresponding to the water subphase.

Fig. 11. The nanoparticle surface coverage based on BAM measurement along with the surface elastic modulus as a function of the Ag nanoparticle layer area during compression.

We have to keep in mind that the calculation is correct only at microscale as the nanoscale vacancies are invisible due to the BAM diffraction limit. The Fig. 11 shows the calculated nanoparticle surface coverage as a function of the film area. The graph shows also the calculated elastic modulus based on the measured nanoparticle layer surface pressure. The nanoparticle surface coverage reaches its maximum value of 100% short before the maximum in the film elastic modulus appears during the compression cycle. This is in a very good correlation with the GISAXS measurement that relates the nanoparticle monolayer collapse to the maximum in elastic modulus. The BAM measurements underestimate the nanometer-sized vacancies in the forming monolayer. This is the reason that the BAM indicate formation of nanoparticle monolayer already before the monolayer collapse. An alternative would be the imaging ellipsometry being able to track the nanoparticle layer formation at microscale more quantitatively than the BAM technique (Roth and et al. 2011).

In order to understand the formation of nanoparticle monolayer at nanoscale we deposited the nanoparticle layers on silicon substrates. The probes were deposited at different surface pressures by simply immersing the substrate into the nanoparticle covered water subphase. The selected areas of nanoparticle layers were studied by the non-contact atomic force microscopy (AFM) rather than the scanning electron microscopy as the latter one cannot provide the information on the layer height.

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 455

Fig. 13. The height histograms of the Ag nanoparticle layers deposited at different surface

The number of nanoparticles occupying the second layer is steadily growing with the increasing surface pressure. At the surface pressure of 30 mN/m already more than 50% of the second nanoparticle layer was formed. The ex-situ AFM measurements provide important additional information to the in-situ GISAXS and BAM measurements. However we cannot rule out possible relaxations in the nanoparticle assemblies due to their transfer

Based on the previous analyses we can conclude that the optimum deposition conditions for the nanoparticle monolayer deposition occur at the surface pressure slightly below the threshold pressure for the monolayer collapse. To achieve homogenous nanoparticle deposition over large areas of solid substrates, we modified the conventional Langmuir-Schaefer deposition (Chitu, Siffalovic et al. 2010). The scheme of the deposition trough is

pressures obtained by analysis of the AFM images.

Fig. 14. The scheme of the modified Langmuir-Blodgett trough.

from the liquid to solid surface.

shown in Fig. 14.

Fig. 12. The AFM images of Ag nanoparticle layers taken at the following surface pressures: a) 10 mN/m, b) 15 mN/m, c) 20 mN/m and d) 30 mN/m.

The Fig. 12 shows the AFM images of Ag nanoparticle layers deposited at different surface pressures. The nanoparticle monolayer deposited at the 10 mN/m shown in Fig. 12a displays vacancies in the nanoparticle coverage. At this stage the isolated nanoparticle clusters are coalescing into a single nanoparticle layer. The Fig. 12b shows a nanoparticle layer deposited at 15 mN/m. This AFM image shows the nanoparticle clusters forming almost a closed nanoparticle monolayer. The maximum of the surface elastic modulus was reached shortly after 15 mN/m. The AFM image shown in Fig. 12c deposited at the 20 mN/m clearly demonstrates the formation of the second nanoparticle layer after the monolayer collapse. The preferential sites for the formation of the second layer are located at the boundaries of the nanoparticle clusters. The final AFM image shown in Fig. 12d deposited at the surface pressure of 30 mN/m exhibits already a significant number of nanoparticles forming the second layer. The Fig. 13 shows calculated AFM height histograms of the nanoparticle layers deposited at different surface pressures. Only a single peak located at 6 nm corresponding to the height of monolayer is present up to the surface pressure of 15 mN/m. For the sample deposited at 20 mN/m shown in Fig. 12c, appearance of a shoulder suggests onset of formation of a second nanoparticle layer. For higher surface pressures, the newly formed peak at 12 nm in the height histogram distribution gives clear evidence of the second nanoparticle layer.

Fig. 12. The AFM images of Ag nanoparticle layers taken at the following surface pressures:

The Fig. 12 shows the AFM images of Ag nanoparticle layers deposited at different surface pressures. The nanoparticle monolayer deposited at the 10 mN/m shown in Fig. 12a displays vacancies in the nanoparticle coverage. At this stage the isolated nanoparticle clusters are coalescing into a single nanoparticle layer. The Fig. 12b shows a nanoparticle layer deposited at 15 mN/m. This AFM image shows the nanoparticle clusters forming almost a closed nanoparticle monolayer. The maximum of the surface elastic modulus was reached shortly after 15 mN/m. The AFM image shown in Fig. 12c deposited at the 20 mN/m clearly demonstrates the formation of the second nanoparticle layer after the monolayer collapse. The preferential sites for the formation of the second layer are located at the boundaries of the nanoparticle clusters. The final AFM image shown in Fig. 12d deposited at the surface pressure of 30 mN/m exhibits already a significant number of nanoparticles forming the second layer. The Fig. 13 shows calculated AFM height histograms of the nanoparticle layers deposited at different surface pressures. Only a single peak located at 6 nm corresponding to the height of monolayer is present up to the surface pressure of 15 mN/m. For the sample deposited at 20 mN/m shown in Fig. 12c, appearance of a shoulder suggests onset of formation of a second nanoparticle layer. For higher surface pressures, the newly formed peak at 12 nm in the height histogram distribution gives clear

a) 10 mN/m, b) 15 mN/m, c) 20 mN/m and d) 30 mN/m.

evidence of the second nanoparticle layer.

Fig. 13. The height histograms of the Ag nanoparticle layers deposited at different surface pressures obtained by analysis of the AFM images.

The number of nanoparticles occupying the second layer is steadily growing with the increasing surface pressure. At the surface pressure of 30 mN/m already more than 50% of the second nanoparticle layer was formed. The ex-situ AFM measurements provide important additional information to the in-situ GISAXS and BAM measurements. However we cannot rule out possible relaxations in the nanoparticle assemblies due to their transfer from the liquid to solid surface.

Based on the previous analyses we can conclude that the optimum deposition conditions for the nanoparticle monolayer deposition occur at the surface pressure slightly below the threshold pressure for the monolayer collapse. To achieve homogenous nanoparticle deposition over large areas of solid substrates, we modified the conventional Langmuir-Schaefer deposition (Chitu, Siffalovic et al. 2010). The scheme of the deposition trough is shown in Fig. 14.

Fig. 14. The scheme of the modified Langmuir-Blodgett trough.

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 457

At the lowest magnification we notice the absence of any cracks in the deposited monolayer. On the contrary the traditional vertical Langmuir-Blodgett deposition is forming a series of long cracks and is not suitable for large-scale deposition. At the highest magnification we can observe a dense hexagonally ordered layer of the iron oxide nanoparticles. The SEM is suitable for detailed analysis of the selected areas of the nanoparticle monolayer but is not convenient for a rapid screening across the large areas. We have already shown that the scanning GISAXS technique provides a fast probe of the nanoparticle order at nanoscale over macroscopic areas. The Fig. 16a shows the GISAXS reciprocal space map of an arbitrarily selected location at the substrate. The integral intensity and the position of the side maxima are the measure of the nanoparticle order in the X-ray probed area. Comparing the GISAXS patterns from the different locations at the substrate we obtain the information on the homogeneity of the deposited nanoparticle monolayer. The Fig. 16b shows six line cuts extracted from the GISAXS patterns measured at different locations. The differences between the measured curves are less than ±5% that indicates a relatively high homogeneity

**5. Processing and application of the self-assembled nanoparticle layers** 

In this section we focus on the issues connected with applications of deposited selfassembled nanoparticle layers. We discuss possibilities of removing the nanoparticle surfactant to increase the electrical conductivity of the nanoparticle layer as required for many applications. We address deposition of the nanoparticle layers onto thin membranes for sensor applications. We present also embedded self-assembled nanoparticle layers for

The surfactant molecules terminating the nanoparticles are inevitable for the synthesis and deposition of nanoparticles. However for many applications the electrical conductivity is required (Schmid 2010) while non-conductive organics is mostly used as surfactant. The surfactant molecules can be eliminated by the vacuum annealing, plasma etching, UV/ozone cleaning and many other techniques. In this section we analyze the impact of the UV/ozone cleaning on the Fe-O nanoparticle arrangement in self-assembled arrays. The UV/ozone cleaning is based on the reaction of UV light (=6.7 eV) with the oxygen molecules producing the highly reactive ozone. The UV light initiates photo-dissociation of the surfactant molecules that further react with the ozone molecules and are removed from the nanoparticle surface. Also a direct reaction of the surfactant molecules with the ozone molecules also called ozonolysis removes the surfactant molecules from the nanoparticle surface. In our experiment we removed the surfactant molecules from the self-assembled monolayer of iron oxide nanoparticle with the core diameter of 6.1±0.6 nm. The SEM micrographs along with the calculated nanoparticle pair correlation functions for the asdeposited sample and the sample processed in UV/ozone reactor are shown in Fig. 17a and Fig. 17b, respectively. For the as deposited nanoparticle monolayer the mean interparticle distance is given by the position of the first maximum in the pair correlation function that is 7.4 nm. After removal of the surfactant molecules terminating the nanoparticles the mean interparticle distance decreased to 6.4 nm. Moreover the nanoparticle array re-assembled into a labyrinth-like structure as shown by the SEM micrograph in Fig. 17b. This is very important for the electrical conductivity as the new nanoparticle assembly contains

of the deposited monolayer.

organic solar cells and spintronic devices.

percolated conductive paths across the nanoparticle array.

Differently to the conventional Langmuir-Schaefer deposition, the deposited substrate is immersed into the subphase. After spreading the nanoparticles at the water subphase and adjusting the deposition surface pressure, the water is slowly removed by opening an outlet valve. The moving water/air interface will slowly cross the inclined substrate, depositing the nanoparticle array onto it. This deposition technique produces highly homogenous nanoparticle layers on large substrates. The Fig. 15a shows a silicon wafer with the total area of some 18 cm2 homogenously covered with an iron oxide nanoparticle monolayer (6.1±0.6 nm).

Fig. 15. a) Photograph of the homogenous Fe-O nanoparticle monolayer deposited onto silicon substrate. b) The SEM micrographs of a selected spot at the different magnifications.

To check the monolayer homogeneity we arbitrarily selected one spot at the deposited substrate and analyzed it with the SEM. The Fig. 15b shows four SEM micrographs of the selected spot at different magnification levels.

Fig. 16. a) The GISAXS pattern of the Fe-O nanoparticle monolayer. b) The extracted GISAXS line-cuts at the critical exit angle from six different locations at the substrate.

Differently to the conventional Langmuir-Schaefer deposition, the deposited substrate is immersed into the subphase. After spreading the nanoparticles at the water subphase and adjusting the deposition surface pressure, the water is slowly removed by opening an outlet valve. The moving water/air interface will slowly cross the inclined substrate, depositing the nanoparticle array onto it. This deposition technique produces highly homogenous nanoparticle layers on large substrates. The Fig. 15a shows a silicon wafer with the total area of some 18 cm2 homogenously covered with an iron oxide nanoparticle monolayer

Fig. 15. a) Photograph of the homogenous Fe-O nanoparticle monolayer deposited onto silicon substrate. b) The SEM micrographs of a selected spot at the different magnifications.

selected spot at different magnification levels.

To check the monolayer homogeneity we arbitrarily selected one spot at the deposited substrate and analyzed it with the SEM. The Fig. 15b shows four SEM micrographs of the

Fig. 16. a) The GISAXS pattern of the Fe-O nanoparticle monolayer. b) The extracted GISAXS

line-cuts at the critical exit angle from six different locations at the substrate.

(6.1±0.6 nm).

At the lowest magnification we notice the absence of any cracks in the deposited monolayer. On the contrary the traditional vertical Langmuir-Blodgett deposition is forming a series of long cracks and is not suitable for large-scale deposition. At the highest magnification we can observe a dense hexagonally ordered layer of the iron oxide nanoparticles. The SEM is suitable for detailed analysis of the selected areas of the nanoparticle monolayer but is not convenient for a rapid screening across the large areas. We have already shown that the scanning GISAXS technique provides a fast probe of the nanoparticle order at nanoscale over macroscopic areas. The Fig. 16a shows the GISAXS reciprocal space map of an arbitrarily selected location at the substrate. The integral intensity and the position of the side maxima are the measure of the nanoparticle order in the X-ray probed area. Comparing the GISAXS patterns from the different locations at the substrate we obtain the information on the homogeneity of the deposited nanoparticle monolayer. The Fig. 16b shows six line cuts extracted from the GISAXS patterns measured at different locations. The differences between the measured curves are less than ±5% that indicates a relatively high homogeneity of the deposited monolayer.

## **5. Processing and application of the self-assembled nanoparticle layers**

In this section we focus on the issues connected with applications of deposited selfassembled nanoparticle layers. We discuss possibilities of removing the nanoparticle surfactant to increase the electrical conductivity of the nanoparticle layer as required for many applications. We address deposition of the nanoparticle layers onto thin membranes for sensor applications. We present also embedded self-assembled nanoparticle layers for organic solar cells and spintronic devices.

The surfactant molecules terminating the nanoparticles are inevitable for the synthesis and deposition of nanoparticles. However for many applications the electrical conductivity is required (Schmid 2010) while non-conductive organics is mostly used as surfactant. The surfactant molecules can be eliminated by the vacuum annealing, plasma etching, UV/ozone cleaning and many other techniques. In this section we analyze the impact of the UV/ozone cleaning on the Fe-O nanoparticle arrangement in self-assembled arrays. The UV/ozone cleaning is based on the reaction of UV light (=6.7 eV) with the oxygen molecules producing the highly reactive ozone. The UV light initiates photo-dissociation of the surfactant molecules that further react with the ozone molecules and are removed from the nanoparticle surface. Also a direct reaction of the surfactant molecules with the ozone molecules also called ozonolysis removes the surfactant molecules from the nanoparticle surface. In our experiment we removed the surfactant molecules from the self-assembled monolayer of iron oxide nanoparticle with the core diameter of 6.1±0.6 nm. The SEM micrographs along with the calculated nanoparticle pair correlation functions for the asdeposited sample and the sample processed in UV/ozone reactor are shown in Fig. 17a and Fig. 17b, respectively. For the as deposited nanoparticle monolayer the mean interparticle distance is given by the position of the first maximum in the pair correlation function that is 7.4 nm. After removal of the surfactant molecules terminating the nanoparticles the mean interparticle distance decreased to 6.4 nm. Moreover the nanoparticle array re-assembled into a labyrinth-like structure as shown by the SEM micrograph in Fig. 17b. This is very important for the electrical conductivity as the new nanoparticle assembly contains percolated conductive paths across the nanoparticle array.

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 459

initial self-assembled state moves slightly to higher *qy*-values and its integral intensity significantly drops. Simultaneously a new peak located at <sup>1</sup> 0 2 *q . nm <sup>y</sup>* develops. The new peak corresponds to the cluster formation that can be seen in the SEM micrograph in Fig. 17b. The measured GISAXS data can be recalculated into a time-resolved nanoparticle pair correlation function shown in Fig. 18b. This function reflects in detail the nanoparticle reassembly due to the removal of the surfactant molecules. The first maximum of the pair correlation function is shifted by some 0.9 nm to lower values within the first 200 seconds. This is in full agreement with the change of the interparticle distance calculated from the SEM micrographs in Fig. 17. This example demonstrates the possibilities of GISAXS to track fast temporal changes in the nanoparticle assemblies even in the strongly reducing

Application of the conductive layers composed of metal oxide nanoparticles can be exemplified on the latest generation of the Fe-O nanoparticle-based gas sensors like SO2, NOX, CO, O3 and CH4. The NO2 sensors are of primary importance for public security as they detect trace amounts of the explosives like EGDN, TNT, PETN, RDX, etc. A large nanoparticle-covered active surface for the gas adsorption is the main advantage when compared to the conventional thin films sensors. The Fig. 19a show a complete sensor based

Fig. 19. a) The photograph of a nanoparticle gas sensor. b) The electrical response of the sensors fabricated with iron oxide (full line) or cobalt iron oxide (dashed line) nanoparticles.

on the metal oxide nanoparticle multilayers (Luby, Chitu et al. 2011).

environments.

Fig. 17. The SEM micrograph and the corresponding pair correlation function for a) as deposited monolayer and b) monolayer treated in UV/ozone reactor.

We have demonstrated that the GISAXS technique is very suitable as an in-situ probe of the processes at nanoscale. We performed a time-resolved measurement of the nanoparticle reassembly directly in the UV/ozone reactor. The above described changes in the nanoparticle pair correlation function in the direct space are manifested here as changes of the interference function in the reciprocal space. The best way of extracting the shape of the nanoparticle interference function from the GISAXS pattern is its lateral line cut along the *<sup>y</sup> q* direction at the critical exit angle. The Fig. 18a shows the temporal evolution of such a line cut constructed from a series of time-resolved GISAXS frames.

Fig. 18. a) The temporal evolution of the GISXAS line cut along the *qy* direction at the critical exit angle. b) The corresponding temporal evolution of the nanoparticle pair correlation function.

The initial as-deposited self-assembled state is characterized by a maximum located at <sup>1</sup> 0 9 *q . nm <sup>y</sup>* . After switching on the UV/ozone reactor the maximum corresponding to the

Fig. 17. The SEM micrograph and the corresponding pair correlation function for a) as

We have demonstrated that the GISAXS technique is very suitable as an in-situ probe of the processes at nanoscale. We performed a time-resolved measurement of the nanoparticle reassembly directly in the UV/ozone reactor. The above described changes in the nanoparticle pair correlation function in the direct space are manifested here as changes of the interference function in the reciprocal space. The best way of extracting the shape of the nanoparticle interference function from the GISAXS pattern is its lateral line cut along the *<sup>y</sup> q* direction at the critical exit angle. The Fig. 18a shows the temporal evolution of such a

Fig. 18. a) The temporal evolution of the GISXAS line cut along the *qy* direction at the critical exit angle. b) The corresponding temporal evolution of the nanoparticle pair correlation

The initial as-deposited self-assembled state is characterized by a maximum located at <sup>1</sup> 0 9 *q . nm <sup>y</sup>* . After switching on the UV/ozone reactor the maximum corresponding to the

deposited monolayer and b) monolayer treated in UV/ozone reactor.

line cut constructed from a series of time-resolved GISAXS frames.

function.

initial self-assembled state moves slightly to higher *qy*-values and its integral intensity significantly drops. Simultaneously a new peak located at <sup>1</sup> 0 2 *q . nm <sup>y</sup>* develops. The new

peak corresponds to the cluster formation that can be seen in the SEM micrograph in Fig. 17b. The measured GISAXS data can be recalculated into a time-resolved nanoparticle pair correlation function shown in Fig. 18b. This function reflects in detail the nanoparticle reassembly due to the removal of the surfactant molecules. The first maximum of the pair correlation function is shifted by some 0.9 nm to lower values within the first 200 seconds. This is in full agreement with the change of the interparticle distance calculated from the SEM micrographs in Fig. 17. This example demonstrates the possibilities of GISAXS to track fast temporal changes in the nanoparticle assemblies even in the strongly reducing environments.

Application of the conductive layers composed of metal oxide nanoparticles can be exemplified on the latest generation of the Fe-O nanoparticle-based gas sensors like SO2, NOX, CO, O3 and CH4. The NO2 sensors are of primary importance for public security as they detect trace amounts of the explosives like EGDN, TNT, PETN, RDX, etc. A large nanoparticle-covered active surface for the gas adsorption is the main advantage when compared to the conventional thin films sensors. The Fig. 19a show a complete sensor based on the metal oxide nanoparticle multilayers (Luby, Chitu et al. 2011).

Fig. 19. a) The photograph of a nanoparticle gas sensor. b) The electrical response of the sensors fabricated with iron oxide (full line) or cobalt iron oxide (dashed line) nanoparticles.

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 461

Another example is the embedded nanoparticle monolayer in the hybrid tunnel junction of novel spintronic devices (Siffalovic, Majkova et al. 2009). Here the surfactant shell is inevitable to provide the tunnelling effect. The Fig. 21a shows schematically the multilayer structure containing iron oxide nanoparticle monolayer. The first fabrication step is the vacuum deposition of a metallic layer forming the bottom electrode. The second step is the deposition of the nanoparticle monolayer that is overcoated by another vacuum deposited metallic layer in the final step. The Fig. 21b shows the evolution of a line cut in the GISAXS pattern with the growing thickness of the metallic overlayer. The peak at <sup>1</sup> 0 83 *q . nm <sup>y</sup>* marked with the dashed line corresponding to the nanoparticle layer can be seen throughout the entire deposition process. These examples demonstrate that the buried nanoparticle monolayer confined to the interface with a thin metallic film can be monitored

Fig. 21. a) A sketch of the spintronic structure that contains a Fe-O nanoparticle monolayer. b) Extracted line-cuts from the GISAXS reciprocal space maps at the critical exit angle in the

The nanoparticle monolayers and multilayers can be deposited also on flexible membranes to be employed for monitoring mechanical properties like strain (Herrmann, Müller et al. 2007). The principle of a strain sensor is based on a change of electrical current across the nanoparticle layer as a function of the applied mechanical stress that modifies the interparticle distance in the film and consequently the electrical resistivity. The sensitivity of the nanoparticle-based strain sensors is roughly by two orders of magnitude better than that of the conventional thin metallic film ones. We investigated the nanoscale response of the nanoparticle monolayer to the applied external stress (Siffalovic, Chitu et al. 2010). We deposited a monolayer composed of iron oxide nanoparticles (6.2±0.7 nm) onto a mylar foil (1 m thickness). The mylar foil was fixed in a stretching device for in-situ SAXS tensile

different fabrication stages of spintronic structure.

stress measurements as shown in Fig. 22a.

using the GISAXS technique.

Visible is the heating meander as the sensor working temperature is 350°C. The active area of the sensor is composed of seven monolayers of Fe2O3 or CoFe2O4 nanoparticles. The Fig. 19b shows the dynamic electrical response of the sensors to 5 ppm of NO2 gas.

The nanoparticle layers exhibiting plasmonic properties in the visible and near-infrared parts of the solar spectra are potential candidates for the next generation of plasmonic solar cells (Catchpole and Polman 2008; Atwater and Polman 2010). The enhanced scattering cross-section of the plasmonic nanoparticles can efficiently trap the light into the active layer of the solar cells and to increase their external quantum efficiency.

Fig. 20. a) The GISAXS reciprocal space map of the active layer deposited on Ag nanoparticle monolayer. The vertical b) and horizontal c) line-cuts across the GISAXS reciprocal space map.

The Ag nanoparticles fulfill both requirements for application in solar cells. In particular, they exhibit plasmon resonance in visible region and are highly electrically conductive. We deposited a monolayer of Ag nanoparticles (6.2±0.7 nm) at the ITO (indium tin oxide) transparent conductive layer supported on a glass substrate. Subsequently an organic active layer composed of polymer blend of P3HT (poly(3-hexylthiophene)) and PCBM (phenyl-C61-butyric acid methyl ester) of a 100 nm thickness was spin-coated on the nanoparticle monolayer. The Fig. 20a shows the GISAXS pattern of the final structure.

A prominent Bragg peak at <sup>1</sup> 3 65 *qz . nm* originates from the molecular P3HT stacking with the inter-molecular distance of 1.7 nm and is clearly visible also in the vertical line cut in Fig. 20b The nanoparticle correlation is visible as a small peak at <sup>1</sup> 0 66 *q . nm <sup>y</sup>* in the Fig. 20c that corresponds to the mean interparticle distance of some 9.5 nm. Here the GISAXS method provides the information on the correlations in the nanoparticle monolayer located at the buried interface hardly accessible by other analytical techniques.

Visible is the heating meander as the sensor working temperature is 350°C. The active area of the sensor is composed of seven monolayers of Fe2O3 or CoFe2O4 nanoparticles. The

The nanoparticle layers exhibiting plasmonic properties in the visible and near-infrared parts of the solar spectra are potential candidates for the next generation of plasmonic solar cells (Catchpole and Polman 2008; Atwater and Polman 2010). The enhanced scattering cross-section of the plasmonic nanoparticles can efficiently trap the light into the active layer

Fig. 19b shows the dynamic electrical response of the sensors to 5 ppm of NO2 gas.

Fig. 20. a) The GISAXS reciprocal space map of the active layer deposited on Ag nanoparticle monolayer. The vertical b) and horizontal c) line-cuts across the GISAXS

monolayer. The Fig. 20a shows the GISAXS pattern of the final structure.

at the buried interface hardly accessible by other analytical techniques.

The Ag nanoparticles fulfill both requirements for application in solar cells. In particular, they exhibit plasmon resonance in visible region and are highly electrically conductive. We deposited a monolayer of Ag nanoparticles (6.2±0.7 nm) at the ITO (indium tin oxide) transparent conductive layer supported on a glass substrate. Subsequently an organic active layer composed of polymer blend of P3HT (poly(3-hexylthiophene)) and PCBM (phenyl-C61-butyric acid methyl ester) of a 100 nm thickness was spin-coated on the nanoparticle

A prominent Bragg peak at <sup>1</sup> 3 65 *qz . nm* originates from the molecular P3HT stacking with the inter-molecular distance of 1.7 nm and is clearly visible also in the vertical line cut in Fig. 20b The nanoparticle correlation is visible as a small peak at <sup>1</sup> 0 66 *q . nm <sup>y</sup>* in the Fig. 20c that corresponds to the mean interparticle distance of some 9.5 nm. Here the GISAXS method provides the information on the correlations in the nanoparticle monolayer located

reciprocal space map.

of the solar cells and to increase their external quantum efficiency.

Another example is the embedded nanoparticle monolayer in the hybrid tunnel junction of novel spintronic devices (Siffalovic, Majkova et al. 2009). Here the surfactant shell is inevitable to provide the tunnelling effect. The Fig. 21a shows schematically the multilayer structure containing iron oxide nanoparticle monolayer. The first fabrication step is the vacuum deposition of a metallic layer forming the bottom electrode. The second step is the deposition of the nanoparticle monolayer that is overcoated by another vacuum deposited metallic layer in the final step. The Fig. 21b shows the evolution of a line cut in the GISAXS pattern with the growing thickness of the metallic overlayer. The peak at <sup>1</sup> 0 83 *q . nm <sup>y</sup>* marked with the dashed line corresponding to the nanoparticle layer can be seen throughout the entire deposition process. These examples demonstrate that the buried nanoparticle monolayer confined to the interface with a thin metallic film can be monitored using the GISAXS technique.

Fig. 21. a) A sketch of the spintronic structure that contains a Fe-O nanoparticle monolayer. b) Extracted line-cuts from the GISAXS reciprocal space maps at the critical exit angle in the different fabrication stages of spintronic structure.

The nanoparticle monolayers and multilayers can be deposited also on flexible membranes to be employed for monitoring mechanical properties like strain (Herrmann, Müller et al. 2007). The principle of a strain sensor is based on a change of electrical current across the nanoparticle layer as a function of the applied mechanical stress that modifies the interparticle distance in the film and consequently the electrical resistivity. The sensitivity of the nanoparticle-based strain sensors is roughly by two orders of magnitude better than that of the conventional thin metallic film ones. We investigated the nanoscale response of the nanoparticle monolayer to the applied external stress (Siffalovic, Chitu et al. 2010). We deposited a monolayer composed of iron oxide nanoparticles (6.2±0.7 nm) onto a mylar foil (1 m thickness). The mylar foil was fixed in a stretching device for in-situ SAXS tensile stress measurements as shown in Fig. 22a.

Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 463

evaporation was described shortly while a detailed study of the self-assembly process at the liquid/air interface was the core of the chapter. This interface represents an ideal system for the nanoparticle assembling as the nanoparticles are confined to the interface but still keep translational mobility along it. The processes accompanying the formation of a nanoparticle monolayer and its transition to a multilayer were described in detail. Ideal deposition conditions for the nanoparticle monolayer formation were derived relying on the surface pressure and surface elastic modulus measurements. A modified Langmuir-Schaefer technique suitable for large-area deposition of nanoparticle arrays was presented. Selected

It has to be stressed that the colloidal nanoparticle self-assembly is a complex process resulting from an interplay between many factors where the nanoparticle type and size as well as the chemical composition of surfactant play a crucial role. Therefore none of the selfassembly techniques described in the chapter is generally applicable to any colloidal nanoparticle solution. It is also the reason why different techniques were presented with

It has to be also noted that in addition to the spontaneous nanoparticle self-assembly treated in this chapter of limited length, other approaches to assembling based on recent developments are of growing interest in the nanoparticle community. These include e.g. directed self-assembly of nanoparticles on pre-patterned substrates, chemically driven self-assembly, nanoparticle self-assembly stimulated by a magnetic or electro-magnetic

This publication is the result of the project implementation Center of Applied Nanoparticle research, ITMS code 26240220011, supported by the Research & Development Operational Program funded by the ERDF. The support of Grant Agency VEGA Bratislava, project No.

Atwater, H. A. and Polman, A. (2010). Plasmonics for improved photovoltaic devices. *Nature* 

Barnes, G., Gentle, I., et al. (2005). *Interfacial science: an introduction*. Oxford [u.a.], Oxford

Born, M. and Wolf, E. (1999). *Principles of optics: electromagnetic theory of propagation,* 

Catchpole, K. R. and Polman, A. (2008). Design principles for particle plasmon enhanced

Chitu, L., Siffalovic, P., et al. (2010). Modified Langmuir-Blodgett deposition of

solar cells. *Applied Physics Letters* 93(19): 191113.

*interference and diffraction of light*. Cambridge; New York, Cambridge University

nanoparticles - measurement of 2D to 3D ordered arrays. *Measurement Science* 

applications of the deposited self-assembled layers were reviewed.

different types of nanoparticles.

**7. Acknowledgment** 

**8. References** 

2/0041/11, is also acknowledged.

Univ. Press.

Press.

*Materials* 9(3): 205-213.

*Review* 10(5): 162-165.

field.

Fig. 22. a) Scheme of the experimental setup with an in-situ SAXS tensile stage. b) The evaluated interparticle separation as a function of the strain in two perpendicular directions.

The mylar foil was strained up to 11% in the *z*-direction and the SAXS patterns were recorded. Relying on them, the mean interparticle distance was evaluated in the applied stress direction and in the direction perpendicular to it. The results are shown in Fig. 22b. In the direction perpendicular to the applied stress the nanoparticle separation remained constant. However in the direction of the applied stress the interparticle distance followed linearly the measured foil strain. These measurements provide the test basis for the future strain sensors based on the nanoparticle layers.

In this section we included only a few of a large variety of practical applications of the nanoparticle monolayers. The nanoparticle deposition, eventual post-deposition processing of the nanoparticle layer and the test measurements of the macroscopic properties of interest are common for all these applications. The presented SAXS/GISAXS techniques offer an efficient and direct access to the nanoparticle arrangement within the final device.

## **6. Conclusion**

The chapter provides an introductory guide to X-ray scattering studies of nanoparticle selfassembly processes at liquid/air and solid/air interfaces. It is primarily intended for graduate and post-graduate students but it is aimed also at other scientific community in the field addressing the issues of general interest. In particular, it shows the latest advances in the rapidly growing field of self-assembled nanoparticle layers. The X-ray scattering diagnostic technique was reviewed that provides an easy access even to buried nanoparticle assemblies. The main advantage of the X-ray scattering analysis is the possibility to track technologically important processes connected with the nanoparticle self-assembly or reassembly in real time. The self-assembly process after colloidal drop casting and

Fig. 22. a) Scheme of the experimental setup with an in-situ SAXS tensile stage. b) The evaluated interparticle separation as a function of the strain in two perpendicular directions.

strain sensors based on the nanoparticle layers.

**6. Conclusion** 

The mylar foil was strained up to 11% in the *z*-direction and the SAXS patterns were recorded. Relying on them, the mean interparticle distance was evaluated in the applied stress direction and in the direction perpendicular to it. The results are shown in Fig. 22b. In the direction perpendicular to the applied stress the nanoparticle separation remained constant. However in the direction of the applied stress the interparticle distance followed linearly the measured foil strain. These measurements provide the test basis for the future

In this section we included only a few of a large variety of practical applications of the nanoparticle monolayers. The nanoparticle deposition, eventual post-deposition processing of the nanoparticle layer and the test measurements of the macroscopic properties of interest are common for all these applications. The presented SAXS/GISAXS techniques offer an

The chapter provides an introductory guide to X-ray scattering studies of nanoparticle selfassembly processes at liquid/air and solid/air interfaces. It is primarily intended for graduate and post-graduate students but it is aimed also at other scientific community in the field addressing the issues of general interest. In particular, it shows the latest advances in the rapidly growing field of self-assembled nanoparticle layers. The X-ray scattering diagnostic technique was reviewed that provides an easy access even to buried nanoparticle assemblies. The main advantage of the X-ray scattering analysis is the possibility to track technologically important processes connected with the nanoparticle self-assembly or reassembly in real time. The self-assembly process after colloidal drop casting and

efficient and direct access to the nanoparticle arrangement within the final device.

evaporation was described shortly while a detailed study of the self-assembly process at the liquid/air interface was the core of the chapter. This interface represents an ideal system for the nanoparticle assembling as the nanoparticles are confined to the interface but still keep translational mobility along it. The processes accompanying the formation of a nanoparticle monolayer and its transition to a multilayer were described in detail. Ideal deposition conditions for the nanoparticle monolayer formation were derived relying on the surface pressure and surface elastic modulus measurements. A modified Langmuir-Schaefer technique suitable for large-area deposition of nanoparticle arrays was presented. Selected applications of the deposited self-assembled layers were reviewed.

It has to be stressed that the colloidal nanoparticle self-assembly is a complex process resulting from an interplay between many factors where the nanoparticle type and size as well as the chemical composition of surfactant play a crucial role. Therefore none of the selfassembly techniques described in the chapter is generally applicable to any colloidal nanoparticle solution. It is also the reason why different techniques were presented with different types of nanoparticles.

It has to be also noted that in addition to the spontaneous nanoparticle self-assembly treated in this chapter of limited length, other approaches to assembling based on recent developments are of growing interest in the nanoparticle community. These include e.g. directed self-assembly of nanoparticles on pre-patterned substrates, chemically driven self-assembly, nanoparticle self-assembly stimulated by a magnetic or electro-magnetic field.

## **7. Acknowledgment**

This publication is the result of the project implementation Center of Applied Nanoparticle research, ITMS code 26240220011, supported by the Research & Development Operational Program funded by the ERDF. The support of Grant Agency VEGA Bratislava, project No. 2/0041/11, is also acknowledged.

## **8. References**


Self-Assembly of Nanoparticles at Solid and Liquid Surfaces 465

Niederberger, M. and Pinna, N. (2009). Metal Oxide Nanoparticles in Organic Solvents

Park, J., An, K., et al. (2004). Ultra-large-scale syntheses of monodisperse nanocrystals.

Roth, S. V., Döhrmann, R., et al. (2006). Small-angle options of the upgraded ultrasmall-

Roth, S. V. and et al. (2011). In situ observation of cluster formation during nanoparticle

Rycenga, M., Cobley, C. M., et al. (2011). Controlling the Synthesis and Assembly of

Salditt, T., Metzger, T. H., et al. (1994). Kinetic Roughness of Amorphous Multilayers Studied by Diffuse-X-Ray Scattering. *Physical Review Letters* 73(16): 2228-2231.

Siffalovic, P., Chitu, L., et al. (2010). Kinetics of Nanoparticle Reassembly Mediated by UV-

Siffalovic, P., Chitu, L., et al. (2010). Towards strain gauges based on a self-assembled

Siffalovic, P., Jergel, M., et al. (2011). GISAXS - probe of buried interfaces in multilayered

Siffalovic, P., Majkova, E., et al. (2009). Fabrication and Characterization of Hybrid Tunnel

Siffalovic, P., Majkova, E., et al. (2008). Real-Time Tracking of Superparamagnetic

Siffalovic, P., Majkova, E., et al. (2007). Self-assembly of iron oxide nanoparticles studied by

Siffalovic, P., Vegso, K., et al. (2010). Measurement of nanopatterned surfaces by real and reciprocal space techniques. *Measurement Science Review* 10(5): 153-156.

Ulman, A. (1991). *An introduction to ultrathin organic films : from Langmuir-Blodgett to self-*

Vegso, K., Siffalovic, P., et al. (2011). In situ GISAXS monitoring of Langmuir nanoparticle

multilayer degradation processes induced by UV photolysis. *physica status solidi (a)*:

thin films. In: *X-Ray Scattering*. C. M. Bauwens. New York, Nova Science

Magnetoresistance Structures with Embedded Self-Assembled Nanoparticle

time-resolved grazing-incidence small-angle x-ray scattering. *Physical Review B*

Schmid, G. (2010). *Nanoparticles from theory to application*. Weinheim, Wiley-VCH.

nanoparticle monolayer-SAXS study. *Nanotechnology* 21(38).

Photolysis of Surfactant. *Langmuir* 26(8): 5451-5455.

Templates. *Acta Physica Polonica a* 115(1): 332-335.

Nanoparticle Self-Assembly. *Small* 4(12): 2222-2228.

Stribeck, N. (2007). *X-ray scattering of soft matter*. Berlin, Springer.

*assembly*. Boston [u.a.], Acad. Press.

(accepted, in press).

Pileni, M.-P. (2005). *Nanocrystals forming mesoscopic structures*. Weinheim, Wiley-VCH. Renaud, G., Lazzari, R., et al. (2009). Probing surface and interface morphology with

*Processes*. London, Springer London.

*Nature Materials* 3(12): 891-895.

380.

77(8): 085106.

254208.

3669-3712.

Publishers.

76(19).

Synthesis, Formation, Assembly and Application. *Engineering Materials and* 

Grazing Incidence Small Angle X-Ray Scattering. *Surface Science Reports* 64(8): 255-

angle x-ray scattering beamline BW4 at HASYLAB. *Review of Scientific Instruments*

solution casting on a colloidal film. *Journal of Physics: Condensed Matter* 23(25):

Silver Nanostructures for Plasmonic Applications. *Chemical Reviews* 111(6):


Chushkin, Y., Ulmeanu, M., et al. (2003). Structural study of self-assembled Co

Daillant, J. and Gibaud, A. (2009). *X-ray and neutron reflectivity : principles and applications*.

Deegan, R. D., Bakajin, O., et al. (1997). Capillary flow as the cause of ring stains from dried

Feigin, L. A., Svergun, D. I., et al. (1987). *Structure analysis by small-angle X-ray and neutron* 

Feldheim, D. L. (2002). *Metal nanoparticles: synthesis, characterization, and applications*. New

Glatter, O. and Kratky, O. (1982). *Small angle x-ray scattering*. London; New York, Academic

Guinier, A. (1963). *X-ray diffraction in crystals, imperfect crystals, and amorphous bodies*. San

Henon, S. and Meunier, J. (1991). Microscope at the Brewster-Angle - Direct Observation of

Herrmann, J., Müller, K. H., et al. (2007). Nanoparticle films as sensitive strain gauges.

Holý, V., Pietsch, U., et al. (1999). *High-resolution X-ray scattering from thin films and* 

Hosemann, R. and Bagchi, S. N. (1962). *Direct analysis of diffraction by matter*. Amsterdam,

Kraft, P., Bergamaschi, A., et al. (2009). Performance of single-photon-counting PILATUS

Lazzari, R. (2002). IsGISAXS: a program for grazing-incidence small-angle X-ray scattering analysis of supported islands. *Journal of Applied Crystallography* 35: 406-421. Lazzari, R. (2009). Grazing Incidence Small-Angle X-Ray Scattering from Nanostructures. In:

Luby, S., Chitu, L., et al. (2011). Oxide nanoparticle arrays for sensors of CO and NO2 gases.

Michaelsen, C., Wiesmann, J., et al. (2002). Recent developments of multilayer mirror optics

Müller-Buschbaum, P. (2009). A Basic Introduction to Grazing Incidence Small-Angle X-Ray

Nagarajan, R. (2008). *Nanoparticles: synthesis, stabilization, passivation, and functionalization*.

*X-ray and Neutron Reflectivity*. J. Daillant and A. Gibaud, Springer Berlin /

for laboratory x-ray instrumentation. *X-Ray Mirrors, Crystals, and Multilayers Ii* 4782:

Scattering. In: *Applications of Synchrotron Light to Scattering and Diffraction in Materials and Life Sciences*. M. Gomez, A. Nogales, M. C. Garcia-Gutierrez and T. A.

detector modules. *Journal of Synchrotron Radiation* 16(3): 368-375.

1st-Order Phase-Transitions in Monolayers. *Review of Scientific Instruments* 62(4):

Guinier, A. and Fournet, G. (1955). *Small-angle scattering of X-rays*. New York,, Wiley.

nanoparticles. *Journal of Applied Physics* 94(12): 7743-7748.

Berlin Heidelberg, Springer.

York [u.a.], Dekker.

Francisco,, W.H. Freeman.

*Applied Physics Letters* 91(18): 183105.

North-Holland Publ. Comp.

Heidelberg. 770: 283-342.

143-151.

*Vacuum* In Press, Corrected Proof.

*multilayers*. Berlin; New York, Springer.

Kittel, C. (2005). *Introduction to solid state physics*. Hoboken, NJ, Wiley.

Ezquerra, Springer Berlin / Heidelberg. 776: 61-89.

Washington, DC, American Chemical Soc.

Press.

936-939.

liquid drops. *Nature* 389(6653): 827-829.

*scattering*. New York [etc.], Plenum Press.


**21** 

**View on the Magnetic Properties of** 

**Nanoparticles Com (m=6,8,10,12,14)** 

*1Vilnius Uinversity, Institute of Theoretical Physics and Astronomy, Vilnius,* 

Currently there are several potential applications for magnetic nanomaterials in medicine including magnetic resonance imaging contrast agents, magnetic-field-directed drug delivery systems, bio-toxin removal, gene therapy, and magnetic fluid hyperthermia. Cobalt nanoparticles are is one the most promising material for both technological applications and academic studies as model system how effects the nanoparticle size, shape, structure, and surface anisotropy on macroscopic magnetic response. The magnetic behaviour of Co nanoparticles reveals how the magnetic metal nanoparticles can be used to enhance the

Today it is very well known that in a paramagnetic material there are unpaired electrons, that are free to align their magnetic moment in any direction, while paired electrons by the Pauli Exclusion Principle are to have their intrinsic ('spin') magnetic moments in to opposite directions, causing their magnetic fields to cancel out. It implies, that in many cases, the magnetic properties of the Co nanoparticles are explained by the presence of unpaired electrons because the particles consist of an odd number of cobalt atoms. However, in experimental studies the number of atoms in the particle has never been mentioned only the description of their size and main structure along with their magnetic properties have been provided. It is not a surprise, because a magnetic behaviour of materials depends on their electron configuration that is strongly related with a geometrical structure, and on

The dependence of magnetic anisotropy energy on crystal symmetry and atomic composition is observed in both ferromagnetic bulk materials and thin films. Even the structural parameters such as the shape of particles or the inter-atomic distances, in some cases, are affected by the above dependence. The importance of the electronic structure of

**1. Introduction** 

temperature.

signal due to their magnetic resonance imaging.

**and Co6On (n=1-9)** 

*4Vilnius University, Vilnius,* 

*1,2,4Lithuania 3Spain* 

Jelena Tamulienė1, Rimas Vaišnoras2,

*2Vilnius Pedagogical University, Vilnius,* 

*3Institut de Ciences Fotoniques ICFO, Barcelona,* 

Goncal Badenes3 and Mindaugas L. Balevičius4

Wiesmann, J., Graf, J., et al. (2009). X-Ray Diffractometry with Low Power Microfocus Sources - New Possibilities in the Lab. *Particle & Particle Systems Characterization* 26(3): 112-116.

Yoneda, Y. (1963). Anomalous Surface Reflection of X Rays. *Physical Review* 131(5): 2010.

## **View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9)**

Jelena Tamulienė1, Rimas Vaišnoras2, Goncal Badenes3 and Mindaugas L. Balevičius4 *1Vilnius Uinversity, Institute of Theoretical Physics and Astronomy, Vilnius, 2Vilnius Pedagogical University, Vilnius, 3Institut de Ciences Fotoniques ICFO, Barcelona, 4Vilnius University, Vilnius, 1,2,4Lithuania 3Spain* 

## **1. Introduction**

466 Smart Nanoparticles Technology

Wiesmann, J., Graf, J., et al. (2009). X-Ray Diffractometry with Low Power Microfocus

Yoneda, Y. (1963). Anomalous Surface Reflection of X Rays. *Physical Review* 131(5): 2010.

26(3): 112-116.

Sources - New Possibilities in the Lab. *Particle & Particle Systems Characterization*

Currently there are several potential applications for magnetic nanomaterials in medicine including magnetic resonance imaging contrast agents, magnetic-field-directed drug delivery systems, bio-toxin removal, gene therapy, and magnetic fluid hyperthermia. Cobalt nanoparticles are is one the most promising material for both technological applications and academic studies as model system how effects the nanoparticle size, shape, structure, and surface anisotropy on macroscopic magnetic response. The magnetic behaviour of Co nanoparticles reveals how the magnetic metal nanoparticles can be used to enhance the signal due to their magnetic resonance imaging.

Today it is very well known that in a paramagnetic material there are unpaired electrons, that are free to align their magnetic moment in any direction, while paired electrons by the Pauli Exclusion Principle are to have their intrinsic ('spin') magnetic moments in to opposite directions, causing their magnetic fields to cancel out. It implies, that in many cases, the magnetic properties of the Co nanoparticles are explained by the presence of unpaired electrons because the particles consist of an odd number of cobalt atoms. However, in experimental studies the number of atoms in the particle has never been mentioned only the description of their size and main structure along with their magnetic properties have been provided. It is not a surprise, because a magnetic behaviour of materials depends on their electron configuration that is strongly related with a geometrical structure, and on temperature.

The dependence of magnetic anisotropy energy on crystal symmetry and atomic composition is observed in both ferromagnetic bulk materials and thin films. Even the structural parameters such as the shape of particles or the inter-atomic distances, in some cases, are affected by the above dependence. The importance of the electronic structure of

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 469

aiming to prevent them from both irreversible aggregation and loosing of magnetic

For coating of Co nanoparticle different materials such as graphite, nanoroads, nanocapsules and oxygen are used. The core-shell nanoparticles (Co-CoO) are examined and, it is established, that the magnetic properties of these particle strongly depend on the plane coverage. The results reported demonstrate the essential role played by shells in stabilizing the magnetism of Co-CoO nanoparticles. Few reports on the preparation and properties of pure CoO in bulk are due to difficulties to obtain the materials in pure form by simple methods. The particles are often contaminated with Co3O4 or Co metal. The greater stability

Herein, we report on the several very important issues related to magnetic properties of Co

1. What are electronic and geometric structure properties of pure and oxidized Co nanoparticles and how these properties change with the increase of the size of particle ; 2. Could Co nanoparticles consisting of the even number of atoms exhibit magnetic properties because their electronic structure is such that an uncompensated electronmagnetic-moment appears? What are the main reasons of the above appearance? 3. Some Co oxide particles exhibited magnetic properties and have large perspective to be

The structural origin of clusters has been studied by using the generalized gradient approximation for the exchange-correlation potential in the density functional theory (DFT) as it is described by Becke's three-parameter hybrid functional, using the non-local correlation provided by Lee, Yang, and Parr. The DFT method is commonly referred to as B3LYP, - a representative standard DFT method. The 6-31G basis set has been used as well. The basis set was chosen keeping in mind relatively minimum computational costs. The structures of the investigated nanoparticles have been optimized globally without any symmetry constraint and by starting from various initial geometries which have been constructed according to a certain symmetry in order to determine the lowest energy structures of each cluster. The GAMESS and Gaussian program suites were used for all

It is necessary to mention that there are different ways to theoretically investigate the magnetic properties of the materials. Aiming to exhibit why closed shell particles could be paramagnetic, we have chosen the most simple method to investigate magnetic properties of the Co nanoparticles. Hence, magnetizability (commonly known as susceptibility) was investigated. The magnetizability is the second-order response to an external magnetic

<sup>2</sup>

*2 B=*

Where E is energy, B is an external magnetic field.

*<sup>δ</sup> E B <sup>ξ</sup> = | <sup>δ</sup><sup>B</sup>*

0

properties.

of Co3O4 than CoO is also established.

nanoparticles such as:

used in electronics.

**2. Description of method** 

simulations here.

field:

particles exhibits the dependence of magnetic anisotropy energy on a single-atom coordination. Current, experiments exhibited that the coercivity of some particles at 10 K increased from 640 to 1250 Oe while the particle size increased from 1.8 to 4.4 nm. The saturation magnetization increases with decreasing of particle size. Pure CoO nanoparticles in the 4.5-18 nm exhibit a super-paramagnetic behaviour at room temperature, and a large orbital contribution to the magnetic moment at low temperatures was also observed.

It was mentioned, that an electronic structure of both the materials and particles is strongly related with the geometrical structure. However, there are some difficulties to identify the structure of a cobalt nanoparticle. The crystallinity was evidenced by the transmission electron microscope (TEM) indicating that Co particles sized around 4.7 nm are a wellcrystallized FCC. While the particles with the average diameter smaller than 4,7 nm are almost perfectly spherical. The lattice of Co nanoparticles with inter-planar distance of around 0.23 nm was obtained and explained that such crystalline structure could originate either from BCC cobalt particles observed along the [001] direction or due to Co-FCC particles since the lattice would be formed by two [002] perpendicular planes. Both a highresolution TEM and powder x-ray diffraction profiles reveal the presence of 8-15 nm diameter crystallites that are identified as hcp-Co, FCC-Co nanocrystals. S. Ram reports two crystalline phases of cobalt FCC and BCC structures, while S. P. Gubin and et al. report that hcp and FCC structures or their combination can be realized in Co nanoparticles. C. G. Zimmermann and et al. investigate Co nanoparticles the diameter of which is 13 nm and the variance of 4 nm; the first four FCC rings were visible in the diffraction pattern. Hence, there is no evidence what a crystalline phase of cobalt is more preferable and it is difficult to define which structure type of Co is realized in nanoparticles. Theoretical investigations of the Co clusters are not complete. J. Guevara and et al. calculated those Co clusters that are part of FCC or BCC block without distortion of the initial geometry structure. In other works, the structural distortion of the above clusters was performed by moving one or several atoms along the main axis of the clusters, i.e. this operation does not change the symmetry if the configuration of the cluster belongs to a point group with a single main axis. Hence, we begin at the results of the investigation of the structure of the Co nanoparticles aiming to recognize the most important structure features influencing the magnetic properties of the Co nanoparticles.

Other very important results obtained are that the nanoparticle behaviour is influenced by the proximity of neighbouring particles, i.e. dipolar inter-particle interactions lead to the appearance of collective behaviour. Such a collective behaviour due to dipolar interactions has been observed in the low susceptibility measurements corresponding to a highly ordered fine particles system. Puntes and et al. observe that when the density of particles per unit area is higher than a determined threshold, the two-dimensional self-assemblies behave as a continuous ferromagnetic thin film. A weak interaction among the assemblies of the Co nanoparticle is obtained by Park and et al. and this assembly leads to hysteresis disappearance. We shortly explain why the assembly of Co nanoparticles leads to loosing of the particle magnetic properties and make predictions how to avoid the loosing.

One of the reasons of the above assembly of the particles is their stability that is an important factor for the particle application in technology. Small cobalt nanoparticles not only self-assemble, but also easily oxidize in the air and, as a consequence, loose their magnetic properties. Thus, Co nanoparticles need to be coated with organic surfactants aiming to prevent them from both irreversible aggregation and loosing of magnetic properties.

For coating of Co nanoparticle different materials such as graphite, nanoroads, nanocapsules and oxygen are used. The core-shell nanoparticles (Co-CoO) are examined and, it is established, that the magnetic properties of these particle strongly depend on the plane coverage. The results reported demonstrate the essential role played by shells in stabilizing the magnetism of Co-CoO nanoparticles. Few reports on the preparation and properties of pure CoO in bulk are due to difficulties to obtain the materials in pure form by simple methods. The particles are often contaminated with Co3O4 or Co metal. The greater stability of Co3O4 than CoO is also established.

Herein, we report on the several very important issues related to magnetic properties of Co nanoparticles such as:


## **2. Description of method**

468 Smart Nanoparticles Technology

particles exhibits the dependence of magnetic anisotropy energy on a single-atom coordination. Current, experiments exhibited that the coercivity of some particles at 10 K increased from 640 to 1250 Oe while the particle size increased from 1.8 to 4.4 nm. The saturation magnetization increases with decreasing of particle size. Pure CoO nanoparticles in the 4.5-18 nm exhibit a super-paramagnetic behaviour at room temperature, and a large

It was mentioned, that an electronic structure of both the materials and particles is strongly related with the geometrical structure. However, there are some difficulties to identify the structure of a cobalt nanoparticle. The crystallinity was evidenced by the transmission electron microscope (TEM) indicating that Co particles sized around 4.7 nm are a wellcrystallized FCC. While the particles with the average diameter smaller than 4,7 nm are almost perfectly spherical. The lattice of Co nanoparticles with inter-planar distance of around 0.23 nm was obtained and explained that such crystalline structure could originate either from BCC cobalt particles observed along the [001] direction or due to Co-FCC particles since the lattice would be formed by two [002] perpendicular planes. Both a highresolution TEM and powder x-ray diffraction profiles reveal the presence of 8-15 nm diameter crystallites that are identified as hcp-Co, FCC-Co nanocrystals. S. Ram reports two crystalline phases of cobalt FCC and BCC structures, while S. P. Gubin and et al. report that hcp and FCC structures or their combination can be realized in Co nanoparticles. C. G. Zimmermann and et al. investigate Co nanoparticles the diameter of which is 13 nm and the variance of 4 nm; the first four FCC rings were visible in the diffraction pattern. Hence, there is no evidence what a crystalline phase of cobalt is more preferable and it is difficult to define which structure type of Co is realized in nanoparticles. Theoretical investigations of the Co clusters are not complete. J. Guevara and et al. calculated those Co clusters that are part of FCC or BCC block without distortion of the initial geometry structure. In other works, the structural distortion of the above clusters was performed by moving one or several atoms along the main axis of the clusters, i.e. this operation does not change the symmetry if the configuration of the cluster belongs to a point group with a single main axis. Hence, we begin at the results of the investigation of the structure of the Co nanoparticles aiming to recognize the most important structure features influencing the

Other very important results obtained are that the nanoparticle behaviour is influenced by the proximity of neighbouring particles, i.e. dipolar inter-particle interactions lead to the appearance of collective behaviour. Such a collective behaviour due to dipolar interactions has been observed in the low susceptibility measurements corresponding to a highly ordered fine particles system. Puntes and et al. observe that when the density of particles per unit area is higher than a determined threshold, the two-dimensional self-assemblies behave as a continuous ferromagnetic thin film. A weak interaction among the assemblies of the Co nanoparticle is obtained by Park and et al. and this assembly leads to hysteresis disappearance. We shortly explain why the assembly of Co nanoparticles leads to loosing of

One of the reasons of the above assembly of the particles is their stability that is an important factor for the particle application in technology. Small cobalt nanoparticles not only self-assemble, but also easily oxidize in the air and, as a consequence, loose their magnetic properties. Thus, Co nanoparticles need to be coated with organic surfactants

the particle magnetic properties and make predictions how to avoid the loosing.

orbital contribution to the magnetic moment at low temperatures was also observed.

magnetic properties of the Co nanoparticles.

The structural origin of clusters has been studied by using the generalized gradient approximation for the exchange-correlation potential in the density functional theory (DFT) as it is described by Becke's three-parameter hybrid functional, using the non-local correlation provided by Lee, Yang, and Parr. The DFT method is commonly referred to as B3LYP, - a representative standard DFT method. The 6-31G basis set has been used as well. The basis set was chosen keeping in mind relatively minimum computational costs. The structures of the investigated nanoparticles have been optimized globally without any symmetry constraint and by starting from various initial geometries which have been constructed according to a certain symmetry in order to determine the lowest energy structures of each cluster. The GAMESS and Gaussian program suites were used for all simulations here.

It is necessary to mention that there are different ways to theoretically investigate the magnetic properties of the materials. Aiming to exhibit why closed shell particles could be paramagnetic, we have chosen the most simple method to investigate magnetic properties of the Co nanoparticles. Hence, magnetizability (commonly known as susceptibility) was investigated. The magnetizability is the second-order response to an external magnetic field:

$$\xi = \frac{-\delta^2 E(B)}{\delta B^2}|\_{B=0}$$

Where E is energy, B is an external magnetic field.

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 471

Let us remember that, there is an infinite number of possible surfaces which can be exposed for every crystal system. In practice, only a limited number of planes are found to exist in any significant amount. Thus, the attention was concentrated on the above surfaces, because it is possible to predict the ideal atomic arrangement for a given surface of a particular metal by considering how the bulk structure is intersected by the surface. It is necessary to remember that investigated nanoparticles consist of a small number of atoms, thus, it is not possible to obtain a very strict crystalline structure; the crystalline structure that is expected to be in the investigated Co nanoparticles was obtained on the basis of the symmetry of a

It is necessary to mention that the structure of the Co4 particle was found, too. The results obtained indicate that Co4 is planar and a nice equilateral is formed. In the case of Co6 nanoparticle, we have the three-dimensional structure with a slightly disordered cubic symmetry. The structure was obtained after global optimization of the D4h isomer of a Co6 particle. It is important that each atom of the Co6 nanoparticle is possible to approximately be located in the centre of the plane of the cubic cell (Fig. 1). The three surfaces are obtained.

It is possible to see two planes of the Co8 nanoparticle (Fig. 2). The location of atoms on these planes as well as the symmetry of bonds allows us to predict that the element of FCC structure has been formed, too. This assumption is supported by following: i) each Co atom is four-fold coordinated; ii) the structural element of the Co6 particle is obtained (see the structure that form atoms 5, 6, 7, 8 or 1, 2, 3, 4 in Fig. 2). So, the element of FCC structure has also been obtained in the Co8 nanoparticle. The conformation of Co8 nanoparticle has

One of more interesting situations arises in case of Co10 nanoparticle. In this case, we have the two-dimensional disordered symmetry structure consisting of two planes and two atoms in the middle of each plane (Fig.3). The atoms mentioned join these planes. Roughly speaking, the structure of the Co10 nanoparticle is formed when the planes of the Co8 nanoparticle are rotated in respect of each other when two Co atoms are added and a nice cubic structure is formed. This has also been confirmed by bond order investigations. On the

bond and atom location in the planes.

Fig. 1. Co6 nanoparticle located in the cubic cell.

So, this nanoparticle is the element of a FCC structure.

proved to be the most stable.

When *ξ* < 0, the induced magnetic moment is opposite to the applied field, i.e. the investigated materials are diamagnetic; while for paramagnetic materials the magnetizability is larger than zero (ξ > 0) in this case the induced magnetic moment enforces the magnetic field. Experimentally, magnetizability is often poorly determined or it is only known in the liquid or solid state, thus it is difficult comparisons between calculated and experimental results, while rotational g-tensors are known as precisely determined. However, a rotational g-tensor behaves in the same manner as magnetizability, with a near cancellation of large nuclear and electronic contributions in a large system.

A calculation of rotational g tensors is closely related to that of magnetizabilities via:

$$\mathbf{g} = -4\mathbf{m}\_p \left(\boldsymbol{\xi}^{LAO} - \boldsymbol{\xi}\_{cm}^{dia}\right) \mathbf{I}\_{muc}^{-1} + \frac{1}{2\mu\_N} \sum \mathbf{Z}\_k \left(\mathbf{R}\_K^T \mathbf{R}\_K \boldsymbol{I}\_3 - \mathbf{R}\_K \mathbf{R}\_K^T\right) \mathbf{I}\_{muc}^{-1}$$

where mp is the proton mass, *LAO ξ* is the magnetizability tensor calculated with London orbitals, *dia <sup>ξ</sup>cm* is the diamagnetic contribution to the magnetizability tensor calculated with conventional orbitals and the gauge origin at the centre of mass, and the sum of all nuclei with charges ZK and positions RK, while Inuc is the moment-of-inertia tensor. Although not explored in a large number of studies, obtained theoretical results fit experimental. Hence, the above close relationship allows us to expect that our methods chosen that are well suited to the calculation of rotational g tensors should also be well suited to the calculations of magnetizabilities. Moreover, this simple enough method is suitable to describe general magnetic properties of the investigated particles and to explain the results obtained.

The isotropic magnetizability of the most stable clusters was calculated by adopting quantum mechanical response theory and London atomic orbital to ensure both gaugeorigin independent results and fast basis set convergence by using Dalton program. The approach used allows us to calculate accurate magnetizability even for quite large molecules at a moderate cost of computing time. In this case, the B3LYP method with Ahlrichs-pVDZ basis set was used. These basis sets were obtained by optimizing the exponents and contraction coefficients in the ground state ROHF calculations. There are total 241 contracted functions in the basis mentioned. It is showed, that the isotropic magnezitability and its anisotropy are remarkably constant with respect to the basis set and close to the experiment. So, the performances obtained allow us to foresee how magnetic properties of the particles depend on their structures.

## **3. Structure, stability and magnetic properties of Com (m=6, 8, 10,12, 14) nanoparticles**

#### **3.1 Structure and stability**

Let us remember that magnetic properties of the materials are related with an electronic structure. The electronic structure is mostly geometrical-structure-depended. On the other, hand when the geometrical structure of a compound is know, it is possible to predict some properties of the compound. Thus, the first step to understand the nature of the magnetizability of the Co nanoparticles and why this property is shape- and size-depended is to investigate the geometrical structure.

Let us remember that, there is an infinite number of possible surfaces which can be exposed for every crystal system. In practice, only a limited number of planes are found to exist in any significant amount. Thus, the attention was concentrated on the above surfaces, because it is possible to predict the ideal atomic arrangement for a given surface of a particular metal by considering how the bulk structure is intersected by the surface. It is necessary to remember that investigated nanoparticles consist of a small number of atoms, thus, it is not possible to obtain a very strict crystalline structure; the crystalline structure that is expected to be in the investigated Co nanoparticles was obtained on the basis of the symmetry of a bond and atom location in the planes.

Fig. 1. Co6 nanoparticle located in the cubic cell.

470 Smart Nanoparticles Technology

When *ξ* < 0, the induced magnetic moment is opposite to the applied field, i.e. the investigated materials are diamagnetic; while for paramagnetic materials the magnetizability is larger than zero (ξ > 0) in this case the induced magnetic moment enforces the magnetic field. Experimentally, magnetizability is often poorly determined or it is only known in the liquid or solid state, thus it is difficult comparisons between calculated and experimental results, while rotational g-tensors are known as precisely determined. However, a rotational g-tensor behaves in the same manner as magnetizability, with a near

cancellation of large nuclear and electronic contributions in a large system.

<sup>1</sup> 4m

the particles depend on their structures.

is to investigate the geometrical structure.

**nanoparticles** 

**3.1 Structure and stability** 

A calculation of rotational g tensors is closely related to that of magnetizabilities via:

magnetic properties of the investigated particles and to explain the results obtained.

**3. Structure, stability and magnetic properties of Com (m=6, 8, 10,12, 14)** 

Let us remember that magnetic properties of the materials are related with an electronic structure. The electronic structure is mostly geometrical-structure-depended. On the other, hand when the geometrical structure of a compound is know, it is possible to predict some properties of the compound. Thus, the first step to understand the nature of the magnetizability of the Co nanoparticles and why this property is shape- and size-depended

The isotropic magnetizability of the most stable clusters was calculated by adopting quantum mechanical response theory and London atomic orbital to ensure both gaugeorigin independent results and fast basis set convergence by using Dalton program. The approach used allows us to calculate accurate magnetizability even for quite large molecules at a moderate cost of computing time. In this case, the B3LYP method with Ahlrichs-pVDZ basis set was used. These basis sets were obtained by optimizing the exponents and contraction coefficients in the ground state ROHF calculations. There are total 241 contracted functions in the basis mentioned. It is showed, that the isotropic magnezitability and its anisotropy are remarkably constant with respect to the basis set and close to the experiment. So, the performances obtained allow us to foresee how magnetic properties of

1 1

2μ *LAO dia <sup>T</sup> <sup>T</sup> p cm nuc k K K K K nuc N g = ξ ξ I + Z RRI RR I*

where mp is the proton mass, *LAO ξ* is the magnetizability tensor calculated with London orbitals, *dia <sup>ξ</sup>cm* is the diamagnetic contribution to the magnetizability tensor calculated with conventional orbitals and the gauge origin at the centre of mass, and the sum of all nuclei with charges ZK and positions RK, while Inuc is the moment-of-inertia tensor. Although not explored in a large number of studies, obtained theoretical results fit experimental. Hence, the above close relationship allows us to expect that our methods chosen that are well suited to the calculation of rotational g tensors should also be well suited to the calculations of magnetizabilities. Moreover, this simple enough method is suitable to describe general

3

It is necessary to mention that the structure of the Co4 particle was found, too. The results obtained indicate that Co4 is planar and a nice equilateral is formed. In the case of Co6 nanoparticle, we have the three-dimensional structure with a slightly disordered cubic symmetry. The structure was obtained after global optimization of the D4h isomer of a Co6 particle. It is important that each atom of the Co6 nanoparticle is possible to approximately be located in the centre of the plane of the cubic cell (Fig. 1). The three surfaces are obtained. So, this nanoparticle is the element of a FCC structure.

It is possible to see two planes of the Co8 nanoparticle (Fig. 2). The location of atoms on these planes as well as the symmetry of bonds allows us to predict that the element of FCC structure has been formed, too. This assumption is supported by following: i) each Co atom is four-fold coordinated; ii) the structural element of the Co6 particle is obtained (see the structure that form atoms 5, 6, 7, 8 or 1, 2, 3, 4 in Fig. 2). So, the element of FCC structure has also been obtained in the Co8 nanoparticle. The conformation of Co8 nanoparticle has proved to be the most stable.

One of more interesting situations arises in case of Co10 nanoparticle. In this case, we have the two-dimensional disordered symmetry structure consisting of two planes and two atoms in the middle of each plane (Fig.3). The atoms mentioned join these planes. Roughly speaking, the structure of the Co10 nanoparticle is formed when the planes of the Co8 nanoparticle are rotated in respect of each other when two Co atoms are added and a nice cubic structure is formed. This has also been confirmed by bond order investigations. On the

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 473

Let us describe the structure of this Co16 particle on the basis of the Co14 particle. Firstly, it is necessary to mention that the additional atoms are joined with three-fold coordinated atoms placed above the centre of the cube face. The joining leads to the deformation of the cube because the above atoms of the Co14 particle are pushed to the centre of the cube face. On the other hand, several structures of the Co6 particle are possible to be seen. Hence, in this case, the deformed FCC structure also takes place, but the BCC structure element tends to disappear in the inner part of the particles although the exterior part the element remains unchanged. So, the tendency to form FCC is possible to predict. It allows us to speculate, that in large particles (particles with the diameter more than 10 Å) the main structure could

When considering the electronic properties of the above Con particles, a singlet state is a ground one. The triplet state of these particles lies higher in total energy. These results disagree with the results presented by H.J. Fan and et al. It is necessary to mention that in the paper of H.J. Fan and et al. only high spin multiplicity particles were investigated applying Amsterdam density functional method with STO basis set with no report on how the geometry of the most stable compound was obtained. The calculated binding energies (per atom) of the Co nanoparticles, as a function of the number of these atoms in the particle, indicate that the Co14 particle with the primitive cell of FCC structure is one of the most stable species among those presented in this section (Table 1). We also received, that Co6 and Co12 particles are more stable among the investigated by us particles that consist of less than 12 atoms and this result coincides with that presented by Q. M. Ma and et al. very

**Number of atom Binding energy per atom, eV HOMO-LUMO gap, eV**  6 0.45 1.47 8 0.20 1.32 10 0.36 1.18 12 0.48 1.53 14 0.69 1.64 16 0.78 1.24 Table 1. The dependence of calculated binding energy per atom and HOMO-LUMO gap on

Hence, the main important observations on the geometrical structure of the pure Co

The Co8, Co10, Co12 , Co14, Co16 particles consist of Co6 , thus this particle can be regarded

 The face centered cubic structure which is slightly less close packed occurred in the Co14 nanoparticle, while the other particles described are the elements of the FCC structure. When increasing the number of Co atoms in the particle, the atoms that are above the centre of the cube face are pushed both to the cube face centre and the inner part of the particle. Hence, in the inner part of the particle there is a FCC structure while the BCC structure element is obtained in the exterior part the particle. Thus, the obtained results allow us to speculate that in a large cobalt nanoparticle the FCC structure should be

be FCC, while in the external part the BCC structure could be present.

The above results confirm the investigation of HOMO-LUMO gap.

to as the key element of the large Co nanoparticles.

well.

the atom number in the particle.

nanoparticle are the following:

other hand, each Co atom is four-fold-coordinated and a structural element of the Co6 particle could also be foreseen. In case of Co12 and Co14 particles there are three planes where the location of atoms is as in the FCC structure: the atoms lie on the corners of the cube with additional atoms in the center of each of four cube of faces. The structure of Co6 particle is also obtained. The element of BCC structure is also present because some atoms are out of the cube face. The most important for us is that the structure of a Co6 particle was also obtained.

Fig. 2. The view of two planes of Co8 particle from two different sides take places. T

Fig. 3. The views of two formed by atoms 4,5,8,9 and 1,2, 7, 10 planes where atoms 3 and 6 is between the planes in Co10 particle.

other hand, each Co atom is four-fold-coordinated and a structural element of the Co6 particle could also be foreseen. In case of Co12 and Co14 particles there are three planes where the location of atoms is as in the FCC structure: the atoms lie on the corners of the cube with additional atoms in the center of each of four cube of faces. The structure of Co6 particle is also obtained. The element of BCC structure is also present because some atoms are out of the cube face. The most important for us is that the structure of a Co6 particle was

Fig. 2. The view of two planes of Co8 particle from two different sides take places. T

Fig. 3. The views of two formed by atoms 4,5,8,9 and 1,2, 7, 10 planes where atoms 3 and 6 is

between the planes in Co10 particle.

also obtained.

Let us describe the structure of this Co16 particle on the basis of the Co14 particle. Firstly, it is necessary to mention that the additional atoms are joined with three-fold coordinated atoms placed above the centre of the cube face. The joining leads to the deformation of the cube because the above atoms of the Co14 particle are pushed to the centre of the cube face. On the other hand, several structures of the Co6 particle are possible to be seen. Hence, in this case, the deformed FCC structure also takes place, but the BCC structure element tends to disappear in the inner part of the particles although the exterior part the element remains unchanged. So, the tendency to form FCC is possible to predict. It allows us to speculate, that in large particles (particles with the diameter more than 10 Å) the main structure could be FCC, while in the external part the BCC structure could be present.

When considering the electronic properties of the above Con particles, a singlet state is a ground one. The triplet state of these particles lies higher in total energy. These results disagree with the results presented by H.J. Fan and et al. It is necessary to mention that in the paper of H.J. Fan and et al. only high spin multiplicity particles were investigated applying Amsterdam density functional method with STO basis set with no report on how the geometry of the most stable compound was obtained. The calculated binding energies (per atom) of the Co nanoparticles, as a function of the number of these atoms in the particle, indicate that the Co14 particle with the primitive cell of FCC structure is one of the most stable species among those presented in this section (Table 1). We also received, that Co6 and Co12 particles are more stable among the investigated by us particles that consist of less than 12 atoms and this result coincides with that presented by Q. M. Ma and et al. very well.


Table 1. The dependence of calculated binding energy per atom and HOMO-LUMO gap on the atom number in the particle.

The above results confirm the investigation of HOMO-LUMO gap.

Hence, the main important observations on the geometrical structure of the pure Co nanoparticle are the following:


View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 475

both the increase of the number of oxygen atoms in the compound and the changeability of the oxidation state of the Co atoms led to the increase of the Co–Co bond length and weakening of the Co–Co bonds. The weakening of these bonds is important for the magnetic properties of these compounds. The results obtained indicate that the displacement of the two electrons on dz2 orbitals of Co atoms creates Co–Co bonds. The energy of these orbitals is similar to that of other ones. Thus, the repulsion between the electrons on the dz2 orbitals is larger than in other cases investigated, therefore these electrons tend to be as far as possible from each other and the correlation between them is weakened, resulting in the

Let us remember that in the Co derivatives the number of bonding molecular orbitals that may be occupied is insufficient to locate all electrons of the system. As example, in Co6 compounds all bonding orbitals are occupied and, as it has already been mentioned, some electrons are displaced on the anti-bonding orbitals, the energy of which is higher than that

It should be mentioned that the increased number of Co atoms in the compound leads to weakening of Co-Co bonds what, as we think, is important for the magnetic properties of these compounds, because magnetic properties depend on the bonds' nature and the number of bonds as well as on the charge distribution. Thus, aiming to explain the magnetic properties of the investigated particles, the attention is paid to the bonds' nature (what orbitals consist of bonds), the dipole moment and its components as well as on the isotropic

In Table 3 the data on magnetizability, dipole moment, isotropic g tensor and the number of bonds consisting of anti-bonding orbitals are presented. The analysis of the most important orbitals (HOMO) of the described particles has been performed (Figs. 4-9). Fig.6 represents a full view of the HOMO of the Co6 particle and the additional schematic presentation of the

> Dipole moment, a.u.

Number of bonds consist of anti-bonding character

bond places in the particle is given to better illustrate the results presented.

Co6 58.77 -0.513 0.097 5 Co8 25.79 -0.289 0.468 3 Co10 -26.13 -0.071 0.084 5 Co12 -35.11 -0.038 0.213 20 Co14 -39.27 -0.046 0.157 8 Co16 69.84 -0.163 0.331 3

Table 3. The data on magnetizability, dipole moment, g tensor and the number of bonds

Firstly, it is necessary to mention, that in the g-tensor of a molecule, there is a nuclear contribution and an electronic sum-over-states contribution. The electronic contribution represents an isotropic g-tensor. Here, it should be mentioned, that an isotropic g-tensor along with magnetizability is calculated to recognize what contributions (nuclear or electronic) are more important for the magnetic properties of the particle investigated.

Isotropic g-tensor

elongation of Co–Co bonds and, as a consequence, presence of an unpaired spin.

of the bonding orbitals.

Compound Magnetizability,

consisting of anti-bonding orbitals.

a.u.

g-tensor which depends on a spin angular moment.

clearly seen, while in a smaller one the FCC structure with the element of BCC structure should be obtained.

It is necessary to mention that the bond length and the bond order were also investigated. The obtained results are summarized in Table 2.


Table 2. The bond lengths obtained in the investigated particles

It is emphasized, that EXAFS MFT provides a Co-Co inter-atomic distance in the nanoparticle as equal to 2.561±0.015 Å. The comparison of the theoretical investigation of the Co particles with the corresponding experimental data is rather complicated quantitatively. The use of a restricted basis set of Co which can limit the quantitative analysis in the theoretical calculations should be taken into account. Hence, the obtained bond length fits well enough into the above-mentioned results. That obtained structures of the Co nanoparticle are to be mentioned as not fully spherical. The results obtained fit the results of the high magnification TEM image perfectly. In any case it is possible to see that double bonds are ruptured when the number of Co atoms is increased while coordinate bonds remain. The Co-Co bond elongation within the increasing atom number in the particles is not possible to explicitly be exhibited, while the presence of the coordinated bond allow us to foresee that the total electron density in this Co–Co bond is smaller than that in the other bonds what leads to non-compensation of the electron spins. On the other hand, the results exhibit that investigated Co nanoparticles are not homogeneous systems, i.e. the systems consist of different-fold-coordinated atoms. The obtained results indicate that a Co atom is three-to-seven-fold coordinated in the most stable nanoparticles. The presence of a coordinated bond, that is a kind of 2-centre, 2-electron covalent bond in which the two electrons derive from the same atom, prove the above results, too. Additionally performed analysis of the molecular orbital nature indicates that in the Co derivatives the number of bonding molecular orbitals, that may be occupied, is insufficient to locate all electrons of the system. It implies that some electrons are displaced on the anti-bonding orbitals, the energy of which is higher than that of the bonding orbitals. This electronic non-uniformity (a different oxidation state of an atom in the particle) of Co atoms, as we will prove below, and the electron displacement on the anti-bonding orbitals are important for the magnetic properties of the Co nanoparticles consisting of the even number of atoms.

#### **3.1.1 Magnetic properties of the pure Co nanoparticles**

Aiming to explain the results on magnetic properties of the particles investigated as well as particle dependence on the size, we paid our attention to the nature of molecular orbitals and their placements, because the studies on the Co2Om (m=0-7) compound indicate that

It is necessary to mention that the bond length and the bond order were also investigated.

6 2.2 2.0 2.3 8 2.1 - 2.2 2.0 2.3 10 2.1 - 2.2 2.4 12 2.27 2.3 14 2.15- 2.27 2.3 16 2.15- 2.27 2.3

It is emphasized, that EXAFS MFT provides a Co-Co inter-atomic distance in the nanoparticle as equal to 2.561±0.015 Å. The comparison of the theoretical investigation of the Co particles with the corresponding experimental data is rather complicated quantitatively. The use of a restricted basis set of Co which can limit the quantitative analysis in the theoretical calculations should be taken into account. Hence, the obtained bond length fits well enough into the above-mentioned results. That obtained structures of the Co nanoparticle are to be mentioned as not fully spherical. The results obtained fit the results of the high magnification TEM image perfectly. In any case it is possible to see that double bonds are ruptured when the number of Co atoms is increased while coordinate bonds remain. The Co-Co bond elongation within the increasing atom number in the particles is not possible to explicitly be exhibited, while the presence of the coordinated bond allow us to foresee that the total electron density in this Co–Co bond is smaller than that in the other bonds what leads to non-compensation of the electron spins. On the other hand, the results exhibit that investigated Co nanoparticles are not homogeneous systems, i.e. the systems consist of different-fold-coordinated atoms. The obtained results indicate that a Co atom is three-to-seven-fold coordinated in the most stable nanoparticles. The presence of a coordinated bond, that is a kind of 2-centre, 2-electron covalent bond in which the two electrons derive from the same atom, prove the above results, too. Additionally performed analysis of the molecular orbital nature indicates that in the Co derivatives the number of bonding molecular orbitals, that may be occupied, is insufficient to locate all electrons of the system. It implies that some electrons are displaced on the anti-bonding orbitals, the energy of which is higher than that of the bonding orbitals. This electronic non-uniformity (a different oxidation state of an atom in the particle) of Co atoms, as we will prove below, and the electron displacement on the anti-bonding orbitals are important for the magnetic

should be obtained.

Atom number in a particle

The obtained results are summarized in Table 2.

Single bond length, Å

Table 2. The bond lengths obtained in the investigated particles

properties of the Co nanoparticles consisting of the even number of atoms.

Aiming to explain the results on magnetic properties of the particles investigated as well as particle dependence on the size, we paid our attention to the nature of molecular orbitals and their placements, because the studies on the Co2Om (m=0-7) compound indicate that

**3.1.1 Magnetic properties of the pure Co nanoparticles** 

clearly seen, while in a smaller one the FCC structure with the element of BCC structure

Double bond length, Å

Coordinated bond length

both the increase of the number of oxygen atoms in the compound and the changeability of the oxidation state of the Co atoms led to the increase of the Co–Co bond length and weakening of the Co–Co bonds. The weakening of these bonds is important for the magnetic properties of these compounds. The results obtained indicate that the displacement of the two electrons on dz2 orbitals of Co atoms creates Co–Co bonds. The energy of these orbitals is similar to that of other ones. Thus, the repulsion between the electrons on the dz2 orbitals is larger than in other cases investigated, therefore these electrons tend to be as far as possible from each other and the correlation between them is weakened, resulting in the elongation of Co–Co bonds and, as a consequence, presence of an unpaired spin.

Let us remember that in the Co derivatives the number of bonding molecular orbitals that may be occupied is insufficient to locate all electrons of the system. As example, in Co6 compounds all bonding orbitals are occupied and, as it has already been mentioned, some electrons are displaced on the anti-bonding orbitals, the energy of which is higher than that of the bonding orbitals.

It should be mentioned that the increased number of Co atoms in the compound leads to weakening of Co-Co bonds what, as we think, is important for the magnetic properties of these compounds, because magnetic properties depend on the bonds' nature and the number of bonds as well as on the charge distribution. Thus, aiming to explain the magnetic properties of the investigated particles, the attention is paid to the bonds' nature (what orbitals consist of bonds), the dipole moment and its components as well as on the isotropic g-tensor which depends on a spin angular moment.

In Table 3 the data on magnetizability, dipole moment, isotropic g tensor and the number of bonds consisting of anti-bonding orbitals are presented. The analysis of the most important orbitals (HOMO) of the described particles has been performed (Figs. 4-9). Fig.6 represents a full view of the HOMO of the Co6 particle and the additional schematic presentation of the bond places in the particle is given to better illustrate the results presented.


Table 3. The data on magnetizability, dipole moment, g tensor and the number of bonds consisting of anti-bonding orbitals.

Firstly, it is necessary to mention, that in the g-tensor of a molecule, there is a nuclear contribution and an electronic sum-over-states contribution. The electronic contribution represents an isotropic g-tensor. Here, it should be mentioned, that an isotropic g-tensor along with magnetizability is calculated to recognize what contributions (nuclear or electronic) are more important for the magnetic properties of the particle investigated.

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 477

Fig. 6. The views of Co6 particle (on the left) and their most important orbital (HOMO) (in the centre). The same view (on the right) is given when the bonds form of anti-bonding

Fig. 7. the views of Co8 particle (on the left) and the same view are given when the bonds

Hence, it is possible to see that Co12 and Co14 are diamagnetic because in these particles there are 18 and 4 respectively symmetrically placed bonds with weakly interacting electrons what leads to the disappearance of non-compensate spins. These non-compensated spins quench each other what indicates the isotropic g-tensor value being equal to 0.038 and 0.046 in comparison to the value 2.00 for a free electron and indicates the absence of free

orbitals are marked by dash lines for simple guidance.

consisting of anti-bonding orbitals are marked by dash lines.

electrons or a non-compensate spin.

It is possible to see that only Co6, Co8 and Co16 particles exhibit paramagnetic properties although the bonds that are of anti-bonding character are present in all the particles investigated. The different number of bonds formed of anti-bonding orbitals is present in the Co6, Co8 and Co16 particles. The view of the particles and location of the above bonds are presented in Figs. 4-9. The conclusion on the character of bonds was made on the basis of the analysis of the most important atomic orbitals on atoms, bond lengths, bond order and views of the orbitals.

Fig. 4. The views of Co12 particle on the left and the view (on the right) when the bonds form of anti-bonding orbitals are marked by dash lines.

Fig. 5. The view of Co14 particle on the left and the view (on the right) when the bonds form of anti-bonding orbitals are marked by dash lines.

It is possible to see that only Co6, Co8 and Co16 particles exhibit paramagnetic properties although the bonds that are of anti-bonding character are present in all the particles investigated. The different number of bonds formed of anti-bonding orbitals is present in the Co6, Co8 and Co16 particles. The view of the particles and location of the above bonds are presented in Figs. 4-9. The conclusion on the character of bonds was made on the basis of the analysis of the most important atomic orbitals on atoms, bond lengths, bond order and

Fig. 4. The views of Co12 particle on the left and the view (on the right) when the bonds form

Fig. 5. The view of Co14 particle on the left and the view (on the right) when the bonds form

of anti-bonding orbitals are marked by dash lines.

of anti-bonding orbitals are marked by dash lines.

views of the orbitals.

Fig. 6. The views of Co6 particle (on the left) and their most important orbital (HOMO) (in the centre). The same view (on the right) is given when the bonds form of anti-bonding orbitals are marked by dash lines for simple guidance.

Fig. 7. the views of Co8 particle (on the left) and the same view are given when the bonds consisting of anti-bonding orbitals are marked by dash lines.

Hence, it is possible to see that Co12 and Co14 are diamagnetic because in these particles there are 18 and 4 respectively symmetrically placed bonds with weakly interacting electrons what leads to the disappearance of non-compensate spins. These non-compensated spins quench each other what indicates the isotropic g-tensor value being equal to 0.038 and 0.046 in comparison to the value 2.00 for a free electron and indicates the absence of free electrons or a non-compensate spin.

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 479

The magnetizability and g-tensor of the Co6 particle are approximately twice larger than those of the Co8 particle. In the Co6 particle the number of bonds of anti-bonding character is five and these bonds are non-parallel. The dipole moment of the particle is approximately zero. It allows us to conclude that this particle is paramagnetic due to the electronic contribution, i.e. the repulsion between the electrons located on the anti-bonding orbital is large, therefore, they tend to be as far as possible from each other and become non-strongly correlated. Thus the spins of the electrons are not compensated, while the unparalleled displacement of the bonds leads to that that spins of all non-strongly-correlated-electrons are not compensated. It implies, that magnetic properties of the Co6 particle are related with

A similar situation is obtained in case of Co8 particle. Approximately twice smaller magnetizability of this particle than that of Co6 is present because in the particle the number

The largest magnetizability is the Co16 particle, although, its isotropic g-tensor is approximately twice smaller than that of Co6 particle. To explain the above mentioned contradictions, we investigated a dipole moment of these particles. The dipole moment indicates electron concentration places in a particle. On the other hand, the components of these dipole moments allow us to foresee the distribution of the above places. Both the concentration of electrons and their distribution helps us to find the appearance of the additional spins due to the different oxidation states of the Co atoms, i.e. if the even number of atoms loose the odd number of electrons and the particle possesses a dipole moment, we may suspect the presence of the localization of electrons and non-compensation of their

The dipole moment components of the particles are presented in Table 4 and indicate the electron charge delocalization in the Co8 and Co16 particles, while in case of the Co10 and Co12 particles, the charge localization occurs (see the component of dipole moment). It is necessary to add, that in Co8 and Co12 cases, the oxidation states of Co atoms are even. It allows us to predict, that electron spins occurring when the atoms loose an electron are

In case of Co16 particle, the dipole moment components indicate charge delocalization, while the isotropic g- tensor value is smaller than that of Co6 and Co8. It allows us to conclude that the magnetic properties of this particle are mostly related with nuclear contribution. However, it is not explicitly possible to recognize the folding of atoms such as 3.49 or 3.51 on the results of these calculations. Thus, it is only speculation based on the comparison of the magnetizability of the investigated results that, in case of Co16 particle, the ion spins and

The Co6, Co8 and Co16 particles are paramagnetic, while Co10, that possesses the odd number of anti-bonding character bonds as the particles mentioned, indicates diamagnetic properties. In case of Co10 particle, the oxidation state of the Co1 atom is +5 (Fig. 8). The four bonds with anti-bonding character are displaced like in case of Co6, however, one bond is in the same direction of the largest component of the dipole moment. Thus, it is possible to suspect, that in this case a weakly interacting electron spin is quenched by the ion spin. It may be concluded that paramagnetic behaviour is dominating when the uncompensated

of non-strongly- correlated electrons is smaller than that in Co6.

spins. We named the above spin an ion one to simplify the discussion.

an electronic contribution.

compensated.

electron spins are not compensated.

 In case of Co12, the oxidation state of Co atoms is even. So, a non-compensate spin can not appear because the atoms of this particle loose the even number of electrons (below, it is exhibited that the oxidation state of atoms is also important to the explanation of Co particle magnetic properties).

The electronic properties of the Co14 particle fit described properties of the bond nature and oxidation state of the atoms very well. In the case the even number of bonds that are of antibonding character is found. Hence, electron spins are compensated and this particle exhibits diamagnetic properties. Additionally, even number (four) of atoms with oxidation state +3 are present

In case of Co6, Co8, Co10, Co16 there are non - symmetrically placed bonds with weakly interacting electrons. Thus, we may suspect that these particles could be paramagnetic.

Fig. 8. The views of Co10 particle (on the left) and the view (on the right) when the bonds form of anti-bonding orbitals are marked by dash lines.

Fig. 9. The views of Co16 particle (on the left) and the view (on the right) when the bonds form of anti-bonding orbitals are marked by dash lines.

 In case of Co12, the oxidation state of Co atoms is even. So, a non-compensate spin can not appear because the atoms of this particle loose the even number of electrons (below, it is exhibited that the oxidation state of atoms is also important to the explanation of Co particle

The electronic properties of the Co14 particle fit described properties of the bond nature and oxidation state of the atoms very well. In the case the even number of bonds that are of antibonding character is found. Hence, electron spins are compensated and this particle exhibits diamagnetic properties. Additionally, even number (four) of atoms with oxidation state +3

In case of Co6, Co8, Co10, Co16 there are non - symmetrically placed bonds with weakly interacting electrons. Thus, we may suspect that these particles could be paramagnetic.

Fig. 8. The views of Co10 particle (on the left) and the view (on the right) when the bonds

Fig. 9. The views of Co16 particle (on the left) and the view (on the right) when the bonds

form of anti-bonding orbitals are marked by dash lines.

form of anti-bonding orbitals are marked by dash lines.

magnetic properties).

are present

The magnetizability and g-tensor of the Co6 particle are approximately twice larger than those of the Co8 particle. In the Co6 particle the number of bonds of anti-bonding character is five and these bonds are non-parallel. The dipole moment of the particle is approximately zero. It allows us to conclude that this particle is paramagnetic due to the electronic contribution, i.e. the repulsion between the electrons located on the anti-bonding orbital is large, therefore, they tend to be as far as possible from each other and become non-strongly correlated. Thus the spins of the electrons are not compensated, while the unparalleled displacement of the bonds leads to that that spins of all non-strongly-correlated-electrons are not compensated. It implies, that magnetic properties of the Co6 particle are related with an electronic contribution.

A similar situation is obtained in case of Co8 particle. Approximately twice smaller magnetizability of this particle than that of Co6 is present because in the particle the number of non-strongly- correlated electrons is smaller than that in Co6.

The largest magnetizability is the Co16 particle, although, its isotropic g-tensor is approximately twice smaller than that of Co6 particle. To explain the above mentioned contradictions, we investigated a dipole moment of these particles. The dipole moment indicates electron concentration places in a particle. On the other hand, the components of these dipole moments allow us to foresee the distribution of the above places. Both the concentration of electrons and their distribution helps us to find the appearance of the additional spins due to the different oxidation states of the Co atoms, i.e. if the even number of atoms loose the odd number of electrons and the particle possesses a dipole moment, we may suspect the presence of the localization of electrons and non-compensation of their spins. We named the above spin an ion one to simplify the discussion.

The dipole moment components of the particles are presented in Table 4 and indicate the electron charge delocalization in the Co8 and Co16 particles, while in case of the Co10 and Co12 particles, the charge localization occurs (see the component of dipole moment). It is necessary to add, that in Co8 and Co12 cases, the oxidation states of Co atoms are even. It allows us to predict, that electron spins occurring when the atoms loose an electron are compensated.

In case of Co16 particle, the dipole moment components indicate charge delocalization, while the isotropic g- tensor value is smaller than that of Co6 and Co8. It allows us to conclude that the magnetic properties of this particle are mostly related with nuclear contribution. However, it is not explicitly possible to recognize the folding of atoms such as 3.49 or 3.51 on the results of these calculations. Thus, it is only speculation based on the comparison of the magnetizability of the investigated results that, in case of Co16 particle, the ion spins and electron spins are not compensated.

The Co6, Co8 and Co16 particles are paramagnetic, while Co10, that possesses the odd number of anti-bonding character bonds as the particles mentioned, indicates diamagnetic properties. In case of Co10 particle, the oxidation state of the Co1 atom is +5 (Fig. 8). The four bonds with anti-bonding character are displaced like in case of Co6, however, one bond is in the same direction of the largest component of the dipole moment. Thus, it is possible to suspect, that in this case a weakly interacting electron spin is quenched by the ion spin. It may be concluded that paramagnetic behaviour is dominating when the uncompensated

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 481

Firstly, it is necessary to mention that oxygen stabilizes the Co nanoparticle and the increasing number of oxygen atoms increases the binding energy per atom up to n=7 (Table 5). Furthermore,when a certain limit is reached, oxygen atoms do not influence the stability

The Co6O12 particle was investigated too. The binding energy per atom of this particle is equal to 3.26 eV what is similar to that of Co6On (n=7, 8, 9). The difference of the binding energy of the above particles is too small (0.2 eV or less) to make the conclusion on the most

Fig. 10. Views of the particles investigated. Grey lines do not indicate real chemical bonds,

but are implemented for the sake simple guidance.

The most stable structures of the Co6On derivatives are presented in Fig.10.

of the Co6On particles.

stable particle.


spin is present due to the presence of a weakly interacting electron on the anti-bonding orbital and this spin is not quenched by the ion spins.

Table 4. Dipole moments and their components of the investigated particles that are paramagnetic or weakly diamagnetic.

It is possible to see that the investigated systems are very flexible and it is possible to predict that any dipole interaction or Co particle agglomeration could change their magnetic properties. To confirm the above prediction, the magnetic properties of the Co6 and Co6 as well as those of Co6 and Co12 derivatives have also been investigated.

The structure of Co6 and Co6 particles was found after global optimization. The results obtained indicate possible agglomeration of these particles, i.e. the Co12 particle should formed. The magnetizability of this compound is -12.55 a.u., what indicates diamagnetic properties.

In case of the Co6 and Co12 compound, we did not perform any geometry optimization to avoid agglomeration of particles because the changes of geometrical structure lead to dramatical changes of the electronic structure and consequential changes of magnetic properties. The investigated particles were placed randomly. Indeed, a compound consisting of Co12 and Co6 particles is paramagnetic and its magnetizability is equal to 24.65 a.u. The results clearly indicate that dipole interaction and particle agglomeration change magnetic properties of the Co nanoparticle.

## **4. Structure, stability and magnetic properties of Co6 Om nanoparticles**

## **4.1 Structure and stability of Co6Om Particles**

As exhibited above, the stability of small Co nanoparticles is not very high. On the basis of our previous investigations it was speculated that those nanoparticles were non-rigid structures. It implies that the geometrical structure of these particles could change very quickly due to the tunnelling effect. Let us remember that Co6 particle is found as the most stable one and it is the key element of other particles investigated. So, Co6On (n=0-9) derivatives were also investigated to establish how the magnetic properties of the Co particles may change due to oxidation. On the other hand, these investigations allow us to foresee the conditions under which the metal Co-Co bond is broken. It is also proved our prediction that the particles consisting of the even number of atoms possess magnetic properties due to the weakly interacting electrons on the anti-bonding orbital and this spin is not quenched by additional spins that occurred because some atoms of the nanoparticle loose the odd number of electrons.

The most stable structures of the Co6On derivatives are presented in Fig.10.

480 Smart Nanoparticles Technology

spin is present due to the presence of a weakly interacting electron on the anti-bonding

 **x y z**  Co6 0.097 -0.09 -0.01 -0.01 Co8 0.468 0.147 0.298 0.329 Co10 0.084 0.076 0.031 0.021 Co12 0.213 0.198 -0.051 -0.061 Co14 0.157 -0.077 0.094 -0.098 Co16 0.331 -0.107 0.167 -0.264

It is possible to see that the investigated systems are very flexible and it is possible to predict that any dipole interaction or Co particle agglomeration could change their magnetic properties. To confirm the above prediction, the magnetic properties of the Co6 and Co6 as

The structure of Co6 and Co6 particles was found after global optimization. The results obtained indicate possible agglomeration of these particles, i.e. the Co12 particle should formed. The magnetizability of this compound is -12.55 a.u., what indicates diamagnetic properties.

In case of the Co6 and Co12 compound, we did not perform any geometry optimization to avoid agglomeration of particles because the changes of geometrical structure lead to dramatical changes of the electronic structure and consequential changes of magnetic properties. The investigated particles were placed randomly. Indeed, a compound consisting of Co12 and Co6 particles is paramagnetic and its magnetizability is equal to 24.65 a.u. The results clearly indicate that dipole interaction and particle agglomeration change

**4. Structure, stability and magnetic properties of Co6 Om nanoparticles** 

As exhibited above, the stability of small Co nanoparticles is not very high. On the basis of our previous investigations it was speculated that those nanoparticles were non-rigid structures. It implies that the geometrical structure of these particles could change very quickly due to the tunnelling effect. Let us remember that Co6 particle is found as the most stable one and it is the key element of other particles investigated. So, Co6On (n=0-9) derivatives were also investigated to establish how the magnetic properties of the Co particles may change due to oxidation. On the other hand, these investigations allow us to foresee the conditions under which the metal Co-Co bond is broken. It is also proved our prediction that the particles consisting of the even number of atoms possess magnetic properties due to the weakly interacting electrons on the anti-bonding orbital and this spin is not quenched by additional spins that occurred because some atoms of the nanoparticle

Table 4. Dipole moments and their components of the investigated particles that are

well as those of Co6 and Co12 derivatives have also been investigated.

**Dipole moment components, a.u.** 

orbital and this spin is not quenched by the ion spins.

**a.u.** 

**Compounds Dipole moment,** 

paramagnetic or weakly diamagnetic.

magnetic properties of the Co nanoparticle.

**4.1 Structure and stability of Co6Om Particles** 

loose the odd number of electrons.

Firstly, it is necessary to mention that oxygen stabilizes the Co nanoparticle and the increasing number of oxygen atoms increases the binding energy per atom up to n=7 (Table 5). Furthermore,when a certain limit is reached, oxygen atoms do not influence the stability of the Co6On particles.

The Co6O12 particle was investigated too. The binding energy per atom of this particle is equal to 3.26 eV what is similar to that of Co6On (n=7, 8, 9). The difference of the binding energy of the above particles is too small (0.2 eV or less) to make the conclusion on the most stable particle.

Fig. 10. Views of the particles investigated. Grey lines do not indicate real chemical bonds, but are implemented for the sake simple guidance.

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 483

that the most stable structure of Co6O8 (prototype of Co3O4) has a deformed spinel structure. Thus, it is not surprising that a large effective magnetic moment estimated from the inverse

Co6 2.15 2.33 2.15 2.24 2.04 2.23 2.04 2.31 2.33

Co6O5 2.25 2.61 2.25 2.39 Co6O6 2.83 2.67 2.89 2.32 2.87 2.44

Co6O7 2.92 2.93 3.21 2.21\* 3.07 3.11 2.92 2.91 2.22\* Co6O8 2.88 2.90 3.21 2.24\* 3.18 3.16 3.03 3.03 2.93 Co6O9 3.04 3.04 3.15 3.04 3.14 3.15 3.04 3.05 3.05

According to the results of our investigations, the Co-Co bond length of the single bond is longer (2.2 Å) than the bond length of a double bond (2.0 Å) in a Co6 particle. On the other hand, three bonds were obtained where the length is equal to 2.3 Å. The bond order of the largest bond is twice smaller than that of a single bond. Here, we the commonly observed that the Co-Co bond lengths are marginally changed only between the atoms that are connected with the oxygen atom (Table 6) and, as a consequence, the bond enlargement leads to Co-Co bond dissolving. For example: in the Co6 particle the bond order between Co1-Co5 is equal to 1.018, while that in Co6O4 is approximately twice smaller and equals to 0.55. Additionally, the two, one and zero Co-Co bonds are respectively found in the Co6O7, Co6O8 and Co6O9 nanoparticles. To shed some light on the present observation, the analyzes of the most important orbitals of the Co6 particles have been investigated. HOMO (the highest occupied orbital)- LUMO (the lowest unoccupied orbital) gap dependence on the number of oxygen atoms is represented in Fig. 11. The HOMO-LUMO gap indicates that chemical stability of Co6 , Co6O4 and Co6O6 is very low, i.e. they tend to form new chemical

**1-2 1-3 1-4 1-6 2-3 2-6 4-5 4-6 3-4** 

**1-2 1-3 1-4 2-3 2-5 3.6 4-5 4-6 5-6** 

susceptibility has not been explained properly.

Co6O2 3.01

Co6O 2.54

\* the Co-Co bond is present.

the oxidation state of Co atoms.

**Compound Co-Co bond length, Å** 

Co6O3 2.18 2.37 2.33 2.14

Co6O4 2.27 2.27 2.27 4.72 2.27

Co6O7 2.93 3.11 2.93 2.93 2.93

Table 6. The distance between the Co atoms which are connected with the O atom.

bonds. These results coincide well with the results of binding energy per atoms.

However, the electronic structure of the investigated particles is quite different because the oxidation state of Co atoms exchanges when the number of oxygen atoms in the particle is increased. For example, in Co6O particle oxidation state of Co atoms is +3 and +4; in the Co6O2 particle the oxidation state of these atoms is +4 and +5 and in Co6O4 it is +1 and +3. We have not observed any relationship between number of oxygen atom in the particle and

Let us remember that in the Co derivatives the number of bonding molecular orbitals, that may be occupied, is insufficient to locate all the electrons of the system. This leads to the


Table 5. Binding energy per atoms for the Co6On (n=0-9) particles

The difference of the binding energy per atom for Co6 and Co6O is equal to 0.48 eV, while that between Co6O6 and Co6O7 is only 0.21 eV, i.e. twice less. On the other hand, the changing of the number of oxygen atoms from 2 to 3 leads to the largest increase of the binding energy per atom (1.01eV), while the binding energy per atom increase only up to 0.27 eV when the oxygen atom number in a particle increases from 3 to 4. Thus, the results of our investigations allow us to foresee that starting with n=6 (n is the number of oxygen atoms) the further increase of the number of oxygen atoms will not influence the stability of these particles very strongly and the main structure *(*the key-element) is not considerably changed (Fig. 10). The binding energy per atom of the Co6O6, Co6O7, Co6O8 and Co6O9 is approximately equal and proves these particles to be the most stable. These results coincide with the experimental measurements that indicate the presence of CoO and Co3O4; CoO2, Co2O3 and Co6O7 particles should also be found among them what was proved by the results we obtained.

Such a changeability of the binding energy per atom in some cases could be explained by changes in geometrical structure of Co particle. In case when the additional oxygen atom does not significantly increase the binding energy per atom, the main part of the energy of this atom is used to deform the structure of the key element (Co*6*). Thus, the binding energies per atom of Co6O3 and Co6O4 or Co6O6, and Co6O7 are approximately equal.

The key element of the Co6 is also present in the Co6On (n=0-9) derivatives. However, this key element is slightly deformed. The changeability of the initial form is oxygen atom depended. The largest deformation is obtained in Co6O7, when the distance between the planes (formed of atoms 1, 2, 3 and of 4, 5, 6) is increased and one plane is rotated in respect of the other one by angle of π/4. Actually, one more structure of the Co6O7 which looks like Co6O6 was also obtained, but the energy of this formation of the particle is 1.23 eV higher than that of the particle, the structure of which was described above.

In the Co6O4 particle the key element (Co6) is deformed twice: 1. firstly, when the distances between the atoms Co2-Co5 decrease; 2. Secondly, when Co1 and Co6 positions in respect of the plane that is formed of atoms 2,3,4,5 is changed. Here, it should be emphasized, that this structure of the particle has been obtained after global geometry optimization starting with several completely different initial geometries. Thus, the geometrical structure of the Co6O4 particle is confirmed.

Hence, the largest deformations of the Co6 particle are obtained when the number of oxygen atoms is changed from 3 to 4 and from 6 to 7. In these cases the stabilization energy per atom is smaller than in other cases investigated. Thus, the main part of Oxygen energy is used to deform the key structure of Co6.

It is necessary to mention, when the number of oxygen atom is 2 and 6, the structure of the Co6Om particle looks like the octahedron, while in case of odd numbers of oxygen the octahedron form is strongly deformed (except the results for Co6O4). It is interesting to note


Co6O8 2.88 2.90 3.21 2.24\* 3.18 3.16 3.03 3.03 2.93 Co6O9 3.04 3.04 3.15 3.04 3.14 3.15 3.04 3.05 3.05

that the most stable structure of Co6O8 (prototype of Co3O4) has a deformed spinel structure. Thus, it is not surprising that a large effective magnetic moment estimated from the inverse susceptibility has not been explained properly.

\* the Co-Co bond is present.

482 Smart Nanoparticles Technology

Binding energy

results we obtained.

particle is confirmed.

used to deform the key structure of Co6.

Particle Co6 Co6O Co6O2 Co6O3 Co6O4 Co6O5 Co6O6 Co6O7 Co6O8 Co6O9

per atom, eV 0.45 0.93 1.21 2.22 2.49 2.85 3.22 3.43 3.33 3.48

The difference of the binding energy per atom for Co6 and Co6O is equal to 0.48 eV, while that between Co6O6 and Co6O7 is only 0.21 eV, i.e. twice less. On the other hand, the changing of the number of oxygen atoms from 2 to 3 leads to the largest increase of the binding energy per atom (1.01eV), while the binding energy per atom increase only up to 0.27 eV when the oxygen atom number in a particle increases from 3 to 4. Thus, the results of our investigations allow us to foresee that starting with n=6 (n is the number of oxygen atoms) the further increase of the number of oxygen atoms will not influence the stability of these particles very strongly and the main structure *(*the key-element) is not considerably changed (Fig. 10). The binding energy per atom of the Co6O6, Co6O7, Co6O8 and Co6O9 is approximately equal and proves these particles to be the most stable. These results coincide with the experimental measurements that indicate the presence of CoO and Co3O4; CoO2, Co2O3 and Co6O7 particles should also be found among them what was proved by the

Such a changeability of the binding energy per atom in some cases could be explained by changes in geometrical structure of Co particle. In case when the additional oxygen atom does not significantly increase the binding energy per atom, the main part of the energy of this atom is used to deform the structure of the key element (Co*6*). Thus, the binding

The key element of the Co6 is also present in the Co6On (n=0-9) derivatives. However, this key element is slightly deformed. The changeability of the initial form is oxygen atom depended. The largest deformation is obtained in Co6O7, when the distance between the planes (formed of atoms 1, 2, 3 and of 4, 5, 6) is increased and one plane is rotated in respect of the other one by angle of π/4. Actually, one more structure of the Co6O7 which looks like Co6O6 was also obtained, but the energy of this formation of the particle is 1.23 eV higher

In the Co6O4 particle the key element (Co6) is deformed twice: 1. firstly, when the distances between the atoms Co2-Co5 decrease; 2. Secondly, when Co1 and Co6 positions in respect of the plane that is formed of atoms 2,3,4,5 is changed. Here, it should be emphasized, that this structure of the particle has been obtained after global geometry optimization starting with several completely different initial geometries. Thus, the geometrical structure of the Co6O4

Hence, the largest deformations of the Co6 particle are obtained when the number of oxygen atoms is changed from 3 to 4 and from 6 to 7. In these cases the stabilization energy per atom is smaller than in other cases investigated. Thus, the main part of Oxygen energy is

It is necessary to mention, when the number of oxygen atom is 2 and 6, the structure of the Co6Om particle looks like the octahedron, while in case of odd numbers of oxygen the octahedron form is strongly deformed (except the results for Co6O4). It is interesting to note

energies per atom of Co6O3 and Co6O4 or Co6O6, and Co6O7 are approximately equal.

than that of the particle, the structure of which was described above.

Table 5. Binding energy per atoms for the Co6On (n=0-9) particles

Table 6. The distance between the Co atoms which are connected with the O atom.

According to the results of our investigations, the Co-Co bond length of the single bond is longer (2.2 Å) than the bond length of a double bond (2.0 Å) in a Co6 particle. On the other hand, three bonds were obtained where the length is equal to 2.3 Å. The bond order of the largest bond is twice smaller than that of a single bond. Here, we the commonly observed that the Co-Co bond lengths are marginally changed only between the atoms that are connected with the oxygen atom (Table 6) and, as a consequence, the bond enlargement leads to Co-Co bond dissolving. For example: in the Co6 particle the bond order between Co1-Co5 is equal to 1.018, while that in Co6O4 is approximately twice smaller and equals to 0.55. Additionally, the two, one and zero Co-Co bonds are respectively found in the Co6O7, Co6O8 and Co6O9 nanoparticles. To shed some light on the present observation, the analyzes of the most important orbitals of the Co6 particles have been investigated. HOMO (the highest occupied orbital)- LUMO (the lowest unoccupied orbital) gap dependence on the number of oxygen atoms is represented in Fig. 11. The HOMO-LUMO gap indicates that chemical stability of Co6 , Co6O4 and Co6O6 is very low, i.e. they tend to form new chemical bonds. These results coincide well with the results of binding energy per atoms.

However, the electronic structure of the investigated particles is quite different because the oxidation state of Co atoms exchanges when the number of oxygen atoms in the particle is increased. For example, in Co6O particle oxidation state of Co atoms is +3 and +4; in the Co6O2 particle the oxidation state of these atoms is +4 and +5 and in Co6O4 it is +1 and +3. We have not observed any relationship between number of oxygen atom in the particle and the oxidation state of Co atoms.

Let us remember that in the Co derivatives the number of bonding molecular orbitals, that may be occupied, is insufficient to locate all the electrons of the system. This leads to the

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 485

increasing number of the oxygen atoms in the particle, the number of occupied orbital also

Oxygen atoms in the Co6O4, Co6O3, Co6O2, and Co6O particles are joined to atoms between which the anti-bonding orbitals occur. Having in mind that the joining of oxygen atoms leads to the increase of the bond length and dissolution of Co-Co bonds, what confirms the above mentioned prediction. In case of the Co6O3 particle, one O atom is joined to Co4-Co5 atoms (Fig.10). The anti-bonding nature of the bonds has not been observed between those atoms. In this case, a steric effect is more preferable because other positions of the oxygen atom should complicate Co1-Co2 and Co2-Co6 elongation or leads to the destruction of this particle. Hence, oxygen atoms stabilize Co6 particles due to dissolving of Co-Co bonds that

It is very well known, that a semiconductor must have at least two characteristics: 1. the bonding and anti-bonding orbitals must form a delocalized band; 2. the HOMO-LUMO gap in molecular species should be generally of the order of 0.5eV to 3.5 eV. HOMO-LUMO gaps of the investigated derivatives belong to the above range. However, the number of antibonding orbitals decreases with increasing of the number of oxygen atoms. The results allow us to predict that Co6Om are semiconductors but the particles should loose their

In the above chapter we proved that oxygen atoms stabilize cobalt nanoparticles, although, in some cases, the structure of particles changes insufficiently while the electronic structure is dramatically changed because the increasing number of oxygen atoms decreases the difference between the number of electrons and the number of atomic orbitals that they may occupy. Hence, the bonds of anti-bonding nature as well as uncorrelated spins disappear. So, we may suspect, that all Co oxide particles could be diamagnetics. Let us analyze the

Co6 58,77 -0,51 5 Co6O -11,24 -0,14 6 Co6O2 -15,47 -0,11 6 Co6O3 -3,26 -0,16 5 Co6O4 -9,62 -0,12 4 Co6O5 -15,97 -0,11 2 Co6O6 -2,11 -0,16 1 Co6O7 -25,94 -0,07 2 Co6O8 25,42 -0,18 1 Co6O9 -24,28 -0,05 0 Co6O12 -24,25 -0,07 0 Table 7. Data on magnetizability, isotropic g tensor, and Co-Co bonds number and the number of Co-Co bonds that was found based on the electron density investigation results.

**Isotropic g tenzor a.u** 

**Co-Co bond number** 

increases. i.e. the number of bonds of anti-boding nature decrease.

semiconductor properties if the number of oxygen increases.

**a.u.** 

Only those bonds with unpaired spin electrons are mentioned.

**4.1.1 Magnetic properties of Co6Om particles** 

possess anti-bonding character.

results presented in Table 7.

Compound **Magnetizability,** 

presence of electrons on the anti-bonding orbital and, as a consequence to, the dissolution of Co-Co bonds.

On the other hand, the electronic configuration of cobalt for the ground state neutral gaseous atom is [Ar].3d7.4 s2, while that of oxygen is [He].2s2.2p4. The configuration, associated with Cobalt in its compounds, is not necessarily the same, but it could be used to explain formally obtained results.

As it was mentioned above in Co6 compounds some electrons are displaced on the antibonding orbitals, the energy of which is higher than that of the bonding orbitals. Therefore, the stability of the pure cobalt nanoparticle is low. When the Co6 nanoparticle is joined to one or two oxygen atoms, the number of electrons that occupy anti-bonding orbitals, decreases because these electrons occupy the oxygen orbitals (Fig.12)

Fig. 11. The HOMO-LUMO gap of the Co6On (m = 1 - 9)

Fig. 12. Displacement of orbitals of several Co6Om (m=0, 1, 2, 7, 8, 9) and oxygen atoms in respect of each other. Here, H and L indicate HOMO and LUMO respectively. Additionally, the ground state (triplet) of oxygen atoms are calculated. It is possible to see that with the

increasing number of the oxygen atoms in the particle, the number of occupied orbital also increases. i.e. the number of bonds of anti-boding nature decrease.

Oxygen atoms in the Co6O4, Co6O3, Co6O2, and Co6O particles are joined to atoms between which the anti-bonding orbitals occur. Having in mind that the joining of oxygen atoms leads to the increase of the bond length and dissolution of Co-Co bonds, what confirms the above mentioned prediction. In case of the Co6O3 particle, one O atom is joined to Co4-Co5 atoms (Fig.10). The anti-bonding nature of the bonds has not been observed between those atoms. In this case, a steric effect is more preferable because other positions of the oxygen atom should complicate Co1-Co2 and Co2-Co6 elongation or leads to the destruction of this particle. Hence, oxygen atoms stabilize Co6 particles due to dissolving of Co-Co bonds that possess anti-bonding character.

It is very well known, that a semiconductor must have at least two characteristics: 1. the bonding and anti-bonding orbitals must form a delocalized band; 2. the HOMO-LUMO gap in molecular species should be generally of the order of 0.5eV to 3.5 eV. HOMO-LUMO gaps of the investigated derivatives belong to the above range. However, the number of antibonding orbitals decreases with increasing of the number of oxygen atoms. The results allow us to predict that Co6Om are semiconductors but the particles should loose their semiconductor properties if the number of oxygen increases.

## **4.1.1 Magnetic properties of Co6Om particles**

484 Smart Nanoparticles Technology

presence of electrons on the anti-bonding orbital and, as a consequence to, the dissolution of

On the other hand, the electronic configuration of cobalt for the ground state neutral gaseous atom is [Ar].3d7.4 s2, while that of oxygen is [He].2s2.2p4. The configuration, associated with Cobalt in its compounds, is not necessarily the same, but it could be used to

As it was mentioned above in Co6 compounds some electrons are displaced on the antibonding orbitals, the energy of which is higher than that of the bonding orbitals. Therefore, the stability of the pure cobalt nanoparticle is low. When the Co6 nanoparticle is joined to one or two oxygen atoms, the number of electrons that occupy anti-bonding orbitals,

Fig. 12. Displacement of orbitals of several Co6Om (m=0, 1, 2, 7, 8, 9) and oxygen atoms in respect of each other. Here, H and L indicate HOMO and LUMO respectively. Additionally, the ground state (triplet) of oxygen atoms are calculated. It is possible to see that with the

decreases because these electrons occupy the oxygen orbitals (Fig.12)

Fig. 11. The HOMO-LUMO gap of the Co6On (m = 1 - 9)

Co-Co bonds.

explain formally obtained results.

In the above chapter we proved that oxygen atoms stabilize cobalt nanoparticles, although, in some cases, the structure of particles changes insufficiently while the electronic structure is dramatically changed because the increasing number of oxygen atoms decreases the difference between the number of electrons and the number of atomic orbitals that they may occupy. Hence, the bonds of anti-bonding nature as well as uncorrelated spins disappear. So, we may suspect, that all Co oxide particles could be diamagnetics. Let us analyze the results presented in Table 7.


Table 7. Data on magnetizability, isotropic g tensor, and Co-Co bonds number and the number of Co-Co bonds that was found based on the electron density investigation results. Only those bonds with unpaired spin electrons are mentioned.

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 487

Let us remember, that the nanoparticles could be paramagnetic due to several reasons: 1) the unpaired electron location on the Co-Co bonds; 2) the small total electron charge density between Co atoms which appears due to overlapping of p orbitals of oxygen atoms; 3) the significant contribution of atoms that loose odd number of electrons. The second reason mentioned could not be realized in case of the Co6On particles due to their relatively large size and small number of oxygen atoms. The first and third reasons could be realized thus supporting the previously found results. It is necessary to mention, that non-compensation

Now, we shall describe the particles of group B in detail. Firstly, it is necessary to mention, that the particles of this group have the different number of Co-Co bonds: Co6O7, has two, Co6O8 has one, and Co6O9 has zero. Only Co6O8 particle exhibits paramagnetic properties. Let us remember that in the Co derivatives the number of bonding molecular orbitals, that may be occupied, is insufficient to locate all the electrons of the system. This causes the presence of electrons on the anti-bonding orbital and, as a consequence, a weaker correlation of these electrons. Similar states are obtained in biradicals where the number of atomic orbitals, that may be occupied, is smaller than that of electrons. That leads to the appearance of electrons on the anti-bonding orbitals and serves predicts a large orbital contribution to

of spin for CoO/SiO2 multilayers was also observed.

the magnetic moment of a small ComOn particle (Fig.14).

Fig. 14. HOMO orbital antibonding character of the Co6O8 particle.

but it is essential.

It implies, that a non-compensate electron spin should be obtained. This situation is realized in the Co6O7 and Co6O8 particles. However, in the Co6O7 particle two pairs of weakly correlated electrons are present what leads to the disappearance of non-compensate spins. This is indicated by the isotropic g-tensor value which equals to 0.007. However, in case of the Co6O8 particle, only one Co-Co bond is present and only one pair of weakly correlated electrons should be found. This weak correlation indicates the nature of HOMO orbital that consists of anti-bonding dz2 type orbitals (Fig.14). Hence, the total spin of electrons is not compensated and, as a consequence, the particle exhibits paramagnetic features. This presumption is also confirmed by the isotropic g-tensor value, that is one of the largest between the particles described (Table 7). The small value of the isotropic g-tensor indicates that the electronic contribution to the magnetic properties of the particle is not very large,

It is obvious to see, that the particles with odd number of Co-Co bonds are paramagnetic or lightly diamagnetic. On the other hand, the isotropic g-tensor value of the cobalt oxide particles is not large, thus we may suspect that a ion spin in these cases is very important.

It is necessary to mention that based on the results described above, we may divide the described particles into the following groups:


It has to be pointed out, that a lot of reports concluded that magnetic properties of the nanoparticles depend on their shape. So, we suspected that magnetizability of the particles belonging to one group should be the same. However, the results of our investigations do not prove the above prediction (Table 7).

According to our investigations, the Co6 nanoparticle is a strong paramagnetic, while other particles, belonging to group A, are diamagnetics. The same phenomenon is obtained in case of B group. In this case, the Co6O8 particle is paramagnetic, while other particles are diamagnetics. Moreover, the diamagnetic properties of the similarly shaped particles are quite the same only in the following cases: Co6O7, Co6O12, Co6O9; Co6O3, Co6O6; Co6O2, Co6O5. It implies that the shape of the particle has no influence on the magnetic properties of the nanoparticles. To confirm this conclusion, we have calculated magnetizability of several isomers of Co6O8 particles (Fig. 13). It is possible to see, that the shapes of isomers II and III are similar, but the shape of isomer I differs. However, the magnetizability of isomers II and I with different shapes is approximately alike, while the magnetizability of isomer III is smaller than that of isomer II with the same shape (Table 8).


Table 8. The Magnetizability of different isomers of Co6O8 particle.

Hence, the magnetic properties of these particles does not depend on their shape.

Fig. 13. The view of several isomers of Co6O8.

It is obvious to see, that the particles with odd number of Co-Co bonds are paramagnetic or lightly diamagnetic. On the other hand, the isotropic g-tensor value of the cobalt oxide particles is not large, thus we may suspect that a ion spin in these cases is very important. It is necessary to mention that based on the results described above, we may divide the

1. The particles that posses shape of Co6: Co6, Co6O, Co6O2, Co6O3, Co6O5, Co6O6 (A

2. The particles Co6O7, C6O8, Co6O9 in which the distance between the planes (formed of atoms 1, 2, 3 and of 4, 5, 6) is increased and one plane is rotated in respect the other one

It has to be pointed out, that a lot of reports concluded that magnetic properties of the nanoparticles depend on their shape. So, we suspected that magnetizability of the particles belonging to one group should be the same. However, the results of our investigations do

According to our investigations, the Co6 nanoparticle is a strong paramagnetic, while other particles, belonging to group A, are diamagnetics. The same phenomenon is obtained in case of B group. In this case, the Co6O8 particle is paramagnetic, while other particles are diamagnetics. Moreover, the diamagnetic properties of the similarly shaped particles are quite the same only in the following cases: Co6O7, Co6O12, Co6O9; Co6O3, Co6O6; Co6O2, Co6O5. It implies that the shape of the particle has no influence on the magnetic properties of the nanoparticles. To confirm this conclusion, we have calculated magnetizability of several isomers of Co6O8 particles (Fig. 13). It is possible to see, that the shapes of isomers II and III are similar, but the shape of isomer I differs. However, the magnetizability of isomers II and I with different shapes is approximately alike, while the magnetizability of isomer III is

**Isomers I II III**  Magnetizability, a.u. 25.42 24.76 14.24

Hence, the magnetic properties of these particles does not depend on their shape.

described particles into the following groups:

by the π/4 angle (B group).

not prove the above prediction (Table 7).

smaller than that of isomer II with the same shape (Table 8).

Fig. 13. The view of several isomers of Co6O8.

Table 8. The Magnetizability of different isomers of Co6O8 particle.

group)

3. The rest (Co6O4)

Let us remember, that the nanoparticles could be paramagnetic due to several reasons: 1) the unpaired electron location on the Co-Co bonds; 2) the small total electron charge density between Co atoms which appears due to overlapping of p orbitals of oxygen atoms; 3) the significant contribution of atoms that loose odd number of electrons. The second reason mentioned could not be realized in case of the Co6On particles due to their relatively large size and small number of oxygen atoms. The first and third reasons could be realized thus supporting the previously found results. It is necessary to mention, that non-compensation of spin for CoO/SiO2 multilayers was also observed.

Now, we shall describe the particles of group B in detail. Firstly, it is necessary to mention, that the particles of this group have the different number of Co-Co bonds: Co6O7, has two, Co6O8 has one, and Co6O9 has zero. Only Co6O8 particle exhibits paramagnetic properties.

Let us remember that in the Co derivatives the number of bonding molecular orbitals, that may be occupied, is insufficient to locate all the electrons of the system. This causes the presence of electrons on the anti-bonding orbital and, as a consequence, a weaker correlation of these electrons. Similar states are obtained in biradicals where the number of atomic orbitals, that may be occupied, is smaller than that of electrons. That leads to the appearance of electrons on the anti-bonding orbitals and serves predicts a large orbital contribution to the magnetic moment of a small ComOn particle (Fig.14).

Fig. 14. HOMO orbital antibonding character of the Co6O8 particle.

It implies, that a non-compensate electron spin should be obtained. This situation is realized in the Co6O7 and Co6O8 particles. However, in the Co6O7 particle two pairs of weakly correlated electrons are present what leads to the disappearance of non-compensate spins. This is indicated by the isotropic g-tensor value which equals to 0.007. However, in case of the Co6O8 particle, only one Co-Co bond is present and only one pair of weakly correlated electrons should be found. This weak correlation indicates the nature of HOMO orbital that consists of anti-bonding dz2 type orbitals (Fig.14). Hence, the total spin of electrons is not compensated and, as a consequence, the particle exhibits paramagnetic features. This presumption is also confirmed by the isotropic g-tensor value, that is one of the largest between the particles described (Table 7). The small value of the isotropic g-tensor indicates that the electronic contribution to the magnetic properties of the particle is not very large, but it is essential.

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 489

these particles the ion spin is also presented what indicates a high dipole moment. The number of the Co+3 ions is 2 and 4 respectively in the Co6O3 and Co6O6 particles. However, the components of the dipole moment indicate that the ion spins are delocalized. The interaction between these spins leads to the quench of an electron spin, i.e. both spins (ion and non-compensated spin of electrons located on the anti-bonding orbital of Co-Co bond)

The opposite situation is realized in the Co6O8 particle: an ion spin is localized and one Co-Co bond is present. In this case, the spins are oriented so that they are relatively parallel to each other. This prediction is supported by additional investigations of the isomers of the Co6O8 particle. It is necessary to mention, that one Co-Co bond is present in isomer II and a detailed investigation of the dipole moment indicates that it lies approximately in parallel to the Co-Co bonds. Therefore, the unpaired spins of a different nature support each other. Thus, the magnetizability of the I and II isomers of the Co6O8 particle is the same. In case of isomer III, all Co-Co bonds are dissolved, but an ion non-compensated spin is present. It implies that magnetic properties of the particle are determined by the localized ion spin only. Thus, the

Hence, the paramagnetic behaviour of the cobalt oxide particle is dominating when the noncompensated spin is present due to weakly interacting electrons on the anti-bonding orbital

It is necessary to pay attention to other important observations. As it was earlier mentioned, the cobalt oxide particles are semiconductors and Co6O8 exhibits magnetic properties. It implies that this Co6O8 particle could be magnetic superconductor and could be implemented in electronic devices to provide a new type of the control of conduction, i.e. of the charge carrier and quantum spin state. Hence, this particle could be used in quantum computing.

It is known that the growing metallic particles are stabilized by the absorption of the polymer chains on the surface of the growing metal fragments, lowering their surface energy and creating a barrier to further aggregation. On the other hand, the organic coating of a particle prevents the surface from oxidation, rendering the particle stable over a long period. So, it is necessary to have a tool to investigate and control the process of stabilization of nanoparticles because the stabilization could be related to the oxidation of a metal particle and, as a consequence, it looses its magnetic properties. We believe that the knowledge concerning the shape and the nature of the absorption spectra of the Co6Om particles in the Vis and UV region could be a good tool for the investigation of the oxidation processes of Co nanoparticles. The above assumption is based on the results obtained that indicate the

As it was to mention in 3.1.1 we may divide the described particles into groups based on the

1. The particles that posses a shape of Co6: Co6, Co6O, Co6O2, Co6O3, Co6O5, Co6O6 (group A). 2. The particles in which the distance between the planes (formed by atoms 1, 2, 3 and of 4, 5, and 6) is increased and one plane is rotated in respect of the other one by π/4

magnetizability of isomer III is lower than that of the other isomers investigated.

**5. Absorption spectra of the C6Om (m=1-9) nanoparticles** 

are oriented so that the total spin equals to zero.

and this spin is not quenched by the ion spins.

Co6 particle as a key element of larger particles.

angle: Co6O7, C6O8, Co6O9 (group B).

changes of the Co6 structures. The groups are the following:

Additionally, we may supplement the proposition, that Co6On particles should be paramagnetics when the number of Co-Co bonds on which the unpaired electrons are located might be odd (Table 7). It should be emphasized, that the number of Co-Co bonds was found on the basis of the electron density investigation results and only the bonds, where unpaired spin electrons could be presented, are mentioned. Indeed, the investigated particles with the odd number of Co-Co bonds exhibit paramagnetic or weak diamagnetic properties. However, it is not clear why the magnetic properties are different, i.e., formally, some, different features should appear.

Aiming to explain the above mentioned discrepancy, we investigated a dipole moment of these particles. The dipole moment indicates electron concentration places in the particle. On the other hand, the components of these dipole moments allow us to foresee the distribution of the above places. Both the concentration of electrons and their distribution helps us find additional spins that appeared due to the different oxidation state of the Co atoms (formally, we call the above spin as an ion one). The exception concerns Co6.

The components of the dipole moment of the particles that are paramagnetics or weak diamagnetics are shown in Table 9.


Table 9. Dipole moments and their components of the investigated paramagnetic or weak diamagnetical particles.

The Co6O8 particle is a paramagnetic due to the presence of non-compensate spin what indicates the value of the isotropic g-tensor of 0, 51 (a free electron *g*-value is 2.00) because of the appearance of electrons on the anti-bonding orbitals.

So, as it was mentioned, the following different types of magnetic interactions could be obtained in the Co6Om nanoparticles: 1. an uncompensated spin of weakly interacting electrons on the anti-bonding orbital; 2) the presence of Co ions that looses the odd number of electrons (Co+3 and the like) leads to the emergence of the additional non-compensated spin.

The results obtained exhibit that the magnetic properties of nanoparticles could depend on the above interactions. The paramagnetic behaviour dominates when the non-compensated spin is present due to weakly interacting electrons on the anti-bonding orbital and this spin is not quenched by the ion spins. Let us remember, that Co6O3 and Co6O6 particles are weak diamagnetics, thought the isotropic g-tensor is not smaller than that of the Co6O8 particle. In

Additionally, we may supplement the proposition, that Co6On particles should be paramagnetics when the number of Co-Co bonds on which the unpaired electrons are located might be odd (Table 7). It should be emphasized, that the number of Co-Co bonds was found on the basis of the electron density investigation results and only the bonds, where unpaired spin electrons could be presented, are mentioned. Indeed, the investigated particles with the odd number of Co-Co bonds exhibit paramagnetic or weak diamagnetic properties. However, it is not clear why the magnetic properties are different, i.e., formally,

Aiming to explain the above mentioned discrepancy, we investigated a dipole moment of these particles. The dipole moment indicates electron concentration places in the particle. On the other hand, the components of these dipole moments allow us to foresee the distribution of the above places. Both the concentration of electrons and their distribution helps us find additional spins that appeared due to the different oxidation state of the Co

The components of the dipole moment of the particles that are paramagnetics or weak

 **x y z**  Co6 0.096 -0.09 -0.01 -0.01 Co6O3 1.689 0.55 0.23 -1.58 Co6O6 1.639 -1.06 -1.16 0.44 Co6O8 (I isomer) 2.652 2.60 0.45 0.23 Co6O8 (II isomer) 2.059 -1.08 -0.01 -1.75

isomer) 1.372 1.37 -0.06 -0.03 Table 9. Dipole moments and their components of the investigated paramagnetic or weak

The Co6O8 particle is a paramagnetic due to the presence of non-compensate spin what indicates the value of the isotropic g-tensor of 0, 51 (a free electron *g*-value is 2.00) because of

So, as it was mentioned, the following different types of magnetic interactions could be obtained in the Co6Om nanoparticles: 1. an uncompensated spin of weakly interacting electrons on the anti-bonding orbital; 2) the presence of Co ions that looses the odd number of electrons (Co+3 and the like) leads to the emergence of the additional non-compensated

The results obtained exhibit that the magnetic properties of nanoparticles could depend on the above interactions. The paramagnetic behaviour dominates when the non-compensated spin is present due to weakly interacting electrons on the anti-bonding orbital and this spin is not quenched by the ion spins. Let us remember, that Co6O3 and Co6O6 particles are weak diamagnetics, thought the isotropic g-tensor is not smaller than that of the Co6O8 particle. In

**a.u. Dipole moment components, a.u.** 

atoms (formally, we call the above spin as an ion one). The exception concerns Co6.

some, different features should appear.

diamagnetics are shown in Table 9.

Co6O8 (III

spin.

diamagnetical particles.

Compounds **Dipole moment,** 

the appearance of electrons on the anti-bonding orbitals.

these particles the ion spin is also presented what indicates a high dipole moment. The number of the Co+3 ions is 2 and 4 respectively in the Co6O3 and Co6O6 particles. However, the components of the dipole moment indicate that the ion spins are delocalized. The interaction between these spins leads to the quench of an electron spin, i.e. both spins (ion and non-compensated spin of electrons located on the anti-bonding orbital of Co-Co bond) are oriented so that the total spin equals to zero.

The opposite situation is realized in the Co6O8 particle: an ion spin is localized and one Co-Co bond is present. In this case, the spins are oriented so that they are relatively parallel to each other. This prediction is supported by additional investigations of the isomers of the Co6O8 particle. It is necessary to mention, that one Co-Co bond is present in isomer II and a detailed investigation of the dipole moment indicates that it lies approximately in parallel to the Co-Co bonds. Therefore, the unpaired spins of a different nature support each other. Thus, the magnetizability of the I and II isomers of the Co6O8 particle is the same. In case of isomer III, all Co-Co bonds are dissolved, but an ion non-compensated spin is present. It implies that magnetic properties of the particle are determined by the localized ion spin only. Thus, the magnetizability of isomer III is lower than that of the other isomers investigated.

Hence, the paramagnetic behaviour of the cobalt oxide particle is dominating when the noncompensated spin is present due to weakly interacting electrons on the anti-bonding orbital and this spin is not quenched by the ion spins.

It is necessary to pay attention to other important observations. As it was earlier mentioned, the cobalt oxide particles are semiconductors and Co6O8 exhibits magnetic properties. It implies that this Co6O8 particle could be magnetic superconductor and could be implemented in electronic devices to provide a new type of the control of conduction, i.e. of the charge carrier and quantum spin state. Hence, this particle could be used in quantum computing.

## **5. Absorption spectra of the C6Om (m=1-9) nanoparticles**

It is known that the growing metallic particles are stabilized by the absorption of the polymer chains on the surface of the growing metal fragments, lowering their surface energy and creating a barrier to further aggregation. On the other hand, the organic coating of a particle prevents the surface from oxidation, rendering the particle stable over a long period. So, it is necessary to have a tool to investigate and control the process of stabilization of nanoparticles because the stabilization could be related to the oxidation of a metal particle and, as a consequence, it looses its magnetic properties. We believe that the knowledge concerning the shape and the nature of the absorption spectra of the Co6Om particles in the Vis and UV region could be a good tool for the investigation of the oxidation processes of Co nanoparticles. The above assumption is based on the results obtained that indicate the Co6 particle as a key element of larger particles.

As it was to mention in 3.1.1 we may divide the described particles into groups based on the changes of the Co6 structures. The groups are the following:


View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 491

The obtained absorption spectra of the particles making up groups A and B and their structures are presented in Fig. 15 and Fig. 16. The case of Co6O4 particle is different and should be investigated deeper, although the general tendency of absorption spectra changes

**(a) Co6O7 (b) Co6O8** 

**(c) Co6O9** 

Let us analyze the spectra of group A. It is obvious, that the intensity of absorption decreases especially in the [500;700] nm region with increasing of the oxygen number up till 5, and starts increasing again when the number of oxygen atoms is 6. The appearance of more intense absorption in the above region of the Co6O6 is related to the structure of this particle (Fig.15). The structure of the Co6O6 particle looks like the octahedron, while in the case of other particles investigated, the octahedron form is strongly deformed. The intensity of absorption in the region 300 to 400 nm increases when the number of oxygen atoms in the

It is obvious, that with the increasing of the number of the oxygen atoms by one, the number of occupied orbitals in the [-1;0] a.u increase by three (Table 10). Moreover, the gap of the Co6 particle between occupied orbitals in the]-2; -1[ a.u. region is not filled what is explained

Fig. 16. Absorption spectra of group B: **(a)** at the top on left there is a spectrum of Co6O7 particle, **(b)** on the right -those of Co6O8; **(c)** at the bottom, there are spectra of Co6O9. The

black circle indicates oxygen atoms, while the grey one – those of cobalt.

particle increases from 7 to 9 (Fig.16).

described below are possible to foresee in the spectra of this particle, too.

#### 3. The rest (Co6O4).

Fig. 15. Absorption spectra of group A. At (**a)** there are spectra of a Co6 particle, while **(b)** - those of Co6O; **(c)** in the middle, on the left, there is a spectrum of Co6O2; **(d)** on the right – Co6O3; **(e)** at the bottom, on the left, there are spectra of Co6O5; **(f)** on the right – those of Co6O6. The black circle indicates oxygen atoms, while the grey one – cobalt atoms.

**(a) Co6 (b) Co6O** 

**(c) Co6O2 (d) Co6O3** 

**e) Co6O5 (f) Co6O6** 

Fig. 15. Absorption spectra of group A. At (**a)** there are spectra of a Co6 particle, while

**(b)** - those of Co6O; **(c)** in the middle, on the left, there is a spectrum of Co6O2; **(d)** on the right – Co6O3; **(e)** at the bottom, on the left, there are spectra of Co6O5; **(f)** on the right – those of Co6O6. The black circle indicates oxygen atoms,

while the grey one – cobalt atoms.

3. The rest (Co6O4).

The obtained absorption spectra of the particles making up groups A and B and their structures are presented in Fig. 15 and Fig. 16. The case of Co6O4 particle is different and should be investigated deeper, although the general tendency of absorption spectra changes described below are possible to foresee in the spectra of this particle, too.

Fig. 16. Absorption spectra of group B: **(a)** at the top on left there is a spectrum of Co6O7 particle, **(b)** on the right -those of Co6O8; **(c)** at the bottom, there are spectra of Co6O9. The black circle indicates oxygen atoms, while the grey one – those of cobalt.

Let us analyze the spectra of group A. It is obvious, that the intensity of absorption decreases especially in the [500;700] nm region with increasing of the oxygen number up till 5, and starts increasing again when the number of oxygen atoms is 6. The appearance of more intense absorption in the above region of the Co6O6 is related to the structure of this particle (Fig.15). The structure of the Co6O6 particle looks like the octahedron, while in the case of other particles investigated, the octahedron form is strongly deformed. The intensity of absorption in the region 300 to 400 nm increases when the number of oxygen atoms in the particle increases from 7 to 9 (Fig.16).

It is obvious, that with the increasing of the number of the oxygen atoms by one, the number of occupied orbitals in the [-1;0] a.u increase by three (Table 10). Moreover, the gap of the Co6 particle between occupied orbitals in the]-2; -1[ a.u. region is not filled what is explained

View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 493

Particle Co6 Co6O Co6O2 Co6O3 Co6O5 Co6O6 Co6O7 Co6O8 Co6O9

Hence, the particles with higher symmetry absorb certain wave lengths more intensively, while the absorbance of non-symmetrical particles is not intensive, but a very broad one (Table 11, Figs. 15, 16). It allows us to conclude, that the investigated spectra of the Co nanoparticles in the region of [300; 700] nm could explain the oxidation of the particles and, as a consequence, their structure changes what lead to changes of magnetic

Basing on the results obtained, we speculate that the dependence on the place of excitation could be related with the particle oxidation when considering the excitation of large

Herein, we report on the several important results related to magnetic properties of the Co

The main important observations of the pure Co and oxidized nanoparticle are the

The Co8, Co10, Co12, Co14, Co16 particles consist of Co6, thus these particles could be

 The face centered cubic structure which is slightly less closely packed, occurred in the Co14 and Co16 nanoparticles, while the other particles described are the elements of the

 The present investigations of the magnetic properties of Co and Co oxide particles resulted in the conclusion that a paramagnetic behaviour is dominating when the noncompensated spin is present due to the anti-bonding orbitals and such a spin is not

The results of our investigations indicate that both a dipole interaction and particle

 The intensity of absorption of Co6Om (m=0-9) particles should be decreased in the [500;700] nm region with increasing of the number of the oxygen atom up to 5, and

 The spectra of investigated particles become linear when the number of oxygen atoms in the above particle is even, while the absorption lines in spectra should be difficult to

 It is obtained, that in the spectra of Co6Om (m=0-3) the most intensive excitations correspond to Co3d→Co3d excitations. The Co3dO2p→Co3dO2p excitations are more relevant in the spectra of the particles where the number of oxygen atoms is up to 7, while in the rest particles the Co3d→Co3dO2p or Co3dO2p→Co3d types of excitation

regarded to as the key element of the large Co nanoparticles.

The key element of the Co6 is present in the Co6On (n=0-9, 12) particles.

agglomeration change magnetic properties of the Co nanoparticle.

should be increased again when number of oxygen atoms is 6.

FCC structure in the sense of the above conclusions.

Table 11. Approximate symmetry of the particles investigated.

C2v C1 C2v C1 C1 C2v C2v C1h C3v

Symmetry group

properties.

**6. Conclusions** 

nanoparticle.

following:

particles (approximately of 200 nm).

quenched by the ion spins.

are obtained.

observe with odd number of oxygen.

by the displacement of the orbitals of both Co6Om (m=0-9) and an oxygen atom in respect of each other (Fig. 12). In case of Co6 particle, only three orbitals (HOMO, HOMO -1 and LUMO) of oxygen interact with the occupied orbitals of the particle, while in case of Co6Om particles, the number of interacting orbitals increases. Starting with Co6O, the additional occupied level occurred in the gap of the Co6 particle between the occupied orbitals in the region of ]-2; -1[ a.u. However, the HOMO-LUMO gap increases. So, semiconductor properties of the Co6Om particles become stronger.

Naturally, that with the increasing number of oxygen atoms in the Co6 particle, the mixing orbital (the molecular orbital consists of cobalt and oxygen atomic orbitals) increases due to the Co and O atomic orbital interaction. The analysis of the contribution of the atomic orbital to the molecular orbitals confirms the predicted interaction. Moreover, due to the above interaction, the orbital splits and several orbitals that are occupied in Co or Co oxide nanoparticles should become virtual and vice versa. Hence, the transitions in the spectra region of [350;700] nm are of Co3d → Co3d type and they are allowed in a pure Co particle or particles with the oxygen number of 1-2 because the above mixing is not very strong.

When the number of oxygen atoms in the Co particle is 3-7, the transitions in the spectra region of [350;700] nm are of Co3d→Co3dO2p orCo3dO2p→Co3d types. It is emphasized, that starting with the number of six of oxygen atoms, only occupied orbitals of nanoparticles interact with the occupied orbital of oxygen atom, i.e. the above mentioned interaction between LUMO of the oxygen atom and the occupied orbital of Co6Om nanoparticle does not occur. The analysis of the most important orbitals for excitation indicates, that in the spectra of Co6Om (m=0-5) the most intensive excitations correspond to Co3d→Co3d ones. Other partly allowed excitations correspond to Co3d→Co3dO2p ones. So, the number of Co3d→Co3dO2p excitations increases with the increased mixture of orbitals. Moreover, when the number of oxygen atoms is up to 7, the Co3dO2p→Co3dO2p excitations are more relevant. On the other hand, the symmetry of particles is different what leads to different number of the transitions allowed. It is very well known, that a part of the possible excitations is forbidden when the symmetry group of the particles is high, while all possible excitations are allowed when the symmetry group of the particle is the lowest (C1).


Table 10. The number of states of the Co6Om (m=0-9) particles in the regions of different energy.



Table 11. Approximate symmetry of the particles investigated.

Hence, the particles with higher symmetry absorb certain wave lengths more intensively, while the absorbance of non-symmetrical particles is not intensive, but a very broad one (Table 11, Figs. 15, 16). It allows us to conclude, that the investigated spectra of the Co nanoparticles in the region of [300; 700] nm could explain the oxidation of the particles and, as a consequence, their structure changes what lead to changes of magnetic properties.

Basing on the results obtained, we speculate that the dependence on the place of excitation could be related with the particle oxidation when considering the excitation of large particles (approximately of 200 nm).

## **6. Conclusions**

492 Smart Nanoparticles Technology

by the displacement of the orbitals of both Co6Om (m=0-9) and an oxygen atom in respect of each other (Fig. 12). In case of Co6 particle, only three orbitals (HOMO, HOMO -1 and LUMO) of oxygen interact with the occupied orbitals of the particle, while in case of Co6Om particles, the number of interacting orbitals increases. Starting with Co6O, the additional occupied level occurred in the gap of the Co6 particle between the occupied orbitals in the region of ]-2; -1[ a.u. However, the HOMO-LUMO gap increases. So, semiconductor

Naturally, that with the increasing number of oxygen atoms in the Co6 particle, the mixing orbital (the molecular orbital consists of cobalt and oxygen atomic orbitals) increases due to the Co and O atomic orbital interaction. The analysis of the contribution of the atomic orbital to the molecular orbitals confirms the predicted interaction. Moreover, due to the above interaction, the orbital splits and several orbitals that are occupied in Co or Co oxide nanoparticles should become virtual and vice versa. Hence, the transitions in the spectra region of [350;700] nm are of Co3d → Co3d type and they are allowed in a pure Co particle or particles with the oxygen number of 1-2 because the above mixing is not very strong.

When the number of oxygen atoms in the Co particle is 3-7, the transitions in the spectra region of [350;700] nm are of Co3d→Co3dO2p orCo3dO2p→Co3d types. It is emphasized, that starting with the number of six of oxygen atoms, only occupied orbitals of nanoparticles interact with the occupied orbital of oxygen atom, i.e. the above mentioned interaction between LUMO of the oxygen atom and the occupied orbital of Co6Om nanoparticle does not occur. The analysis of the most important orbitals for excitation indicates, that in the spectra of Co6Om (m=0-5) the most intensive excitations correspond to Co3d→Co3d ones. Other partly allowed excitations correspond to Co3d→Co3dO2p ones. So, the number of Co3d→Co3dO2p excitations increases with the increased mixture of orbitals. Moreover, when the number of oxygen atoms is up to 7, the Co3dO2p→Co3dO2p excitations are more relevant. On the other hand, the symmetry of particles is different what leads to different number of the transitions allowed. It is very well known, that a part of the possible excitations is forbidden when the symmetry group of the particles is high, while all possible

excitations are allowed when the symmetry group of the particle is the lowest (C1).

Co6 11 27 18 6 Co6O 13 30 18 6 Co6O2 13 33 15 5 Co6O3 12 36 17 6 Co6O4 15 39 14 6 Co6O5 13 42 18 4 Co6O6 13 45 18 6 Co6O7 15 48 18 6 Co6O8 15 51 18 6 Co6O9 16 54 18 6 Table 10. The number of states of the Co6Om (m=0-9) particles in the regions of different

[-1;0] a.u. [-1;-0] a.u. [-2;-3] a. u. [-3;-4] a. u.

Particles Virtual orbitals Occupied orbitals

energy.

properties of the Co6Om particles become stronger.

Herein, we report on the several important results related to magnetic properties of the Co nanoparticle.

The main important observations of the pure Co and oxidized nanoparticle are the following:


View on the Magnetic Properties of Nanoparticles Com (m=6,8,10,12,14) and Co6On (n=1-9) 495

Park I.-W. and et al. (2003). Magnetic properties and microstructure of cobalt nanoparticles

Yang H.T.and et al. (2004). Synthesis and magnetic properties of e-Co nanoparticles. S*urface and interface analysis*, Vol. 36, No. 2, (February), pp.155-160, *ISSN* 1096-9918 Becke A. D. (1993) Density-functional thermochemistry. iii. the role of exact exchange. *Journal of Chemical Physics,* Vol. 98, No 7, (April), pp.5648-5652, *ISSN* 0021-9606 Gordon M. S. and et al. (1982) Self-consistent molecular-orbital methods. 22. Small split-

Schmidt M.W. and et al. (2004) *Gaussian, Inc*., Wallingford CT, *ISBN* 0963676938, Pittsburgh,

Lutnæs O. B. and et al. (2005) Benchmarking density-functional-theory calculations of

*Schafer, A.; Horn, H.; Ahlrichs, R. (1992) Fully optimized contracted Gaussian basis sets for atom Li* 

*Wu N. and et al. (2004). Interaction of Fatty Acid Monolayers with Cobalt Nanoparticles. Nano* 

*Fan, H. J.; Liu, Ch. W.; Liao, M. Sh. (1997). Geometry, electronic structure and magnetism of small* 

*Meldrum, A.; Boatner, L. A.; Sorge, K. (2003) Nuclear Instruments and Methods in Physics* 

*Ichiyanaga, Y.; Yamada, S. (2005) The size-depended magnetic properties of Co3O4 nanoparticles.*  Polyhedron*, Vol.24, No. 16-17, (November), pp. 2813-2816, ISSN 0277-5387, Graf, Ch. P.; Birringer, R.; Michels, A. (2006) Sythhesis and magnetic properties of cobalt nanocubes. Physical Review B, Vol. 73, No. 21, (April), pp. 212401 – 212404, ISSN 1550-235x Resnick, D.A and et al. (2006) Magnetic properties of Co3O4 nanoparticles miniralized in Listeria* 

Salavati-Niasari, M.; Afsaneh Khansari, A.; Davar, F. (2009) Synthesis and characterization

Papis, E. and et al. (2009) Engineered cobalt oxide nanoparticles readily enter cells,

Sakurai, K. and et al. (1998) Magic numbers in Fe clusters produced by laser vaporization

Gambardella, P. and et al. (2003) Giant magnetic anisotropy of Co atoms and nanoparticles.

King, S.; Hyunh, K.; Tannenbaum, R. (2003) Kinetics of Nucleation, Growth, and

stabilization of cobalt oxide nanoclusters. *Journal of Physical Chemistry B*, Vol. 107,

Vol. 362, No. 14, (November), p.p. 4937-4942, *ISSN*: 0020-1693

*Toxicology letters,* Vol. 189 ,(June), p.p.253-259, *ISSN*: 0378-4274

source. *Journal of the Physical Society of Japan*, Vol. 8 : p.p. 2571-2573.

*Science,* Vol. 300, N*o. 5622,* (May 16), p.p.1130-1133, *ISSN 1095-9203*

No.44, (October 15), p.p. 10297-12104, *ISSN 1520-6106* 

Vol. 104, No.10, (May), pp. 2797-2803, *ISSN* 0002-7863

*Letters, Vol. 4, No. 2, (January), pp. 383-386, ISSN 1530-6984* 

0038-1098

USA

*0009-2614.* 

144119, *ISSN 0021-9606* 

*pp. 36-44,* ISSN *0168-583X* 

in a polymer film. *Solid State Communications,* Vol. 44, No.7 (May), pp. 385-389 *ISSN*

valence basis sets for second-row elements. *Journal of the American Chemical Society,* 

rotational *g* tensors and magnetizabilities using accurate coupled-cluster calculations . *Journal of Chemical Physics*, Vol. 131, No.14, (September ), pp.144104-

*to Kr. Journal of Chemical Physics, Vol. 97, No.4, (May), pp. 2571-2577, ISSN 0021-9606* 

*Con (n=2-8) clusters. Chemical Physics Letter, Vol. 273, No. 5-6, (July), pp. 353-359, ISSN* 

*Research Section B: Beam Interactions with Materials and Atoms, Vol. 207,No.1, (May),* 

*innoucua Dps.* Journal of Applied Physics*. Vol. 99 (April), 08Q501-3, ISSN 1089-7550* 

of cobalt oxide nanoparticles by thermal treatment process. *Inorganica Chimica Acta*,

## **7. References**


Zalich M. A. and et al. (2006). Structural and Magnetic properties of oxidatively stable cobalt

Simeonidis K. and et al. (2008). Shape and composition oriented synthesis of Cobalt

Neamtu J and et al. (2005). Synthesis and Properties of Magnetic Nanoparticles with

Sakurai M.I. and et al. (1998) Magic Numbers in Fe Clusters Produced by Laser Vaporization

Gambardella P. and et al. (2003) Giant Magnetic Anisotropy of Single Cobalt Atoms and Nanoparticles. Science, Vol.300, No. 1130, (May), pp. *1130-1133, ISSN 0036-8075*  Chen J. P. and et al. (1994) Magnetic properties of nanophase cobalt particles synthesized in

Ghosh M.; Sampathkumaran E. V.; Rao C.N.R. (2005) Synthesis and Magnetic Properties of

Zhao Y. W. and et al.(2003) A simple method to prepare Uniform Co nanoparticles. *IEEE* 

Sun X. Ch.; Reyes-Gasga J.; Dong X. L. (2002) Formation and microstructure of Carbo

Ram S. (2001) Allotropic phase transformations in HCP, FCC and BCC metastable structures

Gubin S.P. and et al. (2003) Magnetic and structural properties of Co nanoparticles in a

Tsukamoto S.; Koguchi N. (2000) Magic numbers in Ga clusters on GaAs (0 0 1) surface. *Journal of Crystal Growth,* Vol. 209, No.1-2, (February), pp. 258-262, *ISSN* 0022-0248 Guevara J.and et al. (1997) Electronic properties of transition-metal clusters:Consideration of

Ma Q. M.and et al. (2006) Structures, stabilities and magnetic properties of small Co clusters. *Physics Letter A,* Vol. 358, No. 4, (October), pp. 289-296, *ISSN 0375-9601*  Galvez N. and et al. (2002). Apoferritin-encapsulated Ni and Co superparamagnetic

nanoparticles encapsulated in graphite shell. *Chemistry of Materials,* Vol. 18,p.p.

nanoparticles, *Physics and Advanced materials Winter school*, pp.1-8, Thessaloniki,

Potential Applications in Cancer Diagnostic. T*echnical Proceedings of the 2005 NSTI Nanotechnology Conference and Trade Show*, Vol. 1, p.p. :222 - 224, ISBN:0-9767985-0-6,

Source. *Journal of the Physical Society of Japan,* Vol. 67, No. 8, (August), pp. 2571-2573,

inversed micelles. *Journal of Applied Physics,* Vol. 76, No. 10, (November), pp. 6316 -

CoO Nanoparticles. *Chemistry Materials,* Vol. 17, No. 9, (March), pp.2348 -2352 ISSN

*Transactions on magnetics*, Vol.39, No. 5, (September) , pp. 2764-2766, ISSN 0018-9464

encapsulated superparamagnetic Co nanoparticles. *Molecular Physics*, Vol. 100, No

in Co- nanoparticles. *Material Science and Engineering A,* Vol. 304-306, (May), pp.

polymeric matrix. *Journal of Magnetism and Magnetic Materials,Vol.* 265, No. 2,

the spillover in a bulk parametrization. *Physical Review B,* Vol. 55, No. 19, (May),

nanoparticles. *Erophysics. Letter* , Vol. 76, No.5, (December), pp.142-148, *ISSN* 0295-

**7. References** 

2648-2655, ISSN 0897-4756

Anaheim, California, USA,May 8-12, 2005.

19, (March), pp. 314-315, *ISSN 0026-8976* 

(September) pp. 234-242 *ISSN 0304-8853* 

pp.13283-13287 *ISSN* 1098-0121

Greece, January 14-18

ISSN 0031-9015

6318 ISSN 021-8979

923-927, *ISSN* 0921-5093

0897-4756

5075


**1. Introduction** 

on the review on these aspects of nanofluids.

**2. Preparation methods for nanofluids** 

big concern, especially for high temperature applications.

**2.1 Two-step method** 

**Nanofluids** 

*P. R. China* 

Wei Yu, Huaqing Xie and Lifei Chen *Shanghai Second Polytechnic University* 

Nanofluids are a new class of fluids engineered by dispersing nanometer-sized materials (nanoparticles, nanofibers, nanotubes, nanorods, nanosheet, or droplets) in base fluids. In other words, nanofluids are nanoscale colloidal suspensions containing solid nanomaterials. They are two-phase systems with one phase (solid phase) in another (liquid phase). For a two-phase system, there are some important issues we have to face. One of the most important issues is the stability of nanofluids and it remains a big challenge to achieve desired stability of nanofluids. In this paper we will review the new progress in the methods for preparing stable nanofluids and summarize the stability mechanisms. In recent years, nanofluids have attracted more and more attention. The main driving force for nanofluids research lies in a wide range of applications. Although some review articles involving the progress of nanofluid investigation were published in the past several years [1-6], most of the reviews are concerned on the experimental and theoretical studies of the thermophysical properties or the convective heat transfer of nanofluids. The purpose of this paper will focuses on the new preparation methods and stability mechanisms, especially the new application trends for nanofluids in addition to the heat transfer properties of nanofluids. We will try to find some challenging issues that need to be solved for future research based

Two-step method is the most widely used method for preparing nanofluids. Nanoparticles, nanofibers, nanotubes or other nanomaterials used in this method are first produced as dry powders by chemical or physical methods. Then the nanosized powder will be dispersed into a fluid in the second processing step with the help of intensive magnetic force agitation, ultrasonic agitation, high-shear mixing, homogenizing and ball milling. Two-step method is the most economic method to produce nanofluids in large scale, because nanopowder synthesis techniques have already been scaled up to industrial production levels. Due to the high surface area and surface activity, nanoparticles have the tendency to aggregate. The important technique to enhance the stability of nanoparticles in fluids is the use of surfactants. However the functionality of the surfactants under high temperature is also a

*Nogues, J. and et al. (2006) Shell-driven magnetic stability in core-shell nanoparticles.* Physical Review Letter*, Vol 97, No. 15, (October 13), p.p.1572031.1572034, ISSN · 0031-9007* **22** 
