*Solar Thermal Conversion of Plasmonic Nanofluids: Fundamentals and Applications DOI: http://dx.doi.org/10.5772/intechopen.96991*

number of publications on plasmonic nanostructures done with COMSOL Multiphysics has appeared in the literature.

A short comparison of these above calculation methods for NPs are listed in **Table 1**. The choice of the calculation method depends on many factors, such as: NP size, shape and dielectric environment. But the general method, such as: FEM, and FDTD, can be used in most situations by applying the periodic boundary conditions at the sides of the unit cell.

The optical properties of nanofluids also can be calculated based on the above method, such as: FDTD or FEM, which are the direct way to achieve the absorption performance of nanofluids without the strict assumptions. But the computation load is large for nanofluids since the geometry size (� mm) is much larger than NP size or mesh size (� nm). Therefore, the optical properties of nanofluids can be obtained from the optical properties of single NP due to the low NP concentration of plasmonic nanofluids in the solar thermal conversion applications and the independent scattering can be applied in the calculation of nanofluids.

One method is to avoid the scattering effect of NPs due to the small size, resulting in the negligible scattering effect in the nanofluids. Therefore, the absorption efficiency of the nanofluids can be obtained by the independent scattering approximation, which can be described as [9]:

$$k\_{\text{a}\lambda,\text{nf}} = k\_{\text{a}\lambda,\text{bf}} + k\_{\text{a}\lambda,\text{np}} = \frac{4\pi\kappa}{\lambda} + \frac{\text{f}\_{\text{v}}\text{C}\_{\text{abs}}}{V\_{\text{np}}} \tag{7}$$

where *k*a*<sup>λ</sup>*,nf, *k*a*<sup>λ</sup>*,bf, and *k*a*λ*,np are the absorption coefficients of the nanofluid, the base fluid water and the NPs respectively. *κ* is the absorption index of water. *f* <sup>v</sup> is the NP volume fraction. *V*np is the single NP volume. *C*abs is the absorption cross section of the NP. Based on the Beer–Lambert law [61], the radiation intensity decays exponentially along the transmission direction. Therefore, the solar absorption efficiency *η*abs can be calculated as:

$$\eta\_{\rm abs} = \frac{\int\_{0.3\mu\text{m}}^{2.5\mu\text{m}} I\_{\rm abs}(\lambda) \mathbf{d}\lambda}{\int\_{0.3\mu\text{m}}^{2.5\mu\text{m}} I\_{\rm s}(\lambda) \mathbf{d}\lambda} = \frac{\int\_{0.3\mu\text{m}}^{2.5\mu\text{m}} I\_{\rm s}(\lambda) \left(1 - e^{-Hk\_{\rm s}\omega\text{f}}\right) \mathbf{d}\lambda}{\int\_{0.3\mu\text{m}}^{2.5\mu\text{m}} I\_{\rm s}(\lambda) \mathbf{d}\lambda} \tag{8}$$

where *I*sð Þ*λ* is the solar spectra at AM 1.5. *I*absð Þ*λ* is the absorbed spectra. *H* is the depth.


**Table 1.**

*Comparison of calculation methods for plasmonic NPs [60].*

**BEM:** Boundary element method (BEM) is another method to calculate the optical properties of plasmonic nanostructures, which was introduced by García de

> ð *S j*

ð *S j*

where *ϕ*ð Þ*r* is the electric potential, *A r*ð Þ is the vector potential, *σ <sup>j</sup> r*<sup>0</sup> ð Þ is the surface charge density and *h <sup>j</sup> r*<sup>0</sup> ð Þ is the surface current density and *G <sup>j</sup>* is the Green's function of Helmholtz equation inside each homogeneous medium of dielectric function. *S <sup>j</sup>* is the boundary of the medium *j*. *s* is the point of the boundary between medias. *<sup>r</sup>* is the point inside the medium. *<sup>ϕ</sup>ext*ð Þ*<sup>r</sup>* and *Aext*ð Þ*<sup>r</sup>* are the potentials at the interface caused by external sources and the full space is filled by a homogeneous medium *j*. Therefore, a much smaller number of elements is required to evaluate the fields than volume integral based methods, but involving a complex parameteriza-

**FDTD:** Finite-difference time-domain (FDTD) is one of the most popular optical calculation methods in plasmonic nanostructures, which is first developed by Yee in 1966 [55]. The basis of the model is from Maxwell equations in electrodynamics. The second-order precision central difference is used to approximate the discretization of the differential form of Maxwell equations, thereby a set of timedomain propulsion formulas can be used to deal with electromagnetic wave propagation problems. Since the FDTD method directly discretizes the time-domain wave equation, it will not limit its application range due to mathematical models, and can

The popularity of this method has strongly increased in the last two decades, mainly due to the simplicity of implementation, support of arbitrary NP shape, allowing to investigate linear and non-linear properties of NPs, using Maxwell's equations directly without approximations. There are, however, some undesired effects, like the staircase of fields in non-rectangular boundaries, mainly in code implementations without adaptive meshing. To avoid this, very fine discretization or sub-pixel smoothing of the dielectric function must be applied [56]. The dielectric function of the materials requires analytical expressions (e.g.,

**FEM**: Finite element method (FEM) was developed to solve differential equations of boundary-value problems [58]. Physical problems described by differential equations over a domain, like for example the Helmholtz equation in real threedimensional space. Hence, electromagnetic (EM) field propagation around the sin-

<sup>r</sup> <sup>∇</sup> � *<sup>E</sup>* � � � *<sup>k</sup>*<sup>2</sup>

where *E* is the electric field of the medium, *j* is the current density, *k*<sup>0</sup> is the wavenumber, *<sup>ε</sup>*<sup>r</sup> is the dielectric function, which is calculated as *<sup>ε</sup>*<sup>r</sup> <sup>¼</sup> ð Þ *<sup>n</sup>* � *ik* <sup>2</sup>

and *k* are the complex refractive indices. Within each element *E* is approximated

tion point. *N<sup>j</sup>* is chosen basis function and *ξ<sup>j</sup>* is the unknown coefficient. A solution can be obtained by using the variational principle to determine *ξj*. To obtain a meaningful solution, *N<sup>j</sup>* is required to satisfy Gauss's law and appropriate boundary conditions on the surface of all elements. During the last decade, an increasing

*G <sup>j</sup>*ð Þ j j *r* � *s σ <sup>j</sup>*ð Þ*s ds* (4)

*G <sup>j</sup>*ð Þ j j *r* � *s h <sup>j</sup>*ð Þ*s ds* (5)

<sup>0</sup>*ε*r*E* ¼ 0 (6)

*<sup>j</sup>*¼<sup>1</sup>*Njξj*, where the sum is over *<sup>n</sup>* interpola-

, *n*

Abajo and Howie [54] using the following equations:

*Advances in Microfluidics and Nanofluids*

tion of the boundary elements.

Drude–Lorentz) [57].

**116**

effectively simulate various complex structures.

gle NP can be described by the Helmholtz Equation [59]:

using a basis function expansion *<sup>E</sup>* <sup>¼</sup> <sup>P</sup>*<sup>n</sup>*

<sup>∇</sup> � *<sup>μ</sup>*�<sup>1</sup>

*<sup>ϕ</sup>*ð Þ¼ *<sup>r</sup> <sup>ϕ</sup>ext*

*A r*ð Þ¼ *<sup>A</sup>ext*

*<sup>j</sup>* ð Þþ *r*

*<sup>j</sup>* ð Þþ *r*

The optical properties of nanofluids also can be solved by the Monte Carlo (MC) method to obtain the solar absorption performance of nanofluids. MC technique is a flexible method for simulating light propagation in the medium. The simulation is based on the random walks that photons make as they travel, which are chosen by statistically sampling the probability distributions for step size and angular deflection per scattering event. After propagating many photons, the net distribution of all the photon paths yields an accurate approximation to reality. In this method, the scattering effect is considered by the scattering efficiency and scattering phase function. The absorptance, transmittance, and reflectance of nanofluids can be calculated by counting the fate of photons.

complex structures are still difficult and more efforts still are needed to precious

Compared with the other common nanofluids (e.g., SiO2, TiO2, Al), plasmonic Au nanofluids with the small NP size were prepared experimentally to obtain the great solar thermal conversion efficiency [21, 76]. However, the absorption peaks of these common metals usually locate in the visible part especially for the metal sphere. Multi-element NPs (such as: alloy NP [77]) can further enhance solar absorption ability compared with the single-element NPs by tuning the LSPR peak. Various core-shell NPs were also prepared to enhance the solar absorption performance of plasmonic nanofluids [73, 78]. For example: Ag@CdS core-shell NPs were synthesized by a facile method and the optical absorption performance of Ag@CdS nanofluids was enhanced in a wide range of visible light compared with bare Ag and CdS NPs [79]. Sn@SiO2@Ag core-shell NPs were prepared with good abilities of both optical absorption and thermal energy storage [80]. Ag shell can improve light absorption due to LSPR effect, which was also can be found experimentally for CuO@Ag [81] and TiO2@Ag plasmonic nanofluids compared with CuO, TiO2, and

Another simple way is to blend sphere NPs with different materials [83–85]. Various NPs have been blended experimentally to enhance the solar absorption performance of plasmonic nanofluids. For example, hybrid nanofluids containing reduced graphene oxides decorated with Ag NPs [86], multi-wall carbon nanotubes and SiO2@Ag NPs [87], Fe3O4, Cu and Au NPs [88], and Au and TiN NPs [89] showed great solar absorption performance by tuning the ratios of different components to broaden the absorption spectrum. LSPR effect around plasmonic NPs and intrinsic absorption of semiconductor NPs make the hybrid nanofluids possess superior optical absorption to bare NPs at the same concentration. Besides the blended nanofluids with different NP materials discussed above, the other route is to blend the NPs with different shapes. For example, by mixing Au NPs (such as: nanorods [90]) with different shapes in water, a blended plasmonic nanofluid was prepared and absorption spectrum can be broadened due to the various LSPR peaks of different NP shapes [84]. The blended nanofluids based on Ag triangular nanosheets and Au nanorods, were proposed and a high efficiency

of 76.9% is achieved experimentally with a very low volume concentration

performance due to the complex structure experimentally [94].

As discussed above, blending different NPs is a simple way to achieve multi absorption peaks. However, compared with the single component NPs, the interaction between the different NPs in the blended nanofluids is limited due to independent scattering at the low NP fraction, leading that the solar thermal conversion efficiency of blended NPs was almost equal to the arithmetic sum of the efficiency of each component NPs without enhanced coupled effect between different NPs with the incident light [83]. Designing complex structures with multi-resonance peaks experimentally can be an efficient way to enhance the solar absorption performance of plasmonic nanofluids. For example, Au thorn [92] and Au dimer [93] were designed experimentally enhance the light absorption performance of plasmonic nanofluids. In addition, Janus NPs also showed great optical absorption

Nanofluids can either absorb or transmit specific solar spectrum and thus making assorted nanofluids ideal candidates for various solar applications [95]. Based on the tunable optical absorption performance of plasmonic nanofluids, several

control the NP size parameters (e.g., size or shape) experimentally.

*DOI: http://dx.doi.org/10.5772/intechopen.96991*

*Solar Thermal Conversion of Plasmonic Nanofluids: Fundamentals and Applications*

Ag nanofluids [82].

(0.0001%) [91].

**4. Applications**

**119**

For the plasmonic nanofluids applied in the solar thermal applications, the absorption spectral distribution is one of the most important parameters, which is proportional to the NP parameters (concentration, shape and size), Qin et al. theoretically optimized the spectral absorption coefficient of an ideal plasmonic nanofluid for a DASC to maximize the thermal efficiency while maintaining the magnitude of the average absorption coefficient at a certain value [62]. However, considering that the SPR frequency of metallic NPs, such as Au, Ag, and Al, is usually located in the ultraviolet to visible range. The actual plasmonic nanofluids usually have the narrow absorption band due to the SPRs. Two strategies can be adopted to overcome this shortage in the NP theoretical design process.

One is to blend NPs with different absorption peaks to form hybrid plasmonic nanofluids for full utilization of solar energy in a broad spectrum. For example, an ideal distribution of spherical metal NPs, including nanospheres and nanoshells, were designed to match the AM 1.5 solar spectrum with an determination of absorbing and scattering distributions [63]. Based on MC method and FEM, four type of Au nanoshells were blended in the base fluid to enhance the solar absorption performance of plasmonic nanofluids with an extremely low particle concentration (e.g., approximately 70% for a 0.05% particle volume fraction) [64]. By applying the customized genetic algorithm, an optimal combination for a blended nanofluid (metal nanosphere, metal@SiO2 core-shell, and metal nanorod) was designed with the desired spectral distribution of the absorption coefficient [65]. Besides the core-shell NPs, other NP shapes were also designed to expand the absorbance over the entire solar spectrum [66, 67]. Although different blended NPs were designed to broad the absorption spectrum, the comparison or enhancement is usually done based on the single-element nanofluid, which is not enough to compare with the other blend styles.

The other is to design complex NP structures with multiple absorption peaks at different wavelengths or coupled with the great intrinsic absorption materials. For example, core-shell NPs (Al@CdS [68], Ag@SiO2@CdS [69], Au@C [70], Ag@TiO2 [71], and gallium-doped zinc oxide@Cu [72, 73]) were the direct way to enhance the solar absorption performance due to the enhancement and tunable SPRs of shell and intrinsic absorption of core by optical simulations, thus broadening the absorption spectrum and improving the solar absorption performance of plasmonic nanofluids. Results also found that Ag NPs with sharp edges can induce multiple absorption peaks due to both LSPR and lightning rod effect to broad the absorption spectrum [74]. In addition, a plasmonic dimer nanofluid, consisting of the rod and sphere, was proposed to enhance the solar absorption performance by LSPR, PSPR, and gap resonance between the rod and sphere at different wavelengths [17], which was also similar as the thorny NPs [75].

#### **3.2 Experimental design**

Although various NP structures were designed to enhance the solar absorption performance of plasmonic nanofluids theoretically, the synthesizes of these
