**Advance in Tribology Study of Polyelectrolyte Multilayers**

Yanbao Guo and Deguo Wang

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67571

#### **Abstract**

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MoS<sup>2</sup>

254 Nanoscaled Films and Layers


PO4

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nanosheets with exposed

nanoparticles loaded on 3D

/rGO under full spectrum visible

/g-C3 N4

nanosheets loaded ZnO-g-C3

/MoS<sup>2</sup>

on graphene-like

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nanosheets as

N4 nano-

@zeolite photocatalyst and

nanostructures. Materials

heterojunction photocatalysts for

PO4

This review introduced the preparation and structural characterization of polyelectrolyte multilayers in recent years and also summarized the tribology research progress of the polyelectrolyte multilayers, including tribological properties, surface adhesion charac‐ teristics, and wear resistance properties. Statistics analysis indicated that nanoparticles‐ doped polyelectrolyte multilayers present better friction and wear performance than pristine polyelectrolyte multilayers. Furthermore, the in situ growth method resulted in improved structural order of nanoparticles composite molecular deposition film. In situ nanoparticles not only reduced the molecular deposition film surface adhesion force and friction force but also significantly improved the life of wear resistance. That was due to the nanoparticles that possessed a good load‐carrying capacity and reduced the mobility of the polymer‐chain segments, which can undergo reversible shear deformation. Based on this, further research direction of in situ nanoparticles molecular deposition film was proposed.

**Keywords:** tribology, polyelectrolyte multilayers, nanoparticles, friction, antiwear

## **1. Introduction**

With the development of micro‐/nanotechnology, the integration of miniaturized mechani‐ cal components with microelectronic components has spawned a new technology; it is well known as microelectromechanical systems (MEMS)/nanoelectromechanical sys‐ tems (NEMS) [1]. Due to the large surface‐area‐to‐volume ratios of surface and bulk micromachine, micromechanism brings the role of surface and interfacial forces into the

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foreground [2]. Thus, the surface adhesion and friction greatly affect the safety and ser‐ vice life of MEMS or micromechanisms. So the need of developing nanolubricating tech‐ nique is becoming increasingly urgent. Thin organic films as a more effective modification for antifriction treatments involve the application of a molecular film to the micromachine surface [3]. In the recent two decades, with the development of MEMS, magnetic storage, and recording systems, Langmuir‐Blodgett (LB) films and self‐assembled (SA) films were applied to reduce the frictional force between the contacted surfaces of different materials. However, both LB films and SA films were limited in use because of their own shortages: instability and the cost of the apparatus for the LB film, and the difficulty of multilayers assembling for the SA film [4].

Decher et al. [5–8] introduced a method for preparing multilayers by the consecutive depo‐ sition of oppositely charged polyelectrolytes from dilute aqueous solution by way of inter‐ molecular electrostatic forces onto charged substrates. Polyelectrolyte multilayers (PEMs) through this molecular deposition process have been intensively investigated in recent years. The popularity of this molecular deposition procedure is due to its simplicity, ver‐ satility, and systematical control over the structure and the thickness of the resulting films. Moreover, the materials used in molecular deposition studies can be macromolecules [6], small organic molecules [7] or inorganic compounds [8], biomacromolecules such as pro‐ teins [9], DNA [10], or even colloids [11]. Previous work has reported that polyelectrolyte multilayers can decrease the adhesive force on a surface [12], so as to modify the friction surface and reduce the friction force [13, 14]. This shows that the polyelectrolyte multi‐ layers are ideally suited to combat the tribological challenges in MEMS. Up to now, the friction and wear behaviors of polyelectrolyte multilayers were studied popularly. Pavoor et al. has reported that the preparation of a poly(acrylic acid) (PAA) and poly(allylamine hydrochloride) (PAH) polyelectrolyte multilayers using layer‐by‐layer method, and the capacity for these multilayers induced wear reduction at large scales under dry condition [15]. The mechanical property of polyelectrolyte multilayers was characterized by using a nanoindentation tester. The results indicated that the elastic modulus and hardness of the films were independent of the contact depth over a range of penetration where artifacts arising from the free surface and the underlying glass substrate were insignificant [16]. Furthermore, nanoparticles can reduce friction and enhance the lubrication performance of the lubricant [17]. Nanoparticles were also applied to prepared composite polyelectrolyte multilayers, such as TiO2 [18], graphite oxide (GO) [18], graphene oxide [19], SiO2 [20], Ag [21], and so on. The tribological investigation of nanoparticles composite polyelectrolyte multilayers shows that the nanoparticles in the polymer films could enhance the antiwear life of polyelectrolyte multilayers. Then, it indicated that these composite films can improve the tribological performance greatly.

In this review, the correlation between the parameters and the performance was calculated. We defined chemical composition parameter as the molecular structure and ionization behav‐ ior of polyelectrolyte. As a result, it substantially facilitates our fundamental understanding in the mechanism of lubrication and antiwear performance that enables us to design molecular film lubricants with well tribological properties.

## **2. Effects of chemical composition of polyelectrolyte**

foreground [2]. Thus, the surface adhesion and friction greatly affect the safety and ser‐ vice life of MEMS or micromechanisms. So the need of developing nanolubricating tech‐ nique is becoming increasingly urgent. Thin organic films as a more effective modification for antifriction treatments involve the application of a molecular film to the micromachine surface [3]. In the recent two decades, with the development of MEMS, magnetic storage, and recording systems, Langmuir‐Blodgett (LB) films and self‐assembled (SA) films were applied to reduce the frictional force between the contacted surfaces of different materials. However, both LB films and SA films were limited in use because of their own shortages: instability and the cost of the apparatus for the LB film, and the difficulty of multilayers

Decher et al. [5–8] introduced a method for preparing multilayers by the consecutive depo‐ sition of oppositely charged polyelectrolytes from dilute aqueous solution by way of inter‐ molecular electrostatic forces onto charged substrates. Polyelectrolyte multilayers (PEMs) through this molecular deposition process have been intensively investigated in recent years. The popularity of this molecular deposition procedure is due to its simplicity, ver‐ satility, and systematical control over the structure and the thickness of the resulting films. Moreover, the materials used in molecular deposition studies can be macromolecules [6], small organic molecules [7] or inorganic compounds [8], biomacromolecules such as pro‐ teins [9], DNA [10], or even colloids [11]. Previous work has reported that polyelectrolyte multilayers can decrease the adhesive force on a surface [12], so as to modify the friction surface and reduce the friction force [13, 14]. This shows that the polyelectrolyte multi‐ layers are ideally suited to combat the tribological challenges in MEMS. Up to now, the friction and wear behaviors of polyelectrolyte multilayers were studied popularly. Pavoor et al. has reported that the preparation of a poly(acrylic acid) (PAA) and poly(allylamine hydrochloride) (PAH) polyelectrolyte multilayers using layer‐by‐layer method, and the capacity for these multilayers induced wear reduction at large scales under dry condition [15]. The mechanical property of polyelectrolyte multilayers was characterized by using a nanoindentation tester. The results indicated that the elastic modulus and hardness of the films were independent of the contact depth over a range of penetration where artifacts arising from the free surface and the underlying glass substrate were insignificant [16]. Furthermore, nanoparticles can reduce friction and enhance the lubrication performance of the lubricant [17]. Nanoparticles were also applied to prepared composite polyelectrolyte

[18], graphite oxide (GO) [18], graphene oxide [19], SiO2

[21], and so on. The tribological investigation of nanoparticles composite polyelectrolyte multilayers shows that the nanoparticles in the polymer films could enhance the antiwear life of polyelectrolyte multilayers. Then, it indicated that these composite films can improve

In this review, the correlation between the parameters and the performance was calculated. We defined chemical composition parameter as the molecular structure and ionization behav‐ ior of polyelectrolyte. As a result, it substantially facilitates our fundamental understanding in the mechanism of lubrication and antiwear performance that enables us to design molecular

[20], Ag

assembling for the SA film [4].

256 Nanoscaled Films and Layers

multilayers, such as TiO2

the tribological performance greatly.

film lubricants with well tribological properties.

Since the invention of layer‐by‐layer method, many polyelectrolytes are used for preparing multilayers. It mainly includes polycations and polyanions. These groups dissociate in aque‐ ous solutions. Polyelectrolyte thus has properties of both electrolytes as salts and polymer as high‐molecular‐weight compounds. Like salts, their solutions are electrically conductive. Like polymers, their solutions are often viscous. Charged molecular chains are commonly present in soft‐matter systems. Due to its ionization properties, different polyelectrolytes have been utilized in the formation of ultrathin materials known as polyelectrolyte multilayers. During layer‐by‐layer deposition, a suitable growth‐charged substrate is dipped back and forth between dilute baths of positively and negatively charged polyelectrolyte solutions. As shown in the schematic diagram (**Figure 1**), during each dip process an amount of polyelec‐ trolyte molecular is adsorbed on the substrate and the surface charge is reversed.

The statistic analysis was conducted based on the experimental results collected from 42 papers that were related to tribological study of polyelectrolyte multilayers, as listed in **Table 1**. Based on **Table 1**, we can divide reported polyelectrolytes into different types based on their characteristic (strong or weak polyelectrolyte, terminal group). It can be found that the main polyelectrolytes used in references were PAA, PAH, poly(diallyl dimethylammo‐ nium chloride) (PDDA), and poly(4‐styrenesulfonic acid) sodium salt (PSS). Then, we prin‐ cipally review these polyelectrolyte multilayers including the nanoparticles composite films.

The factors affecting the micro‐ or nanofrictional behavior of polyelectrolyte multilayers include the characteristics of molecule assembled, surface morphology, and mechanical prop‐ erties of the films.

The characteristics of the outermost layer molecules forming the films have essential effects on the frictional properties of the polyelectrolyte multilayers. **Table 1** lists the different struc‐ tures adsorbed on the substrate according to the last adsorbed layer polyelectrolyte. **Figure 2** shows the friction coefficient comparison based on different outermost layer polyelectrolyte. According to the results, the polyelectrolyte multilayer‐modified substrate shows a lower fric‐ tion coefficient than that for the bare substrate (glass or silicon). It demonstrated the lubricating

**Figure 1.** The schematic diagram of deposition process of polyelectrolyte multilayers (redrawn from Refs. [5–8]).


**Table 1.** Summary of polyelectrolytes used for tribology.

**Figure 2.** Friction coefficient comparison based on the outermost layer polyelectrolyte.

and antifriction properties of polyelectrolyte multilayers. The polyelectrolyte deposited on the substrate can reduce the friction force, which is mainly influenced by the surface layer. In this case, PAH layer was believed to be the lowest friction coefficient. From the macrofriction tests, the polycationic layer is a better element for improving tribological performance.

**Materials Abbreviation of** 

Poly(allylamine hydrochloride)

258 Nanoscaled Films and Layers

Poly(4‐styrenesulfonic acid) sodium salt

biopolymers chitosan

Poly(diallyl dimethylammonium

chloride)

Natural

**molecular**

Poly(L‐lysine) PLL C [29] Hyaluronic acid HA A [29, 37, 44]

Deoxyribonucleic acid DNA A [33] Diazoresin DR C [41]

**Figure 2.** Friction coefficient comparison based on the outermost layer polyelectrolyte.

**Table 1.** Summary of polyelectrolytes used for tribology.

**Cationic or anionic (C or A)**

Polyethylenimine PEI C [25, 26, 33, 39, 40, 42, 44, 52]

CHI C [37]

Poly(acrylic acid) PAA A [15, 16, 18, 20–22, 24–26, 34, 35, 38, 39, 41–43, 45,

**References**

PAH C [15, 16, 18, 20, 21, 24, 25, 33, 36, 38–40, 44, 45, 52, 54–57]

PSS A [23, 25, 27, 28, 31–33, 36, 40, 44, 46, 48, 50, 52–54]

PDDA C [22, 23, 26–28, 30–32, 34, 35, 43, 46–51, 53]

47, 49, 51, 55, 57]

Pavoor et al. [15, 57] investigated the tribological behavior of PAH/PAA film on UHMWPE. To examine the behavior of PEM structure in the presence of biological lubricant solution, PAH/PAA film with PAA as the last adsorbed polyelectrolyte is used. The lubricant solution was prepared by diluting the bovine calf serum to a protein concentration of 23 g/L, contain‐ ing 20 mMol of the sodium salt of ethylenediaminetetraacetic acid (EDTA) and 0.2% by weight of sodium azide. Moreover, a film with PAH as the last adsorbed layer was also investigated. For film with different periods of time immersing in the lubricant solution, the average thick‐ ness after immersion was observed by using a profilometer (as shown in **Figure 3**). It shows that a slight decrease in thickness was observed initially for the PAA‐topped layer films, but without an obvious effect on the thickness for the PAH adsorbed last. The corresponding friction tests show that the average friction coefficient slightly increased after PEMs depos‐ ited on UHMWPE surface. But the use of the PAH/PAA film reduced ultra‐high molecular weight polyethylene (UHMWPE) wear by up to 33% compared with the uncoated sample. Furthermore, the capacity for PEM‐induced wear reduction was confirmed at larger scales of tests in the dry state a pin on disk tester [57].

It is well known that the mechanical properties influence the tribological behavior of lubri‐ cant. Pavoor et al. [16] investigated the mechanical characteristics of PAH/PAA PEMs using nanoindentation tester. The elastic modulus and hardness of the films were demonstrably

**Figure 3.** Average PEM thickness (on glass substrates) after immersion in bovine calf serum–containing lubricant for different times (adapted from Ref. [15]).

free of the influence by the underlying supporting material. The mechanical properties of these PEMs can be altered significantly by varying the pH values of the PAH and PAA assem‐ bly solutions. Furthermore, in the dry state, the PEM behaviors are virtually unaffected by whether the linkages among the functional groups of the parent polyelectrolytes are ionic or covalent in nature. The essence of mechanical strength of PEMs lies in the linkage density in the film. The modulus values of these interpenetrated polyelectrolyte structures in the swol‐ len state (in water) are about two orders of magnitude lower than the corresponding values in dry conditions. Then, in the swollen state, chemical cross‐links do augment the modulus val‐ ues due to the smaller amount of water uptake in cross‐linked PEMs. Gao et al. [58] composed capsules of PSS/PDDA using layer‐by‐layer deposition on melamine formaldehyde colloidal templates. The results indicated that the elasticity modulus of the PSS/PDDA multilayer as obtained by the osmotic pressure method is 136 MPa, which is considerably smaller than that of the PSS/PAH PEMs. The apparent difference between the PSS/PAH capsules and PSS/ PDDA capsules with regard to their stability and elasticity is explained as the result of the dif‐ ferent chemical nature of PAH and PDDA. It is due to an overall weaker interaction between PDDA and PSS compared with the PAH and PSS interaction.

## **3. Effect of nanoparticle doped into PEMs**

In recent years, nanoparticles composite ultrathin films have increasingly attracted a wide attention. Due to the assemble characteristic of PEMs, many nanoparticles as formation mate‐ rials were introduced for preparing composite PEMs. **Table 2** lists the different nanoparti‐ cles used to prepare nanoparticles‐doped PEMs. For example, Cassagneau et al. synthesized nanoparticles or nanoplates and used these nanoparticles to prepare composite multilayers [59, 60]. Feng et al. [56] prepared surface‐charged graphite oxide (GO) solution and formed PAH/GO multilayers by layer‐by‐layer method. Furthermore, they synthesized PAA‐coated


**Table 2.** Summary of different nanoparticles used to prepare nanoparticle‐doped PEMs.

TiO2 nanoparticles and prepared PAH/PAA(TiO<sup>2</sup> ) multilayers by using the same method [18]. Nanocomposite (PAH‐PSS) containing Au or Ag film was fabricated on a silicon substrate using spin‐assisted layer‐by‐layer self‐assembly technique [52, 54] where the fabrication pro‐ cess is shown in **Figure 4**. Xiao et al. [30] synthesized sodium citrate‐protected silver nanopar‐ ticles and prepared PDDA/Ag composite films. AFM images indicated that the additional nanoparticles were formed on the substrate. With the number of deposited cycles and increas‐ ing deposition time, the particles show an obvious tendency to aggregate, and large particle clusters are observed in the sample.

free of the influence by the underlying supporting material. The mechanical properties of these PEMs can be altered significantly by varying the pH values of the PAH and PAA assem‐ bly solutions. Furthermore, in the dry state, the PEM behaviors are virtually unaffected by whether the linkages among the functional groups of the parent polyelectrolytes are ionic or covalent in nature. The essence of mechanical strength of PEMs lies in the linkage density in the film. The modulus values of these interpenetrated polyelectrolyte structures in the swol‐ len state (in water) are about two orders of magnitude lower than the corresponding values in dry conditions. Then, in the swollen state, chemical cross‐links do augment the modulus val‐ ues due to the smaller amount of water uptake in cross‐linked PEMs. Gao et al. [58] composed capsules of PSS/PDDA using layer‐by‐layer deposition on melamine formaldehyde colloidal templates. The results indicated that the elasticity modulus of the PSS/PDDA multilayer as obtained by the osmotic pressure method is 136 MPa, which is considerably smaller than that of the PSS/PAH PEMs. The apparent difference between the PSS/PAH capsules and PSS/ PDDA capsules with regard to their stability and elasticity is explained as the result of the dif‐ ferent chemical nature of PAH and PDDA. It is due to an overall weaker interaction between

In recent years, nanoparticles composite ultrathin films have increasingly attracted a wide attention. Due to the assemble characteristic of PEMs, many nanoparticles as formation mate‐ rials were introduced for preparing composite PEMs. **Table 2** lists the different nanoparti‐ cles used to prepare nanoparticles‐doped PEMs. For example, Cassagneau et al. synthesized nanoparticles or nanoplates and used these nanoparticles to prepare composite multilayers [59, 60]. Feng et al. [56] prepared surface‐charged graphite oxide (GO) solution and formed PAH/GO multilayers by layer‐by‐layer method. Furthermore, they synthesized PAA‐coated

PDDA and PSS compared with the PAH and PSS interaction.

**Nanoparticles/nanoplates Abbreviation References** Titanium dioxide TiO2 [18, 56, 59] Graphite oxide GO [18, 60] Silicon dioxide SiO2 [20]

Copper Cu [23, 32, 48, 53] Copper sulfide CuS [22, 35, 43, 49, 51] Zinc sulfide ZnS [47, 49, 66] Copper hydroxide Cu(OH)2 [50, 69] Rare earth RE [36]

**Table 2.** Summary of different nanoparticles used to prepare nanoparticle‐doped PEMs.

Silver Ag [21, 30, 34, 46, 54, 61, 65, 68] Gold Au (or complex) [34, 46, 52, 55, 64, 67]

**3. Effect of nanoparticle doped into PEMs**

260 Nanoscaled Films and Layers

The above‐mentioned method as commonly used step is that the prepared nanoparticles or nanoplatelets (surface modified) were processed using surface modification firstly, and then the substrates were coated by nanoparticles or nanoplatelets and polymers layer by layer using molecular deposition method. However, it is difficult to prepare nanoparticles composite MD films using the above‐mentioned steps, since it is difficult to control the size of nanoparticles, preventing the reunion of nanoparticles and making the nanoparticles dispersed in the film uniformity. Recently, polyelectrolyte multilayers have emerged as a useful vessel for novel nanomaterial synthesis [61–64]. The studies show that various nanomaterials with desirable shape and composition can be synthesized by loading the reactants into the PEMs interior and then performing appropriate reactions such as reduction, sulfuration, and so on. This reaction can be called as in situ synthesis. Logar et al. [65, 66] has synthesized the Ag and ZnS nanopar‐ ticles in situ in PAH/PAA PEMs. Gold nanoparticles could be synthesized in the PEMs [67]. This indicated that the in situ nucleation and growth of nanoparticles appeared in PEM films. This technique can be used for synthesizing nanoparticles in the polymer structure domain as nanoreactor that can bind metal cations from an aqueous solution. Then, the postbind‐ ing chemistries include reduction, hydroxide, sulfidation, and growth nanoparticles from the cationic precursors [49, 50, 68]. For instance, the schematic diagram of the preparation process of in situ CuS/ZnS nanoparticles hybrid PEMs is shown in **Figure 5**.

**Figure 4.** Schematic of fabrication of silver nanoparticle‐polyelectrolyte multilayers (redrawn from Refs. [52] and [54]).

**Figure 5.** The schematic diagram of preparation of in situ CuS/ZnS nanoparticles hybrid polyelectrolyte multilayer thin film (adapted from Ref. [49]).

Moreover, some polyelectrolyte solution mixed with metal ions can form polymer complexes. The study shows that the in situ gold and silver nanoparticles in polyelectrolyte multilayer film can be prepared by alternate immersion of a substrate in PDDA‐AuCl4− complexes solu‐ tion and PAA‐Ag<sup>+</sup> complexes solution followed by the reduction of the metal cations (Au3+, Ag<sup>+</sup> ) through immersion of NaBH4 solution [34]. The AFM, SEM, TEM, XPS, and UV‐vis spec‐ trum measurements demonstrated the Au and Ag nanoparticles distributed in the polyelec‐ trolyte multilayers uniformly.

The tribological properties of nanoparticles‐doped composite PEMs were investigated by microtribometer [21–23, 52–56]. The statistic results of friction and wear behaviors are shown in **Figure 6**. It can be seen that the friction coefficient of nanoparticles‐doped composite PEMs has a slight decrease compared with pure PEMs (contrast **Figure 2**). However, the antiwear life has an obvious improvement with nanoparticles hybrid into PEM films. The antiwear life (sliding time or reciprocation cycles) was determined by the time or cycles when the friction coefficient increased sharply. The results indicated that the PEMs filled with nanoparticles showed better tribological performance than the pristine PEMs. This is quite evident that nanoparticles within the PEMs can enhance antiwear life of PEMs. From the tribometer tests, this is due to the nanoparticles possessing good load‐carrying capacity and decreasing the mobility of the polymer‐chain segments which can undergo reversible shear deformation, and the higher shear force must be overcome during relative motion, which results in the increased friction coefficient and shorter antiwear life.

**Figure 6.** Tribological performance comparison based on different nanoparticle‐doped PEMs: (a) average friction coefficient and (b) antiwear enhancement.

More recently, Yang and Guo researched the tribological properties of PEMs filled with in situ nanoparticles. Some conclusions were presented. The in situ nanoparticles exhibited higher durability because of the inorganic nanoparticles enhancing the load‐carrying capacity. The main wear mechanism was adhesive wear, and the in situ nanoparticles mitigated plastic defor‐ mation and slowed down adhesive wear [69]. AFM has been used extensively to measure adhe‐ sive force between surfaces at nanoscale. The surface adhesive force is between the AFM tip and the film surface by force‐curves mode under ambient condition. AFM tests showed that the adhesive forces between the probe and the sample surface decreased, indicating that the surface interactions between the probe and the sample are reduced by compositing in situ nanopar‐ ticles [22, 49]. The adhesive force is mainly dependent on the surface interaction between the probe and the sample surfaces. It is well known that, when the surface is hydrophilic, they would easily form meniscus by adsorbed water molecules in air, thus they had higher adhesive force. From the ultrapure water‐contact angle measurement, the nanoparticles‐filled PEMs film was more hydrophobic than the pristine PEM film and show a lower surface adhesion.

Moreover, some polyelectrolyte solution mixed with metal ions can form polymer complexes. The study shows that the in situ gold and silver nanoparticles in polyelectrolyte multilayer film can be prepared by alternate immersion of a substrate in PDDA‐AuCl4− complexes solu‐

**Figure 5.** The schematic diagram of preparation of in situ CuS/ZnS nanoparticles hybrid polyelectrolyte multilayer thin

trum measurements demonstrated the Au and Ag nanoparticles distributed in the polyelec‐

The tribological properties of nanoparticles‐doped composite PEMs were investigated by microtribometer [21–23, 52–56]. The statistic results of friction and wear behaviors are shown in **Figure 6**. It can be seen that the friction coefficient of nanoparticles‐doped composite PEMs has a slight decrease compared with pure PEMs (contrast **Figure 2**). However, the antiwear life has an obvious improvement with nanoparticles hybrid into PEM films. The antiwear life (sliding time or reciprocation cycles) was determined by the time or cycles when the friction coefficient increased sharply. The results indicated that the PEMs filled with nanoparticles showed better tribological performance than the pristine PEMs. This is quite evident that nanoparticles within the PEMs can enhance antiwear life of PEMs. From the tribometer tests, this is due to the nanoparticles possessing good load‐carrying capacity and decreasing the mobility of the polymer‐chain segments which can undergo reversible shear deformation, and the higher shear force must be overcome during relative motion, which results in the

complexes solution followed by the reduction of the metal cations (Au3+,

solution [34]. The AFM, SEM, TEM, XPS, and UV‐vis spec‐

tion and PAA‐Ag<sup>+</sup>

film (adapted from Ref. [49]).

262 Nanoscaled Films and Layers

) through immersion of NaBH4

increased friction coefficient and shorter antiwear life.

trolyte multilayers uniformly.

Ag<sup>+</sup>

Surface wettability of a solid surface can be controlled by two factors: one is the change and design of geometrical structure (such as surface roughness) in micro‐ or nanosurface structure [70–72]; the other is surface modification with chemical component (surface‐free energy) [73, 74]. Therefore, hydrophobic surfaces can be obtained by using low surface energy materials such as fluoroalkylsilane [75, 76] and wax [77, 78]. In the meantime, the hydrophobicity of the surface can also be increased by enhancing surface roughness [79]. The previous study shows that the surface wetting and adhesion can be changed by using layer‐by‐layer method [80]. These surface properties have an effect on the tribological behavior of PEMs. A 4.5‐bilayer PDDA/PSS PEM on quartz or silicon plate was prepared by spin‐assisted layer‐by‐layer assembly technique. Then, PDDA/PSS doped with Cu nanoparticles was built by immersing PDDA/PSS PEMs in Cu2+ and NaBH4 solutions to allow nucleation of Cu nanoparticles [23]. The relationship between water wettability and tribological properties of PDDA/PSS doped with Cu nanoparticles films showed that the adhesion and tribological behavior were closely related to their wettability. That is, the PEMs with stronger hydrophobicity have a lower sur‐ face energy, which show a lower friction and longer antiwear life. Guo et al. [36] fabricated lanthanum hybrid PEMs using the layer‐by‐layer and self‐assembly methods. The (PAH/PSS)/ RE film has a larger water‐contact angle and lower surface energy than PAH/PSS PEMs. The microtribology study showed that the (PAH/PSS)/RE film with a very low friction coefficient of about 0.09 and a longer antiwear life was obtained than that for the pure PAH/PSS film.

## **4. Nanotribology of PEMs**

The PEMs are desired for the application of MEMS to reduce the adhesion and friction. AFM is a mighty instrument for investigating the nanotribological behavior of PEMs. Wang et al. [4] have investigated the nanotribological of different molecular deposition films by AFM. The test results showed that the process of the anionning and the depositing of a monolayer molecular film on an Au substrate and the process of decorating an alkyl‐terminal to molecu‐ lar deposition film surfaces were all capable of lowering the frictional force and improving the nanolubrication property. Moreover, the film decorated with alkyl chains had lower frictional forces than the undecorated films. Accordingly, it provided a significant thought to seek for a new nanolubrication film. Zhang et al. [18] investigated the surface roughness, hardness, and nanofriction force of PAH/GO and PAH/PAA(TiO<sup>2</sup> ) PEMs. Both of them were heated to change the film forming dynamic force from electrostatic force to covalent bond so as to increase the bonding strength of the films. The surface roughness increased, and the fric‐ tion force was significantly decreased after heating for PAH/GO PEMs. However, the surface roughness and nanofriction force of PAH/PAA(TiO<sup>2</sup> ) PEMs both decreased slightly after heat‐ ing. The AFM images of the five‐layer PAH/PAA(TiO<sup>2</sup> ) before and after heating are shown in **Figure 7**. It was found that these films had a much smaller friction force than their substrates and the friction force was dependent on the morphology and/or hardness of the films.

The nanofriction coefficient of the PDDA/GO was found to decrease with increasing load. However, the decrease in nanofriction coefficient reduced noticeably and maintained if the load was beyond a specific value [81]. The effect of load on nanofrictional properties of dif‐ ferent Ag nanoparticles‐doped PEMs, whose number of bilayers was one to five, respectively, was investigated by Guo et al. [21]. The nanofriction increased linearly for different bilayer composite PEMs with the increasing load. With the bilayer number (thickness) increasing, the fitting friction coefficient decreased slightly from 0.06 (one and two bilayers) to 0.05 (three to five bilayers).

**Figure 7.** AFM images of five‐layer PAH/PAA(TiO<sup>2</sup> ) before (a) and after (b) heating (adapted from Ref. [18]).

The effects of scanning speed of AFM tip on the nanotribological behavior of PEMs were investigated [30]. All the substrates deposited with PDDA/Ag film were found with a lower nanofriction force than the clean substrate at different scanning speeds with a normal load of 5 nA. And with the increase of the scan rate, the increasing amplitude of the friction force of all the films was apparently less than that of the clean substrate. It might be concluded that the films decrease the adhesion force of the substrates. Also, the friction force of the trilayer film was the smallest. This was corresponding with the surface roughness. In these experiments, the surface roughness of trilayer film was the smallest among the films.

microtribology study showed that the (PAH/PSS)/RE film with a very low friction coefficient of about 0.09 and a longer antiwear life was obtained than that for the pure PAH/PSS film.

The PEMs are desired for the application of MEMS to reduce the adhesion and friction. AFM is a mighty instrument for investigating the nanotribological behavior of PEMs. Wang et al. [4] have investigated the nanotribological of different molecular deposition films by AFM. The test results showed that the process of the anionning and the depositing of a monolayer molecular film on an Au substrate and the process of decorating an alkyl‐terminal to molecu‐ lar deposition film surfaces were all capable of lowering the frictional force and improving the nanolubrication property. Moreover, the film decorated with alkyl chains had lower frictional forces than the undecorated films. Accordingly, it provided a significant thought to seek for a new nanolubrication film. Zhang et al. [18] investigated the surface roughness, hardness,

to change the film forming dynamic force from electrostatic force to covalent bond so as to increase the bonding strength of the films. The surface roughness increased, and the fric‐ tion force was significantly decreased after heating for PAH/GO PEMs. However, the surface

**Figure 7**. It was found that these films had a much smaller friction force than their substrates

The nanofriction coefficient of the PDDA/GO was found to decrease with increasing load. However, the decrease in nanofriction coefficient reduced noticeably and maintained if the load was beyond a specific value [81]. The effect of load on nanofrictional properties of dif‐ ferent Ag nanoparticles‐doped PEMs, whose number of bilayers was one to five, respectively, was investigated by Guo et al. [21]. The nanofriction increased linearly for different bilayer composite PEMs with the increasing load. With the bilayer number (thickness) increasing, the fitting friction coefficient decreased slightly from 0.06 (one and two bilayers) to 0.05 (three to

and the friction force was dependent on the morphology and/or hardness of the films.

) PEMs. Both of them were heated

) PEMs both decreased slightly after heat‐

) before (a) and after (b) heating (adapted from Ref. [18]).

) before and after heating are shown in

**4. Nanotribology of PEMs**

264 Nanoscaled Films and Layers

and nanofriction force of PAH/GO and PAH/PAA(TiO<sup>2</sup>

roughness and nanofriction force of PAH/PAA(TiO<sup>2</sup>

**Figure 7.** AFM images of five‐layer PAH/PAA(TiO<sup>2</sup>

five bilayers).

ing. The AFM images of the five‐layer PAH/PAA(TiO<sup>2</sup>

Guo et al. [43] prepared PDDA/PAA and containing CuS PEMs on quartz and glass sub‐ strates. It was found that the CuS nanoparticles were homogeneously distributed throughout the whole film. And these films had a much smaller friction force than their substrates and higher antiwear life than pristine PDDA/PAA PEMs. **Figure 8** shows the surface wearing capacity of the pristine and CuS nanoparticles‐doped PEMs. From the wear tests, it can be found that the wearing capacity increases with the times of reciprocating scan with AFM tip. The pristine PEM's antiwear capacity is lower than that of the CuS nanoparticles‐doped PEMs. From the curves, the wearing capacity of pristine PEMs was about 90 scanning times. But the CuS nanoparticles‐doped PEMs have not been destroyed after 100 scanning times. Moreover, they also prepared the in situ Au nanoparticles hybrid PEMs [55]. The nanotri‐ bological investigation showed that the PAH/PAA PEMs with in situ Au nanoparticles have a lower surface adhesion and friction force than the pure PAH/PAA PEMs. It is due to the nanoparticles in situ synthesized in polyelectrolyte multilayers making the surface morphol‐ ogy change and load‐carrying capacity to increase. Under a normal load, the pure PAH/PAA multilayer deformation against a probe tip was larger than the PAH‐Au/PAA film. From the friction force tests, it can be found that the PEMs with in situ nanoparticles exert good load capacity. Therefore, a slight and gradual increase of friction forces could be observed. Furthermore, with the increasing of normal load, the deformation of pure PAH/PAA PEMs enhanced, which caused the friction force to increase.

**Figure 8.** The surface‐wearing capacity of pristine and CuS nanoparticle‐doped PEMs (adapted from Ref. [43]).

## **5. Conclusions**

Very promising prospects for the tribological application of PEM films have been put forward by recent research. The investigation of PEMs has been extended due to their modification of substrate and reduction of surface friction performance. However, some challenges still exist in applying PEM films into practical application. Thus, for preparing more varieties of PEM films that have better tribological performance and promote the use of PEMs in MEMS or NEMS, some key problems in the research of PEMs should be addressed, such as optimizing conditions of preparation, improvement of the antiwear performance, friction and antiwear mechanism, as well as clarifying the parameters influencing the tribological properties of PEM films. Some new nanolubricant materials could be introduced into PEMs to improve the tribological behavior of PEMs, thereby enhancing the bonding strength between layers and substrates to further improve the antiwear life. Furthermore, more attention needs to be paid to research the antifriction, antiwear, and repair mechanism of in situ nanoparticles‐doped PEMs, as well as the tribological investigation in different conditions, such as atmosphere, liquid medium, and so on in order to assess the application prospect of these PEM films.

## **Acknowledgements**

This research is supported by the Beijing Natural Science Foundation (No. 3162024), the National Natural Science Foundation of China (No. 51305459), Tribology Science Foundation of the State Key laboratory of Tribology (No. SKLTKF14A08), and the Science Foundation of China University of Petroleum, Beijing (Nos. 2462017BJB06, C201602).

## **Author details**

Yanbao Guo1,2\* and Deguo Wang1,2

\*Address all correspondence to: gyb@cup.edu.cn

1 College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing, China

2 Beijing Key Laboratory of Process Fluid Filtration and Separation, Beijing, China

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**5. Conclusions**

266 Nanoscaled Films and Layers

**Acknowledgements**

**Author details**

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Yanbao Guo1,2\* and Deguo Wang1,2

\*Address all correspondence to: gyb@cup.edu.cn

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Yi Zheng

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Nanostructured Layered Media

http://dx.doi.org/10.5772/67395 Additional information is available at the end of the chapter

### Abstract

Thermal radiative transport yields unique thermal characteristics of microscopic thin films—wavelength selectivity. This chapter focuses on a methodology about adjusting the wavelength selectivity of thin films embedded with nanoparticles in the far-field and near-field regimes. For nanostructured layered media doped with nanoparticles, Maxwell-Garnett-Mie theory is applied to determine the effective dielectric function for the calculation of radiative thermal transport. The thermal radiative wavelength selectivity can be affected by volume fraction and/or the size of the embedded nanoparticles in thin films. To characterize wavelength selectivity and optical property of nanostructured materials, both real and imaginary parts of effective refractive index need to be analyzed. It has been shown that the nanoparticles made of polar or metallic materials have different influence on thermal radiative wavelength selectivity of microscopic thin films.

Keywords: thermal radiation, wavelength-selective, far field, near field, nanostructured layered media

## 1. Introduction

Most naturally occurring materials exhibit a broad range of emission spectrum. However, thermal and optical properties of nanomaterials and nanostructures are significantly different than that of bulk materials. They are the basis of development of selective thermal emitters and absorbers that are crucial for the development of solar cells and thermophotovoltaics (TPVs) [1]. Wavelength-selective emitters also have a wide range of potential applications such as biosensors, chemical sensors [2, 3], thermal cooling, and thermal detectors [4]. It has been shown that one-dimensional (1-D) metallo-dielectric periodic structures display great selective

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

emission properties in the infrared and visible regions [5]. Multilayered structures of thin films (1-D photonic crystals) of polar materials can also be used to develop selective emitters [6]. The property of multilayered structures to exhibit wavelength selectivity can be explained by the presence of surface phonon polaritons (SPhPs) for polar materials and surface plasmon polaritons (SPPs) for metals [5, 7]. It has also been demonstrated that two-dimensional (2-D) or three-dimensional (3-D) photonic crystals can be used to develop selective emitters [8, 9]. However, thin-film-layered structures are easy to design and fabricate. Calculation of their emission spectra is also relatively simple.

Wavelength selectivity of 1-D photonic crystals is a far-field phenomenon. When the distance between two objects is of the order of the dominant thermal wavelength, the radiative heat transfer is enhanced to many orders of magnitude due to the coupling of surface waves and is referred to as near-field thermal radiation [10]. If the materials support SPhPs or SPPs, the near-field radiative flux can be shown to be inversely proportional to the square of the distance. The enhancement of heat transfer does not take place at all wavelengths but only at specific wavelengths [10]. This wavelength selectivity in the near field is exhibited by thin films as well as bulk materials. Wavelength selectivity in the near-field limit is due to the coupling of SPPs or SPhPs across the two surfaces [10].

While many articles dedicated to the design and fabrication of selective emitters can be found in the literature, the use of nanoparticles specifically for the application of selective emitters is relatively sparse [11]. Optical properties of materials doped with nanoparticles have been investigated before [12, 13]. Experimental and analytical study of thermal coatings doped with nanoparticles such as Gonome et al. [14, 15] can also be found in literature. However, emissive properties of nanoparticles embedded thin films have not been studied in detail to the best of our knowledge. This chapter presents the multilayered structures, which contain nanoparticles (NPs) doped into the thin films, which are suitable for any of the potential applications in both the far field and the near field. In this chapter, we investigate a methodology that can be used to develop selective thermal emitters for a desired wavelength band. Ideally, one may want to develop a selective emitter for specific wavelength band as per the requirements. As the emission spectrum displays peaks at the wavelengths, which are characteristics of the refractive index of the material, changing the thickness of the film allows control over only a narrow spectral band. We propose to dope the top layer (thin film) with nanoparticles to change the dielectric properties of the material. The usual Maxwell-Garnett equation for effective medium approximation is often employed for such an analysis disregarding the sizes of doped materials [16]. Here, we apply the Maxwell-Garnett-Mie formulation [17] for effective medium approximation to calculate the dielectric function of a composite that consists of a host material embedded with nanoparticles of various sizes and volume fractions, and extend the same approach to calculate radiative heat transfer for thin films doped with nanoparticles. Thin-film structure with nanoparticles would be easy to fabricate as submicron thin films embedded with nanoparticles have been fabricated before [18, 19]. We aim to study the effect on the wavelength selectivity of thin films due to combination of surface polaritons of the films and the nanoparticles and their effects in the near-field radiative heat transfer and spectral heat flux. We consider hypothetical cases of thin film embedded with nanoparticles although the fabrication of these particular NP-embedded films discussed here is relatively unknown. We choose SiC and polystyrene (PS) as the host materials (for thin films). SiC is chosen as a host because it has high permittivity in the infrared region and supports SPhP. Polystyrene is chosen because it does not support either SPPs or SPhPs. BN, which supports SPhP, and Au, which supports SPPs, are picked for the material of inclusion (NPs).

The structure of this chapter is as follows. In Section 2, we present the theoretical background and analytical expressions used for the calculation of emissivity of thin-film structures, calculation of heat transfer between closely placed half spaces, and the application of Maxwell-Garnett-Mie theory. In Section 3, we discuss the results of our calculations obtained using the formulations outlined in Section 2. Subsequently, the ideas and conclusions of this chapter are narrated in Section 4.

## 2. Theoretical fundamentals

emission properties in the infrared and visible regions [5]. Multilayered structures of thin films (1-D photonic crystals) of polar materials can also be used to develop selective emitters [6]. The property of multilayered structures to exhibit wavelength selectivity can be explained by the presence of surface phonon polaritons (SPhPs) for polar materials and surface plasmon polaritons (SPPs) for metals [5, 7]. It has also been demonstrated that two-dimensional (2-D) or three-dimensional (3-D) photonic crystals can be used to develop selective emitters [8, 9]. However, thin-film-layered structures are easy to design and fabricate. Calculation of their

Wavelength selectivity of 1-D photonic crystals is a far-field phenomenon. When the distance between two objects is of the order of the dominant thermal wavelength, the radiative heat transfer is enhanced to many orders of magnitude due to the coupling of surface waves and is referred to as near-field thermal radiation [10]. If the materials support SPhPs or SPPs, the near-field radiative flux can be shown to be inversely proportional to the square of the distance. The enhancement of heat transfer does not take place at all wavelengths but only at specific wavelengths [10]. This wavelength selectivity in the near field is exhibited by thin films as well as bulk materials. Wavelength selectivity in the near-field limit is due to the coupling of

While many articles dedicated to the design and fabrication of selective emitters can be found in the literature, the use of nanoparticles specifically for the application of selective emitters is relatively sparse [11]. Optical properties of materials doped with nanoparticles have been investigated before [12, 13]. Experimental and analytical study of thermal coatings doped with nanoparticles such as Gonome et al. [14, 15] can also be found in literature. However, emissive properties of nanoparticles embedded thin films have not been studied in detail to the best of our knowledge. This chapter presents the multilayered structures, which contain nanoparticles (NPs) doped into the thin films, which are suitable for any of the potential applications in both the far field and the near field. In this chapter, we investigate a methodology that can be used to develop selective thermal emitters for a desired wavelength band. Ideally, one may want to develop a selective emitter for specific wavelength band as per the requirements. As the emission spectrum displays peaks at the wavelengths, which are characteristics of the refractive index of the material, changing the thickness of the film allows control over only a narrow spectral band. We propose to dope the top layer (thin film) with nanoparticles to change the dielectric properties of the material. The usual Maxwell-Garnett equation for effective medium approximation is often employed for such an analysis disregarding the sizes of doped materials [16]. Here, we apply the Maxwell-Garnett-Mie formulation [17] for effective medium approximation to calculate the dielectric function of a composite that consists of a host material embedded with nanoparticles of various sizes and volume fractions, and extend the same approach to calculate radiative heat transfer for thin films doped with nanoparticles. Thin-film structure with nanoparticles would be easy to fabricate as submicron thin films embedded with nanoparticles have been fabricated before [18, 19]. We aim to study the effect on the wavelength selectivity of thin films due to combination of surface polaritons of the films and the nanoparticles and their effects in the near-field radiative heat transfer and spectral heat flux. We consider hypothetical cases of thin film embedded with nanoparticles although the

emission spectra is also relatively simple.

274 Nanoscaled Films and Layers

SPPs or SPhPs across the two surfaces [10].

Consider a structure having N-layer media having (N - 1) interfaces. By solving the boundary conditions at the interfaces, one can obtain the expression for the generalized reflection coefficient at the interface between region i and region i + 1 and is given by [20]

$$\tilde{\mathcal{R}}\_{i,i+1}^{(\mu)} = \frac{\mathcal{R}\_{i,i+1}^{(\mu)} + \tilde{\mathcal{R}}\_{i+1,i+2}^{(\mu)} e^{2jk\_{i+1,z}(d\_{i+1} - d\_i)}}{1 + \mathcal{R}\_{i,i+1}^{(\mu)} \tilde{\mathcal{R}}\_{i+1,i+2}^{(\mu)} e^{2jk\_{i+1,z}(d\_{i+1} - d\_i)}} \tag{1}$$

where <sup>j</sup> <sup>¼</sup> ffiffiffiffiffiffi �<sup>1</sup> <sup>p</sup> , <sup>R</sup><sup>ð</sup>μ<sup>Þ</sup> <sup>i</sup>,iþ<sup>1</sup> is the Fresnel reflection coefficient at the interface between the layer <sup>i</sup> and <sup>i</sup> + 1, and <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>i</sup>þ1,iþ<sup>2</sup> is the generalized reflection coefficient at the interface between the layer i + 1 and i + 2, μ = s (or p) refers to transverse electric (or magnetic) polarization, z = - di is the location of the ith interface. ki, <sup>z</sup> ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi εiðωÞω<sup>2</sup>=c<sup>2</sup> � k 2 ρ q is the normal z-component of the wave vector in medium i wherein εiðωÞ is the relative permittivity of the medium i as a function of angular frequency ω, c is the speed of light in vacuum, and k<sup>ρ</sup> is the magnitude of the in-plane wave vector. With <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>N</sup>,Nþ<sup>1</sup> = 0, the above equation provides a recursive relation to calculate the reflection coefficients <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>i</sup>,iþ<sup>1</sup> in all regions. The generalized transmission coefficient for the layered slab is given by

$$\tilde{T}\_{1,N}^{(\mu)} = \prod\_{i=1}^{N-1} e^{2jk\_{\bar{\alpha}}(d\_i - d\_{i-1})} S\_{i,i+1}^{(\mu)} \tag{2}$$

where S<sup>ð</sup>μ<sup>Þ</sup> <sup>i</sup>,iþ<sup>1</sup> <sup>¼</sup> <sup>T</sup><sup>ð</sup>μ<sup>Þ</sup> <sup>i</sup>,iþ<sup>1</sup><sup>=</sup> � <sup>1</sup> � <sup>R</sup><sup>ð</sup>μ<sup>Þ</sup> <sup>i</sup>,iþ<sup>1</sup>R~<sup>i</sup>þ1,iþ<sup>2</sup>ðμÞe<sup>2</sup>jkiþ<sup>1</sup>, <sup>z</sup> <sup>ð</sup>diþ1�di<sup>Þ</sup> � . Alternatively, the generalized reflection and transmission coefficients can also be calculated using transfer matrix approach [21]. The hemispherical emissivity is given by the expression [6]

$$e(\omega) = \frac{c^2}{\omega^2} \int\_0^{\omega/c} dk\_\rho k\_\rho \sum\_{\mu=s,p} \left( 1 - \left| \begin{matrix} \hat{R} \\ h1 \end{matrix} \right|^2 - \left| \begin{matrix} \hat{T} \\ h1 \end{matrix} \right|^2 \right) \tag{3}$$

where <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>h</sup><sup>1</sup> and <sup>T</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>h</sup><sup>1</sup> are the polarized effective reflection and transmission coefficients, respectively, as shown in Figure 1(a).

Far-field radiative heat transfer is described by Planck's law of thermal radiation [22]. This description, however, does not account for the presence of evanescent (surface) waves that dominate only near the boundaries. The expression of radiative transfer between closely spaced objects can be derived using dyadic Green's function formalism [23], and is given by

$$q\_{1\to 2}(T\_1, T\_2, L) = \bigcap\_{0}^{\prime \prime} \underline{\theta}(\omega, T\_1) - \theta(\omega, T\_2)[T\_{1\to 2}(\omega, L)] \tag{4}$$

where θðω, TÞ¼ðℏω=2Þcothðℏω=2kBTÞ is the energy of harmonic oscillator at frequency ω and temperature T, h is the reduced Planck constant, and kB is the Boltzmann constant. The function Tð1!2<sup>Þ</sup> (ω) corresponds to the spectral transmissivity in radiative transfer between media 1 and 2 separated by distance L and is expressed as [23]

$$\begin{split} T\_{1\rightarrow 2}(\omega) &= \int\_0^{\omega/c} \frac{dk\_\rho k\_\rho}{2\pi} \sum\_{\mu=s,\mu} \frac{\left(1 - \left|\tilde{\mathcal{R}}\_{h1}^{(\mu)}\right|\right)^2 \left(1 - \left|\tilde{\mathcal{R}}\_{h2}^{(\mu)}\right|\right)^2}{\left|1 - \tilde{\mathcal{R}}\_{h1}^{(\mu)}\tilde{\mathcal{R}}\_{h2}^{(\mu)} e^{2\tilde{\mathcal{R}}\_{h1}L}\right|^2} \\ &+ \int\_{\omega/c}^\omega \frac{dk\_\rho k\_\rho}{2\pi} \sum\_{\mu=s,\mu} \frac{4\text{Im}\left(\tilde{\mathcal{R}}\_{h1}^{(\mu)}\right) \text{Im}\left(\tilde{\mathcal{R}}\_{h2}^{(\mu)}\right) e^{-2|k\_\text{k}|L}}{\left|1 - \tilde{\mathcal{R}}\_{h1}^{(\mu)}\tilde{\mathcal{R}}\_{h2}^{(\mu)} e^{2\tilde{\mathcal{R}}\_{h2}L}\right|^2} \end{split} \tag{5}$$

where <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>h</sup><sup>1</sup> and <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>h</sup><sup>2</sup> are polarized khz effective reflection coefficients of the two half spaces (calculated in the absence of other half space) and is the z-component of wave vector in

Figure 1. Configurations of nanoparticle-embedded thin films. (a) Thin film of SiC or polystyrene (PS) on Au thin film of thickness 1 µm, and (b) two half spaces with multilayers with vacuum in between. The top is SiC or PS film embedded with nanoparticles of varying radius and volume fraction on Au thin film.

vacuum. The first term in Eq. (5) corresponds to propagating waves, whereas the second term describes the thermal transport due to evanescent waves, and its contribution is significant only for small values of gap L.

Clausius-Mossotti equation for the effective dielectric function, of the composite medium containing nanoparticle inclusions in a host material, is given by [24, 25]

$$
\varepsilon\_{\it eff} = \varepsilon\_m \left( \frac{r^3 + 2\alpha\_{\it} f}{r^3 - \alpha\_{\it} f} \right) \tag{6}
$$

where ε<sup>m</sup> is the dielectric function of the matrix, α<sup>r</sup> is the electric dipole polarizability, and r and f are the radius and volume fraction of nanoparticles, respectively. The size-dependent extension of Maxwell-Garnett formula can be obtained by deriving an expression for electric dipole polarizability using Mie theory [17]

$$\alpha\_r = \frac{3jc^3}{2\alpha^3 \varepsilon\_m^{3/2}} a\_{1,r} \tag{7}$$

where a1,<sup>r</sup> is the first electric Mie coefficient given by

<sup>e</sup>ðωÞ ¼ <sup>c</sup><sup>2</sup> ω2 ð ω=c

<sup>q</sup><sup>1</sup>!<sup>2</sup>ðT1, <sup>T</sup>2, <sup>L</sup>Þ ¼

media 1 and 2 separated by distance L and is expressed as [23]

ð ω=c

dkρk<sup>ρ</sup> 2π

> dkρk<sup>ρ</sup> 2π

X <sup>μ</sup>¼<sup>s</sup>, <sup>p</sup>

> X <sup>μ</sup>¼<sup>s</sup>, <sup>p</sup>

� 1 � � � � <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> h1 � � � �<sup>2</sup>� 1 � � � � <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> h2 � � � �2

> � � � <sup>1</sup> � <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>h</sup><sup>1</sup> <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>h</sup><sup>2</sup> e<sup>2</sup>jkhzL � � � 2

4Im � <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> h1 � Im � <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> h2 � e�2jkhz <sup>j</sup><sup>L</sup>

(calculated in the absence of other half space) and is the z-component of wave vector in

Figure 1. Configurations of nanoparticle-embedded thin films. (a) Thin film of SiC or polystyrene (PS) on Au thin film of thickness 1 µm, and (b) two half spaces with multilayers with vacuum in between. The top is SiC or PS film embedded

� � � <sup>1</sup> � <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>h</sup><sup>1</sup> <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> <sup>h</sup><sup>2</sup> e<sup>2</sup>jkhzL � � � 2

<sup>h</sup><sup>2</sup> are polarized khz effective reflection coefficients of the two half spaces

0

þ ð ∞

with nanoparticles of varying radius and volume fraction on Au thin film.

ω=c

T<sup>1</sup>!<sup>2</sup>ðωÞ ¼

where <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup>

276 Nanoscaled Films and Layers

where <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup>

<sup>h</sup><sup>1</sup> and <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup>

<sup>h</sup><sup>1</sup> and <sup>T</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup>

tively, as shown in Figure 1(a).

0

dkρk<sup>ρ</sup>

ð ∞

dω 2π

0

X <sup>μ</sup>¼<sup>s</sup>, <sup>p</sup> � 1 � � � � <sup>R</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> h1 � � � 2 � � � � <sup>T</sup><sup>~</sup> <sup>ð</sup>μ<sup>Þ</sup> h1 � � � 2�

Far-field radiative heat transfer is described by Planck's law of thermal radiation [22]. This description, however, does not account for the presence of evanescent (surface) waves that dominate only near the boundaries. The expression of radiative transfer between closely spaced objects can be derived using dyadic Green's function formalism [23], and is given by

where θðω, TÞ¼ðℏω=2Þcothðℏω=2kBTÞ is the energy of harmonic oscillator at frequency ω and temperature T, h is the reduced Planck constant, and kB is the Boltzmann constant. The function Tð1!2<sup>Þ</sup> (ω) corresponds to the spectral transmissivity in radiative transfer between

<sup>h</sup><sup>1</sup> are the polarized effective reflection and transmission coefficients, respec-

½θðω, T1Þ � θðω, T2Þ�T<sup>1</sup>!<sup>2</sup>ðω, LÞ (4)

(3)

(5)

$$a\_{1,r} = \frac{\sqrt{\varepsilon\_{\rm np}} \psi\_1(\mathbf{x\_{np}}) \psi\_1'(\mathbf{x\_m}) - \sqrt{\varepsilon\_m} \psi\_1(\mathbf{x\_m}) \psi\_1'(\mathbf{x\_{np}})}{\sqrt{\varepsilon\_{\rm np}} \psi\_1(\mathbf{x\_{np}}) \xi\_1'(\mathbf{x\_m}) - \sqrt{\varepsilon\_m} \xi\_1(\mathbf{x\_m}) \psi\_1'(\mathbf{x\_{np}})} \tag{8}$$

where ψ<sup>1</sup> and ξ<sup>1</sup> are Riccati-Bessel functions of the first order given by ψ<sup>1</sup> (x) = x j<sup>1</sup> (x) and ξ<sup>1</sup> (x) = xh<sup>ð</sup>1<sup>Þ</sup> <sup>1</sup> (x), where j <sup>1</sup> and h ð1Þ <sup>1</sup> are the first-order spherical Bessel functions and spherical Hankel functions of the first kind, respectively. Here, "'" indicates the first derivative. xm = ωr ffiffiffiffiffi εm <sup>p</sup> <sup>=</sup><sup>c</sup> and xnp <sup>=</sup> <sup>ω</sup><sup>r</sup> ffiffiffiffiffiffi εnp p =c are the size parameters of the matrix and the nanoparticles, respectively; εnp being the dielectric function of nanoparticles.

Effective medium approximation method is applicable when average distance between inclusions is much smaller than the wavelength of interest. If the dielectric inclusions of radius r can be imagined to be arranged in simple cubic lattice of lattice constant a, the condition for validity of the effective medium approximation is λ<sup>h</sup> >> a > 2r. Where λ<sup>h</sup> is the wavelength in the host material [26]. We emphasize that since we use the approximation for thin films doped with nanoparticles, its use may not be correct when the particle size is comparable to the thickness of the films. Also, as discussed by Liu et al. [27], it can be argued that the use of effective medium theory (EMT) is questionable at nanoscale distances. Although such might be the case for the near-field calculations presented here, its detailed analysis is beyond the scope of this work and is left for future work. Despite the limitations of Maxwell-Garnett-Mie theory sand its application in the near-field regime, the results obtained should provide general trends and give considerable insight into optical properties of artificial materials. Further investigations by direct numerical simulation may be necessary to confirm the validity of EMT [28]. Moreover, these results will be constructive when judging the validity of the EMT in the near field by direct numerical calculations. We would like to keep these points open for speculation.

### 3. Results

The dielectric function is related to real (n) and imaginary (κ) parts of refractive index as ffiffi <sup>ε</sup> <sup>p</sup> <sup>=</sup> n+jκ. For SiC and BN, the dielectric function has the form as [29, 30]

$$\varepsilon(\omega) = \varepsilon\_{\ast\ast} \left( \frac{\omega^2 - \omega\_{\rm LO}^2 + j\omega\gamma}{\omega^2 - \omega\_{\rm TO}^2 + j\omega\gamma} \right) \tag{9}$$

where ωTO and ωLO are transverse and longitudinal optical phonon frequencies, respectively, and γ is the damping constant. For SiC, the constants ε∞, ωTO, ωLO, and γ are equal to 6.7, 9.83 · 10-2 eV, 0.12 eV, and 5.90 · 10-2 eV, respectively. The values of ε∞, ωTO, ωLO, and γ for BN are 4.46, 0.1309 eV, 0.1616 eV, and 6.55 · 10-2 eV, respectively. Data for the bulk gold (Au) are taken from Johnson and Christy [31]. Figure 2(a) considers the case of SiC film doped with NPs of BN. SiC film of 0.4 µm is on the top of Au film of 1 µm deposited on a substrate. The effect of change in NPs volume fraction (f) is studied. The volume fraction of BN nanoparticles is changed from 0% to 30% while maintaining the radius of 25 nm. Thin film of pure SiC exhibits emission peaks at λSiC <sup>n</sup> ≈ 10.33 µm and λSiC <sup>n</sup> ≈ 13 µm. λ<sup>n</sup> is the wavelength at which the real part of the refractive index becomes zero (zero-index material) [6, 32]. λ<sup>κ</sup> is the wavelength at which the real part of refractive index (n) is large while the imaginary part of refractive index (κ) is small [6]. These peaks are attributed to the presence of SPhPs, and the characteristic wavelengths of the dielectric function of SiC. The appearance of new peaks upon 5% inclusion of BN nanoparticles has been observed at λ ≈ 8.5 µm and λ ≈ 11.5 µm. When the volume fraction of NPs is increased further, each of these peaks splits into two giving rise to a total of six peaks. Locations of these peaks do not correspond to the characteristic wavelengths of BN (λBN <sup>n</sup> ≈ 7.6 µm and λBN <sup>κ</sup> <sup>≈</sup> 9.8 µm). In addition, there exists a small shift in the emission peak at <sup>λ</sup>SiC <sup>κ</sup> . This suggests an interaction between SiC matrix and BN NPs. Consider the case with 30% inclusion of BN. Figure 3(a) shows that the mixture has two additional locations where the refractive index is zero (λmixture <sup>n</sup><sup>1</sup> ≈ 8.5 µm and λmixture <sup>n</sup><sup>2</sup> ≈ 11.7 µm). Moreover, at two more points n is large while imaginary part of refractive index is small, namely λmixture <sup>k</sup><sup>1</sup> ≈ 9 µm and λmixture <sup>k</sup><sup>2</sup> ≈ 11.1 µm.

These wavelengths correspond to the additional peaks. While the additional peaks are at the location of the characteristics of the refractive index of the mixture, it is interesting to note that peaks at ≈10.33 µm and ≈12.98 µm have no or little shift even at large volume fraction of 30%, because they are characteristic wavelengths of the host. Inclusion of BN leads to new SPhP leading to new peaks. Figure 2(b) shows the effect of Au nanoparticles in SiC thin film. When particle size is small, especially when the size is comparable to the mean free path of the free electrons, confinement effects become significant [25, 33]. The optical properties of metallic nanoparticles have shown size dependence [34]. We utilize a size-dependent dielectric function for Au nanoparticles of radius rthat takes care of electron scattering, which is given by [35]

$$\varepsilon(\omega, r) = \varepsilon\_b(\omega) + \frac{\omega\_p^2}{\omega^2 + j\omega\gamma\_0} - \frac{\omega\_p^2}{\omega^2 + j\omega(\gamma\_0 + A\nu\_f/r)}\tag{10}$$

where εb, ωp, vf , and γ<sup>0</sup> are the bulk dielectric function, the plasma frequency, the Fermi velocity of free electrons, and the electron damping, respectively. The values of ε<sup>b</sup> are taken

3. Results

278 Nanoscaled Films and Layers

exhibits emission peaks at λSiC

<sup>n</sup> ≈ 7.6 µm and λBN

<sup>n</sup><sup>1</sup> ≈ 8.5 µm and λmixture

imaginary part of refractive index is small, namely λmixture

εðω,rÞ ¼ εbðωÞ þ

ffiffi

(λBN

zero (λmixture

The dielectric function is related to real (n) and imaginary (κ) parts of refractive index as

<sup>ω</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup>

<sup>ω</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup>

where ωTO and ωLO are transverse and longitudinal optical phonon frequencies, respectively, and γ is the damping constant. For SiC, the constants ε∞, ωTO, ωLO, and γ are equal to 6.7, 9.83 · 10-2 eV, 0.12 eV, and 5.90 · 10-2 eV, respectively. The values of ε∞, ωTO, ωLO, and γ for BN are 4.46, 0.1309 eV, 0.1616 eV, and 6.55 · 10-2 eV, respectively. Data for the bulk gold (Au) are taken from Johnson and Christy [31]. Figure 2(a) considers the case of SiC film doped with NPs of BN. SiC film of 0.4 µm is on the top of Au film of 1 µm deposited on a substrate. The effect of change in NPs volume fraction (f) is studied. The volume fraction of BN nanoparticles is changed from 0% to 30% while maintaining the radius of 25 nm. Thin film of pure SiC

real part of the refractive index becomes zero (zero-index material) [6, 32]. λ<sup>κ</sup> is the wavelength at which the real part of refractive index (n) is large while the imaginary part of refractive index (κ) is small [6]. These peaks are attributed to the presence of SPhPs, and the characteristic wavelengths of the dielectric function of SiC. The appearance of new peaks upon 5% inclusion of BN nanoparticles has been observed at λ ≈ 8.5 µm and λ ≈ 11.5 µm. When the volume fraction of NPs is increased further, each of these peaks splits into two giving rise to a total of six peaks. Locations of these peaks do not correspond to the characteristic wavelengths of BN

This suggests an interaction between SiC matrix and BN NPs. Consider the case with 30% inclusion of BN. Figure 3(a) shows that the mixture has two additional locations where the refractive index is

These wavelengths correspond to the additional peaks. While the additional peaks are at the location of the characteristics of the refractive index of the mixture, it is interesting to note that peaks at ≈10.33 µm and ≈12.98 µm have no or little shift even at large volume fraction of 30%, because they are characteristic wavelengths of the host. Inclusion of BN leads to new SPhP leading to new peaks. Figure 2(b) shows the effect of Au nanoparticles in SiC thin film. When particle size is small, especially when the size is comparable to the mean free path of the free electrons, confinement effects become significant [25, 33]. The optical properties of metallic nanoparticles have shown size dependence [34]. We utilize a size-dependent dielectric function for Au

nanoparticles of radius rthat takes care of electron scattering, which is given by [35]

ω2 p ω<sup>2</sup> þ jωγ<sup>0</sup>

where εb, ωp, vf , and γ<sup>0</sup> are the bulk dielectric function, the plasma frequency, the Fermi velocity of free electrons, and the electron damping, respectively. The values of ε<sup>b</sup> are taken

LO þ jωγ

(9)

<sup>κ</sup> .

!

TO þ jωγ

<sup>κ</sup> <sup>≈</sup> 9.8 µm). In addition, there exists a small shift in the emission peak at <sup>λ</sup>SiC

� <sup>ω</sup><sup>2</sup>

p

<sup>ω</sup><sup>2</sup> <sup>þ</sup> <sup>j</sup>ωðγ<sup>0</sup> <sup>þ</sup> Avf <sup>=</sup>r<sup>Þ</sup> (10)

<sup>n</sup><sup>2</sup> ≈ 11.7 µm). Moreover, at two more points n is large while

<sup>k</sup><sup>1</sup> ≈ 9 µm and λmixture

<sup>n</sup> ≈ 13 µm. λ<sup>n</sup> is the wavelength at which the

<sup>k</sup><sup>2</sup> ≈ 11.1 µm.

<sup>ε</sup> <sup>p</sup> <sup>=</sup> n+jκ. For SiC and BN, the dielectric function has the form as [29, 30]

<sup>n</sup> ≈ 10.33 µm and λSiC

εðωÞ ¼ ε<sup>∞</sup>

Figure 2. Emissivity spectra for SiC or PS thin film of thickness 0.4 µm embedded with BN or Au nanoparticles of radius 25 nm and various volume fractions. (a) BN nanoparticle-embedded SiC thin film, (b) Au nanoparticle-embedded SiC thin film, (c) BN nanoparticle-embedded PS thin film, and (d) Au nanoparticle-embedded PS thin film.

from Johnson and Christy [31]. The parameters ωp, vf , and γ<sup>0</sup> are taken to be 9.06 eV, 0.077 eV, and 1.4 · 106 m/s, respectively. The proportionality constant A that depends on the electronscattering process at the surface of nanoparticles is assumed to be unity. Volume fraction is varied from 0% to 30% while NPs radius is maintained constant (25 nm). Multiple oscillatory peaks are seen in the lower wavelength region upon the addition of Au nanoparticles. A shift in the original peak of SiC at ≈13 µm is seen when volume fraction is large (30%). While the presence of a peak at ≈10.33 µm and a peak at ≈13 µm can be related to n and κ plots shown in Figure 3(a) and (b), multiple peaks between 0.35 and 8 µm cannot be explained using the refractive index characteristics. While the change in refractive index is seen around 500 nm which corresponds to surface plasmon resonance of Au, one may expect a peak around 500 nm. Multiple peaks are observed instead. Figure 2(c) and (d) shows emission spectra of polystyrene thin film doped with BN nanoparticles and Au nanoparticles, respectively. The dielectric function of PS is in the form of [36]

$$\varepsilon(\omega) = 1 + \sum\_{i=1}^{i=4} \left( \frac{f\_i}{w\_i^2 - \omega^2 - \mathrm{jg}\_i \omega} \right) \tag{11}$$

where the parameters f <sup>i</sup> , wi, and gi are, in the units of eV, given by f <sup>i</sup> = [14.6, 96.9, 44.4, 136.9], wi = [6.35, 14.0, 11.0, 20.1], and gi = [0.65, 5.0, 3.5, 11.5], respectively. In case of BN, the appearance of new peaks is quite similar to that in Figure 2(a) and its relation with the refractive indices shown in Figure 4(a) and (b) is obvious.

Figure 3. Refractive index of SiC and SiC film doped with 30% BN or Au nanoparticles. (a) Real part of refractive index and (b) imaginary part of refractive index.

The appearance of emission peaks at the locations of λmixture <sup>k</sup> and λmixture <sup>n</sup> is evident. However, when polystyrene film is doped with Au nanoparticles, we once again see multiple peaks produced in the region 0.35–6 µm that are not related to the refractive index characteristics. Since polystyrene does not support either of SPhPs or of SPPs, the interaction between SPPs of Au and surface polariton of the host is not responsible for the multiple peaks. We hypothesize that the origin of multiple peaks is due to the interaction of SPPs of Au and the boundaries of the thin film. In case of SiC film doped with Au nanoparticles, the shift in the peak of ≈13 µm is due to the interaction between SPPs of Au and SPhPs of SiC; in either cases (SiC and PS) the inclusion material does not produce new polaritons as seen in refractive index characteristics.

500 nm. Multiple peaks are observed instead. Figure 2(c) and (d) shows emission spectra of polystyrene thin film doped with BN nanoparticles and Au nanoparticles, respectively. The

w2

wi = [6.35, 14.0, 11.0, 20.1], and gi = [0.65, 5.0, 3.5, 11.5], respectively. In case of BN, the appearance of new peaks is quite similar to that in Figure 2(a) and its relation with the

when polystyrene film is doped with Au nanoparticles, we once again see multiple peaks produced in the region 0.35–6 µm that are not related to the refractive index characteristics. Since polystyrene does not support either of SPhPs or of SPPs, the interaction between SPPs of Au and surface polariton of the host is not responsible for the multiple peaks. We hypothesize that the origin of multiple peaks is due to the interaction of SPPs of Au and the boundaries of the thin film. In case of SiC film doped with Au nanoparticles, the shift in the peak of ≈13 µm is due to the interaction between SPPs of Au and SPhPs of SiC; in either cases (SiC and PS) the inclusion material does not produce new polaritons as seen in refractive index

Figure 3. Refractive index of SiC and SiC film doped with 30% BN or Au nanoparticles. (a) Real part of refractive index

f i

!

<sup>i</sup> � ω<sup>2</sup> � jgi

ω

<sup>k</sup> and λmixture

<sup>n</sup> is evident. However,

, wi, and gi are, in the units of eV, given by f <sup>i</sup> = [14.6, 96.9, 44.4, 136.9],

(11)

i¼4

i¼1

<sup>ε</sup>ðωÞ ¼ <sup>1</sup> <sup>þ</sup><sup>X</sup>

dielectric function of PS is in the form of [36]

refractive indices shown in Figure 4(a) and (b) is obvious.

The appearance of emission peaks at the locations of λmixture

and (b) imaginary part of refractive index.

where the parameters f <sup>i</sup>

280 Nanoscaled Films and Layers

characteristics.

Figure 4. Refractive index of PS and PS film doped with 30% BN or Au nanoparticles. (a) Real part of refractive index and (b) imaginary part of refractive index.

Figure 5 shows the effect of NPs size on the emission spectra. In Figure 5(a), SiC film of 0.4 µm is doped with BN nanoparticles and volume fraction of BN NPs is maintained constant at 10% and the radius is varied from 1 to 50 nm. The majority of emission spectrum shows no effect of BN particle size. However, the effect of size is noticeable at wavelengths less than

Figure 5. Emissivity spectra for SiC or PS thin film of thickness 0.4 µm embedded with BN or Au nanoparticles of volume fraction 10% and various radii. (a) BN nanoparticle-embedded SiC thin film doped and (b) Au nanoparticle-embedded PS thin film.

1 µm. This is due to the fact that Mie scattering becomes important at shorter wavelengths giving rise to higher peaks for larger particles. Figure 5(b) presents the calculation of emissivity for 0.4-µm thick polystyrene (PS) film doped with Au NPs. The volume fraction of NPs is fixed at 10% and the particle size is changed from 1 to 50 nm. Unlike Figure 5(a), Figure 5(b) shows a strong influence of particle size on the emissivity. While the spectrum in the visible region shows a negligible response to particle size, gold NPs greatly influence the near-infrared region between 1 and 4 µm. As the NP size is increased from 1 nm, the emissivity peaks reduce in magnitude, showing smaller peaks for 10 and 25 nm. Emissivity for larger particles of 50 nm, however, is increased again and is comparable to that of NPs of 1 nm. This is due to the presence of two counteracting phenomena here. First is the change in dielectric function of Au NPs leading to decreased emissivity of larger particles and the second being Mie scattering of electromagnetic (EM) waves in the host causing an increased emissivity of larger particles.

Next, we present the effect of the doped nanoparticles on radiative heat transfer. We analyze radiative heat transfer between two identical multilayered structures at 300 and 301 K as shown in Figure 1(b). Each structure has a top layer of 0.4 µm deposited on 1 µm of Au. The top layer is doped with nanoparticles of 25 nm and different volume fractions. Figure 6 shows radiative heat flux versus distance between the structures and the normalized spectral density (defined as the ratio of dq/dω to the maximum value over the range of wavelengths considered) at a distance of 100 nm is shown in the inset of figures. Consider a structure with SiC layer doped with BN nanoparticles. Figure 6(a) shows very little change in overall heat transfer. While thin film of pure SiC shows nearly monochromatic heat transfer, selectivity is seen at additional bands of wavelength. These locations are wavelengths where the effective refractive index of the mixture becomes zero (Figure 3(a) and (b)). While the locations of the new peaks depend on the volume fraction, the peak corresponding to the host material is relatively unchanged. In Figure 6(b), SiC film is doped with Au nanoparticles of radius 25 nm with different volume fractions. The change in total heat transfer characteristics is not significant with the addition of nanoparticles. Selectivity is observed near λ = λ<sup>1</sup> ≈ 10.33 µm as in Mulet et al. [10], which is one of characteristic wavelengths of SiC. Moreover, the inclusion of Au nanoparticles has only a small impact on the selectivity in the near-field limit and this can be related to the refractive indices of the mixture (Figure 3(a) and (b)). When the top layer is polystyrene doped with BN nanoparticles (Figure 6(c)), the near-field heat flux is clearly dependent on the volume fraction of the inclusion in both the near-field and the far-field regime. Since polystyrene does not support SPPs/SPhPs, the inclusion of BN clearly makes significant enhancement in heat transfer. The surface becomes selective at the wavelengths at which the real part of the effective refractive index becomes zero. When the PS film is doped with Au nanoparticles instead, the radiative heat transfer in Figure 6(d) shows an increment with an increase in NPs volume fraction, in both the near-field and the far-field limit. However, the normalized spectral density does not show any selectivity in the near field. In summary, the wavelength selectivity of thin films in the near field can be related to its effective refractive index in all four cases. This is logical as the selectivity is due to the

1 µm. This is due to the fact that Mie scattering becomes important at shorter wavelengths giving rise to higher peaks for larger particles. Figure 5(b) presents the calculation of emissivity for 0.4-µm thick polystyrene (PS) film doped with Au NPs. The volume fraction of NPs is fixed at 10% and the particle size is changed from 1 to 50 nm. Unlike Figure 5(a), Figure 5(b) shows a strong influence of particle size on the emissivity. While the spectrum in the visible region shows a negligible response to particle size, gold NPs greatly influence the near-infrared region between 1 and 4 µm. As the NP size is increased from 1 nm, the emissivity peaks reduce in magnitude, showing smaller peaks for 10 and 25 nm. Emissivity for larger particles of 50 nm, however, is increased again and is comparable to that of NPs of 1 nm. This is due to the presence of two counteracting phenomena here. First is the change in dielectric function of Au NPs leading to decreased emissivity of larger particles and the second being Mie scattering of electromagnetic (EM) waves in the host causing an

Next, we present the effect of the doped nanoparticles on radiative heat transfer. We analyze radiative heat transfer between two identical multilayered structures at 300 and 301 K as shown in Figure 1(b). Each structure has a top layer of 0.4 µm deposited on 1 µm of Au. The top layer is doped with nanoparticles of 25 nm and different volume fractions. Figure 6 shows radiative heat flux versus distance between the structures and the normalized spectral density (defined as the ratio of dq/dω to the maximum value over the range of wavelengths considered) at a distance of 100 nm is shown in the inset of figures. Consider a structure with SiC layer doped with BN nanoparticles. Figure 6(a) shows very little change in overall heat transfer. While thin film of pure SiC shows nearly monochromatic heat transfer, selectivity is seen at additional bands of wavelength. These locations are wavelengths where the effective refractive index of the mixture becomes zero (Figure 3(a) and (b)). While the locations of the new peaks depend on the volume fraction, the peak corresponding to the host material is relatively unchanged. In Figure 6(b), SiC film is doped with Au nanoparticles of radius 25 nm with different volume fractions. The change in total heat transfer characteristics is not significant with the addition of nanoparticles. Selectivity is observed near λ = λ<sup>1</sup> ≈ 10.33 µm as in Mulet et al. [10], which is one of characteristic wavelengths of SiC. Moreover, the inclusion of Au nanoparticles has only a small impact on the selectivity in the near-field limit and this can be related to the refractive indices of the mixture (Figure 3(a) and (b)). When the top layer is polystyrene doped with BN nanoparticles (Figure 6(c)), the near-field heat flux is clearly dependent on the volume fraction of the inclusion in both the near-field and the far-field regime. Since polystyrene does not support SPPs/SPhPs, the inclusion of BN clearly makes significant enhancement in heat transfer. The surface becomes selective at the wavelengths at which the real part of the effective refractive index becomes zero. When the PS film is doped with Au nanoparticles instead, the radiative heat transfer in Figure 6(d) shows an increment with an increase in NPs volume fraction, in both the near-field and the far-field limit. However, the normalized spectral density does not show any selectivity in the near field. In summary, the wavelength selectivity of thin films in the near field can be related to its effective refractive index in all four cases. This is logical as the selectivity is due to the

increased emissivity of larger particles.

282 Nanoscaled Films and Layers

Figure 6. Heat flux of microscopic-layered media doped with BN or Au nanoparticles of radius 25 nm and various volume fractions due to near-field radiative effect. Inset: normalized spectral heat flux at a 100-nm gap between each half space with 0.4-µm thick nanoparticle-embedded layer on 1-µm Au layer. (a) BN nanoparticle-embedded SiC thin film, (b) Au nanoparticle-embedded SiC thin film, (c) BN nanoparticle-embedded PS thin film, and (d) Au nanoparticle-embedded PS thin film.

presence of SPPs/SPhPs across the interfaces. It is interesting to note that, unlike in the farfield regime, the selectivity is affected only when BN particles are used as inclusions. The addition of Au particles shows little or no impact on the selectivity in the near field. This supports the idea that metallic nanoparticles do not induce new SPPs/SPhPs in the surfaces while dielectric nanoparticles such as BN produce new SPhP in the material.

## 4. Conclusion

We have demonstrated that nanoparticles influence the emission spectra of the multilayered structures. Wavelength selectivity can be altered and controlled by the size and/or volume fraction of the NPs. The presence of NPs in a host material gives rise to an appearance of new emission peaks and a shift in the existing peaks in the emission spectra. When the metallic NPs are used, the effect of size is stronger as the dielectric function of metallic NPs has a strong dependence of particle size due to electron scattering. We have also shown that the volume fraction of the nanoparticles plays an important role in the near-field radiative heat transfer. If the NPs support SPhP, wavelength selectivity of thin films in the far field is at the locations where the real part of effective refractive index of the mixture becomes zero or the imaginary part of refractive index is small while the real part of the index is large. If the material of inclusion supports SPPs, as in metallic nanoparticles multiple emission peaks are seen which cannot be related to n- and κ-values of the mixtures. (Our observation is limited to the case where the host material is thin film.)

In the near field, for NPs supporting SPhPs or SPPs the heat transfer is nearly monochromatic around the wavelength at which n for the mixture becomes zero. It is observed that only SPhP supporting inclusions can influence the location of λ<sup>n</sup> of the mixture; hence wavelength selectivity of thin films in the near field has little or no effect due to the presence of metallic nanoparticles. This can be understood as the presence of NPs in the thin film does not induce new kind of SPPs/SPhPs resonance across the interfaces. This work broadens the range of designs and methods for wavelength-selective emitters in both the far-field and the near-field regime.

## Acknowledgements

This work is partially funded by the Rhode Island STAC Research Grant under grant number AWD05085 and NIH RI-INBRE Pilot Research Development Award supported in part by an Institutional Development Award (IDeA) Network for Biomedical Research Excellence from the National Institute of General Medical Sciences of the National Institutes of Health under grant number P20GM103430.

## Author details

#### Yi Zheng

presence of SPPs/SPhPs across the interfaces. It is interesting to note that, unlike in the farfield regime, the selectivity is affected only when BN particles are used as inclusions. The addition of Au particles shows little or no impact on the selectivity in the near field. This supports the idea that metallic nanoparticles do not induce new SPPs/SPhPs in the surfaces

We have demonstrated that nanoparticles influence the emission spectra of the multilayered structures. Wavelength selectivity can be altered and controlled by the size and/or volume fraction of the NPs. The presence of NPs in a host material gives rise to an appearance of new emission peaks and a shift in the existing peaks in the emission spectra. When the metallic NPs are used, the effect of size is stronger as the dielectric function of metallic NPs has a strong dependence of particle size due to electron scattering. We have also shown that the volume fraction of the nanoparticles plays an important role in the near-field radiative heat transfer. If the NPs support SPhP, wavelength selectivity of thin films in the far field is at the locations where the real part of effective refractive index of the mixture becomes zero or the imaginary part of refractive index is small while the real part of the index is large. If the material of inclusion supports SPPs, as in metallic nanoparticles multiple emission peaks are seen which cannot be related to n- and κ-values of the mixtures. (Our observation

In the near field, for NPs supporting SPhPs or SPPs the heat transfer is nearly monochromatic around the wavelength at which n for the mixture becomes zero. It is observed that only SPhP supporting inclusions can influence the location of λ<sup>n</sup> of the mixture; hence wavelength selectivity of thin films in the near field has little or no effect due to the presence of metallic nanoparticles. This can be understood as the presence of NPs in the thin film does not induce new kind of SPPs/SPhPs resonance across the interfaces. This work broadens the range of designs and methods for wavelength-selective emitters in both the far-field and the

This work is partially funded by the Rhode Island STAC Research Grant under grant number AWD05085 and NIH RI-INBRE Pilot Research Development Award supported in part by an Institutional Development Award (IDeA) Network for Biomedical Research Excellence from the National Institute of General Medical Sciences of the National Institutes of Health under

while dielectric nanoparticles such as BN produce new SPhP in the material.

is limited to the case where the host material is thin film.)

4. Conclusion

284 Nanoscaled Films and Layers

near-field regime.

Acknowledgements

grant number P20GM103430.

Address all correspondence to: zheng@uri.edu

Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI, USA

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## *Edited by László Nánai*

In recent years, scientific investigations and technological developments have resulted in many new results. Direct applications of quantum mechanical laws to system with length scales lower than 100 nm (nano) had opened a way to construction of new equipment in the field f.e. of nano- and optoelectronics. This book fits into this trend summarizing the results related to discoveries and technological applications of nanolayer in different fields of material science and even life science. The chapters are organized into three subfields.


The presented book provides a description of specific and original results obtained by authors. We hope that the volume will be of interest for a wide range of readers working in the field of material science.

Nanoscaled Films and Layers

Nanoscaled Films

and Layers

*Edited by László Nánai*

Photo by Rost-9D / iStock