Gold-Nanoparticle-Deposited TiO2 Nanorod/Poly(Vinylidene Fluoride) Composites with Enhanced Dielectric Performance

Flexible dielectric polymer composites have been of great interest as embedded capacitor materials in the electronic industry. However, a polymer composite has a low relative dielectric permittivity (ε′ < 100), while its dielectric loss tangent is generally large (tanδ > 0.1). In this study, we fabricate a novel, high-permittivity polymer nanocomposite system with a low tanδ. The nanocomposite system comprises poly(vinylidene fluoride) (PVDF) co-filled with Au nanoparticles and semiconducting TiO2 nanorods (TNRs) that contain Ti3+ ions. To homogeneously disperse the conductive Au phase, the TNR surface was decorated with Au-NPs ~10–20 nm in size (Au-TNRs) using a modified Turkevich method. The polar β-PVDF phase was enhanced by the incorporation of the Au nanoparticles, partially contributing to the enhanced ε′ value. The introduction of the Au-TNRs in the PVDF matrix provided three-phase Au-TNR/PVDF nanocomposites with excellent dielectric properties (i.e., high ε′ ≈ 157 and low tanδ ≈ 0.05 at 1.8 vol% of Au and 47.4 vol% of TNRs). The ε′ of the three-phase Au-TNR/PVDF composite is ~2.4-times higher than that of the two-phase TNR/PVDF composite, clearly highlighting the primary contribution of the Au nanoparticles at similar filler loadings. The volume fraction dependence of ε′ is in close agreement with the effective medium percolation theory model. The significant enhancement in ε′ was primarily caused by interfacial polarization at the PVDF–conducting Au nanoparticle and PVDF–semiconducting TNR interfaces, as well as by the induced β-PVDF phase. A low tanδ was achieved due to the inhibited conducting pathway formed by direct Au nanoparticle contact.


Introduction
With recent developments in the electronic industry, dielectric polymer composite materials have attracted increasing interest for a wide range of applications, such as energy storage devices, dielectric capacitors, and electromechanical actuators [1,2]. Poly(vinylidene fluoride) (PVDF) has been used as a dielectric polymer material due to its high energy density, high electric break down field, and flexibility [3,4]. However, the relative dielectric permittivity (ε ) of PVDF is too low (≈10 [3]) for electronic applications.
To the best of our knowledge, there is a lack of substantial information on polymer composites incorporated with Au-TiO 2 hybrid nanoparticles. Therefore, in this study we aimed to fabricate a novel nanocomposite comprising a PVDF polymer matrix, Au nanoparticles, and TiO 2 nanorods (TNRs). TNRs have higher surface areas than spherical TiO 2 ; therefore, they lead to stronger interfacial polarization and a significantly enhanced ε . Herein, Au-TNR/PVDF nanocomposites with enhanced ε and low tanδ were fabricated. A modified Turkevich method was used to attach Au onto the surfaces of the TNRs. The Au-TNR/PVDF nanocomposites were prepared through liquid-phase-assisted dispersion and hot-pressing methods. Several properties of these nanocomposites such as their morphologies, microstructures, phase structures, chemical stages, and dielectric properties were investigated, and the significantly improved dielectric properties of the nanocomposites are discussed.

Preparation of Heat-Treated TNRs
TNRs (99.5% purity) with particle size <100 nm were purchased from Sigma-Aldrich. Heat treatment at 500 • C for 3 h in air was performed on the TNRs to evaporate the moisture.

Preparation of Au-TNR Hybrid Nanoparticles
Au-TNR hybrid nanoparticles were prepared through a modified Turkevich method. The corresponding procedure is described as follows: heat treatment of TNR powder was carried out by ultrasonically dispersing the powder in deionized water for 30 min. Then, the white TNR suspension was stirred using a magnetic stirrer at~25 • C for 30 min, after which 1 mM HAuCl 4 ·3H 2 O was dissolved in the TNR solution under constant stirring. After the solution was heated to 300 • C, 38.8 mM of sodium citrate (>99.0%, Sigma-Aldrich) solution was dissolved in the TNR solution. To ensure a complete reaction, the suspension was stirred until its color changed from white to purple. The purple suspension was sequentially cooled to room temperature, centrifuged at 8500 rpm, and washed several times with deionized water. Finally, Au-TNR hybrid nanoparticles were obtained without agglomeration by freeze-drying.

Characterization
The phase structures of the PVDF filler and Au-TNR/PVDF nanocomposites were characterized by X-ray diffractometry (XRD, PANalytical, EMPYREAN). The surface morphologies of Au, TNRs, and the Au-TNR nanoparticles were revealed using transmission electron microscopy (TEM, FEI Tecnai G2 20). The chemical composition of each element in the Au-TNR hybrid nanoparticles was analyzed by X-ray photoelectron spectroscopy (XPS, PHI5000 VersaProbe II, ULVAC-PHI, Japan) at the SUT-NANOTEC-SLRI Joint Research Facility, Synchrotron Light Research Institute (SLRI), Thailand. The fracture microstructures, distributions, and percentages of each element in the Au-TNR/PVDF nanocomposites were investigated by focused ion beam-field emission scanning electron microscopy (FIB-FESEM, FEI Helios Nanolab G3 CX). The samples were fractured using liquid N 2 and their surfaces were sputtered with Au before SEM characterization. The crystalline phases of the nanocomposites were determined using Fourier-transform infrared spectroscopy (FTIR, Bruker, TENSOR27) in the 700-1800 cm −1 wavelength range. The dielectric properties of the samples were analyzed using an impedance analyzer (KEYSIGHT E4990A) in the 10 2 -10 6 Hz and −60-150 • C frequency and temperature ranges, respectively, with an oscillation voltage of 0.5 V. Before any dielectric measurement, both sides of each circular sample were coated with Ag to form electrodes. Meanwhile, the heat-treated TNRs are rod-shaped with slightly different aspect ratios, while some Au clusters are dotted on the TNR surfaces of the Au-TNR hybrid nanoparticles, revealing that the Au nanoparticles successfully formed on the TNR surfaces.

Characterization
The phase structures of the PVDF filler and Au-TNR/PVDF nanocomposites were characterized by X-ray diffractometry (XRD, PANalytical, EMPYREAN). The surface morphologies of Au, TNRs, and the Au-TNR nanoparticles were revealed using transmission electron microscopy (TEM, FEI Tecnai G2 20). The chemical composition of each element in the Au-TNR hybrid nanoparticles was analyzed by X-ray photoelectron spectroscopy (XPS, PHI5000 VersaProbe II, ULVAC-PHI, Japan) at the SUT-NANOTEC-SLRI Joint Research Facility, Synchrotron Light Research Institute (SLRI), Thailand. The fracture microstructures, distributions, and percentages of each element in the Au-TNR/PVDF nanocomposites were investigated by focused ion beam-field emission scanning electron microscopy (FIB-FESEM, FEI Helios Nanolab G3 CX). The samples were fractured using liquid N2 and their surfaces were sputtered with Au before SEM characterization. The crystalline phases of the nanocomposites were determined using Fourier-transform infrared spectroscopy (FTIR, Bruker, TENSOR27) in the 700-1800 cm −1 wavelength range. The dielectric properties of the samples were analyzed using an impedance analyzer (KEYSIGHT E4990A) in the 10 2 -10 6 Hz and −60-150 °C frequency and temperature ranges, respectively, with an oscillation voltage of 0.5 V. Before any dielectric measurement, both sides of each circular sample were coated with Ag to form electrodes. Figure 1 displays TEM images showing the morphologies of the Au, TNRs, and Au-TNR hybrid nanoparticles. The Au nanoparticles are spherical with diameters of 10-20 nm. Meanwhile, the heat-treated TNRs are rod-shaped with slightly different aspect ratios, while some Au clusters are dotted on the TNR surfaces of the Au-TNR hybrid nanoparticles, revealing that the Au nanoparticles successfully formed on the TNR surfaces.    Figure 2 shows XPS spectra of the Au-TNR powder. As shown in Figure 2a, Au 4f peaks were observed at 83.33 and 86.98 eV, which are assigned to Au 4f 7/2 and Au 4f 5/2 , respectively [41,42]. This confirmed the existence of Au in the prepared Au-TNR powder. As shown in Figure 2b, small Ti 2p peaks were observed at binding energies of 457.69 and 461.34 eV, respectively, corresponding to the presence of Ti 3+ . Ti 2p signals was observed at binding energies of 458.75 and 464.41 eV, indicating the presence of Ti 4+ [43]. The Ti 3+ /Ti 4+ ratio was found to be 7.52%. Figure 2c shows three of O 1s XPS peaks; the peak at 529.99 eV can be attributed to the oxygen lattice (Ti-O) [28,43]. Additional peaks were observed at 531.29 and 532.32 eV, which can be attributed to the oxygen vacancy in the rutile structure [28] and hydroxyl groups [43], respectively. The detected Ti 3+ in the Au-TNR powder is likely to have originated from oxygen vacancies, which can be explained by Equations (1) and (2).

Results and Discussion
The presence of the Ti 3+ ions can cause a significant increase in conductivity, thereby leading to electron hopping between the Ti 3+ and Ti 4+ ions under an applied electric field. The XPS results confirmed the existence of Au, Ti 3+ , and oxygen vacancies, which affected ε enhancement in the Au-TNR/PVDF nanocomposites.
Polymers 2021, 13, x FOR PEER REVIEW 5 of 15 Figure 2 shows XPS spectra of the Au-TNR powder. As shown in Figure 2a, Au 4f peaks were observed at 83.33 and 86.98 eV, which are assigned to Au 4f7/2 and Au 4f5/2, respectively [41,42]. This confirmed the existence of Au in the prepared Au-TNR powder. As shown in Figure 2b, small Ti 2p peaks were observed at binding energies of 457.69 and 461.34 eV, respectively, corresponding to the presence of Ti 3+ . Ti 2p signals was observed at binding energies of 458.75 and 464.41 eV, indicating the presence of Ti 4+ [43]. The Ti 3+ /Ti 4+ ratio was found to be 7.52%. Figure 2c shows three of O 1s XPS peaks; the peak at 529.99 eV can be attributed to the oxygen lattice (Ti-O) [28,43]. Additional peaks were observed at 531.29 and 532.32 eV, which can be attributed to the oxygen vacancy in the rutile structure [28] and hydroxyl groups [43], respectively. The detected Ti 3+ in the Au-TNR powder is likely to have originated from oxygen vacancies, which can be explained by Equations (1) and (2). The presence of the Ti 3+ ions can cause a significant increase in conductivity, thereby leading to electron hopping between the Ti 3+ and Ti 4+ ions under an applied electric field. The XPS results confirmed the existence of Au, Ti 3+ , and oxygen vacancies, which affected ε′ enhancement in the Au-TNR/PVDF nanocomposites.
The XRD patterns of Au, PVDF, TNRs, Au-TNR nanoparticles, and Au-TNR/PVDF nanocomposites were obtained in the 10-80° 2θ range, as shown in Figure 3. The XRD pattern of the PVDF polymer corresponds to the (100), (020), (110), and (021) planes of the α-phase [4]. The XRD pattern of the TNRs showed peaks similar to those of the tetragonal structure of the rutile phase according to the standard reported in JCPDS 21-1276; no impurity phase was detected. In the case of the Au-TNR hybrid nanoparticles and Au-TNR/PVDF nanocomposites, the XRD peak for Au can be observed at 2θ ≈ 38.11 and assigned as a (111) plane (JCPDS 00-00-1172), confirming the existence of Au in the hybrid particles and Au-TNR/PVDF nanocomposites. Therefore, the Au nanoparticles were confirmed to exist in the Au-TNR nanoparticles and Au-TNR/PVDF nanocomposites. Meanwhile, no PVDF diffraction peaks were observed in the Au-TNR/PVDF nanocomposite sample, which can be attributed to the semicrystalline nature of PVDF, which is shielded by the stronger crystalline diffraction intensity of the TNRs compared to PVDF. The XRD patterns of Au, PVDF, TNRs, Au-TNR nanoparticles, and Au-TNR/PVDF nanocomposites were obtained in the 10-80 • 2θ range, as shown in Figure 3. The XRD pattern of the PVDF polymer corresponds to the (100), (020), (110), and (021) planes of the α-phase [4]. The XRD pattern of the TNRs showed peaks similar to those of the tetragonal structure of the rutile phase according to the standard reported in JCPDS 21-1276; no impurity phase was detected. In the case of the Au-TNR hybrid nanoparticles and Au-TNR/PVDF nanocomposites, the XRD peak for Au can be observed at 2θ ≈ 38.11 and assigned as a (111) plane (JCPDS 00-00-1172), confirming the existence of Au in the hybrid particles and Au-TNR/PVDF nanocomposites. Therefore, the Au nanoparticles were confirmed to exist in the Au-TNR nanoparticles and Au-TNR/PVDF nanocomposites. Meanwhile, no PVDF diffraction peaks were observed in the Au-TNR/PVDF nanocomposite sample, which can be attributed to the semicrystalline nature of PVDF, which is shielded by the stronger crystalline diffraction intensity of the TNRs compared to PVDF. The FTIR spectra of the PVDF polymer nanocomposites filled with the TNRs and Au TNRs are shown in Figure 4. Both nanocomposite systems consisted of α-, β-, and γ-PVD phases. Weak transmittance bands observed at 766 and 976 cm −1 are attributed to the non polar α-phase [4], consistent with the XRD result ( Figure 3). As the characteristic bands o the β-and γ-phase overlapped at 840 cm −1 , they were difficult to distinguish. However the characteristic band at 1279 cm −1 only corresponds to the β-phase [4]. As shown in Fig  ure 4, the transmittance intensity of the β-phase for the three-phase Au-TNR/PVDF-5 com posite is stronger than that of the two-phase TNR/PVDF composite, particularly at 127 cm −1 . To estimate the %β-phases in the nanocomposites, the absorption ratios of the β-and α-phase were compared. Equation (3) was used to quantify the relative fraction of the β phase (F(β)) [4], assuming that only the β-and α-phase exist: where Aα and Aβ are the absorption bands at 766 and 840 cm −1 , respectively, and Kα and Kβ are the absorption coefficients of the respective bands (Kα = 6.1 × 10 4 and Kβ = 7.7 × 10 cm 2 ·mol −1 ). The calculated F(β) of the two-phase and three-phase nanocomposites wer 0.220 and 0.331, respectively. The negative charge of the Au nanoparticles causes an in crease in amount of the polar β-phase of the PVDF nanocomposites [44], leading to a Au TNR/PVDF nanocomposite with a significantly enhanced ε′ [45]. The FTIR spectra of the PVDF polymer nanocomposites filled with the TNRs and Au-TNRs are shown in Figure 4. Both nanocomposite systems consisted of α-, β-, and γ-PVDF phases. Weak transmittance bands observed at 766 and 976 cm −1 are attributed to the nonpolar α-phase [4], consistent with the XRD result ( Figure 3). As the characteristic bands of the βand γ-phase overlapped at 840 cm −1 , they were difficult to distinguish. However, the characteristic band at 1279 cm −1 only corresponds to the β-phase [4]. As shown in Figure 4, the transmittance intensity of the β-phase for the three-phase Au-TNR/PVDF-5 composite is stronger than that of the two-phase TNR/PVDF composite, particularly at 1279 cm −1 . To estimate the %β-phases in the nanocomposites, the absorption ratios of the βand α-phase were compared. Equation (3) was used to quantify the relative fraction of the β-phase (F(β)) [4], assuming that only the βand α-phase exist: where A α and A β are the absorption bands at 766 and 840 cm −1 , respectively, and K α and K β are the absorption coefficients of the respective bands (K α = 6.1 × 10 4 and K β = 7.7 × 10 4 cm 2 ·mol −1 ). The calculated F(β) of the two-phase and three-phase nanocomposites were 0.220 and 0.331, respectively. The negative charge of the Au nanoparticles causes an increase in amount of the polar β-phase of the PVDF nanocomposites [44], leading to a Au-TNR/PVDF nanocomposite with a significantly enhanced ε [45]. The fracture cross-sectional images of the nanocomposites containing various Au-TNR hybrid particles are shown in Figure 5. The microstructure of the PVDF polymer is shown in Figure 5a and reveals that the PVDF molecules form a continuous phase. Figure 5b,c show the microstructures of the Au-TNRs/PVDF-2 and Au-TNRs/PVDF-4 nanocomposites. The Au-TNR hybrid nanoparticles are dispersed homogeneously in the PVDF matrix without aggregation. Some air voids and Au-TNR nanoparticle aggregation were observed with increasing Au-TNR hybrid particle content, as exemplified by Au-TNR/PVDF-6, as shown in Figure 5d.  The fracture cross-sectional images of the nanocomposites containing various Au-TNR hybrid particles are shown in Figure 5. The microstructure of the PVDF polymer is shown in Figure 5a and reveals that the PVDF molecules form a continuous phase. Figure  5b,c show the microstructures of the Au-TNRs/PVDF-2 and Au-TNRs/PVDF-4 nanocomposites. The Au-TNR hybrid nanoparticles are dispersed homogeneously in the PVDF matrix without aggregation. Some air voids and Au-TNR nanoparticle aggregation were observed with increasing Au-TNR hybrid particle content, as exemplified by Au-TNR/PVDF-6, as shown in Figure 5d.   The fracture cross-sectional images of the nanocomposites containing various Au-TNR hybrid particles are shown in Figure 5. The microstructure of the PVDF polymer is shown in Figure 5a and reveals that the PVDF molecules form a continuous phase. Figure  5b,c show the microstructures of the Au-TNRs/PVDF-2 and Au-TNRs/PVDF-4 nanocomposites. The Au-TNR hybrid nanoparticles are dispersed homogeneously in the PVDF matrix without aggregation. Some air voids and Au-TNR nanoparticle aggregation were observed with increasing Au-TNR hybrid particle content, as exemplified by Au-TNR/PVDF-6, as shown in Figure 5d.  SEM element maps and EDS were employed to further confirm the existence of Au in the three-phase nanocomposites. As shown in Figure 6, the microstructure of Au-TNR/PVDF-4 exhibited Au clusters dispersed on the TNR surfaces that are surrounded by the PVDF matrix. EDS was used to determine that Au, Ti, O, C, and F are present in the nanocomposite at levels of 1.3, 57, 24.5, 14.3, and 2.9 wt%, respectively. SEM element maps and EDS were employed to further confirm the existence of Au in the three-phase nanocomposites. As shown in Figure 6, the microstructure of Au-TNR/PVDF-4 exhibited Au clusters dispersed on the TNR surfaces that are surrounded by the PVDF matrix. EDS was used to determine that Au, Ti, O, C, and F are present in the nanocomposite at levels of 1.3, 57, 24.5, 14.3, and 2.9 wt%, respectively. The frequency dependences of ε′, tanδ, and σac of nanocomposites with different volume fractions of Au-TNRs (fAu-TNRs) at room temperature are shown in Figure 7. As shown in Figure 7a, the ε′ increased with increasing fAu-TNRs. A significant enhancement in ε′ was achieved by incorporating small amounts of Au and TNR nanoparticles in the nanocomposite. The enhanced ε′ value of the Au-TNR/PVDF-6 composite was ~226 at 1 kHz, which is ~20 times larger than that of a pure PVDF polymer (ε′ ≈ 10.78). The increase in ε′ for the three-phase Au-TNR/PVDF nanocomposites can be ascribed to the formation of Au-TNR hybrid nanoparticles. A large amount of blocked charges at the interface between TNR-PVDF and Au-PVDF can enhance interfacial polarization, which is known as Maxwell-Wagner-Sillars (MWS) polarization [6,46]. Therefore, in an electric field, the enhanced interfacial polarization enhances the ε′ of the Au-TNR/PVDF nanocomposites. Another factor is the semiconductor nature of the TNR nanoparticles, which can produce interfacial polarization over a wide range of frequencies. Moreover, the ε′ behavior of each sample exhibits a similar trend in the 10 2 -10 6 Hz range. Meanwhile, the tanδ values of the Au-TNR/PVDF nanocomposites decreased as the frequency was increased to approximately 10 4 kHz and gradually increased at higher frequencies, as shown in Figure 7b. This increase in tanδ is generally consistent with the dielectric relaxation of the pure PVDF polymer [6]. Considering a low-frequency range, tanδ of the Au-TNR/PVDF nanocomposites increased with increasing fAu-TNRs. The increased tanδ value as a result of increased filler loading is attributed to the conduction of free charge carriers [6,47], which corresponds to the increase in fAu-TNRs. Furthermore, for the composites with high filler loading, it is observed that tanδ continuously increases with decreasing frequency from 10 3 to 10 2 Hz. This observation was resulted from the conduction of free charge carriers, which is more prominent in a low-frequency range. The increase in tanδ in the high-frequency range is attributed to the αa relaxation from the glass transition in the PVDF polymer [6,48]. Th tanδ of the nanocomposite increases slowly with increasing Au-TNR content. Interestingly, tanδ is exceptionally low for all nanocomposites at 1 kHz. The maximum value of tanδ is less than 0.08 at a frequency of 1 kHz. The tanδ value of Au-TNR/PVDF-6 is 0.05, which is much lower than values obtained in other work (tanδ > 0.1) that used Ag@TiO2 as fillers The frequency dependences of ε , tanδ, and σ ac of nanocomposites with different volume fractions of Au-TNRs (f Au-TNRs ) at room temperature are shown in Figure 7. As shown in Figure 7a, the ε increased with increasing f Au-TNRs . A significant enhancement in ε was achieved by incorporating small amounts of Au and TNR nanoparticles in the nanocomposite. The enhanced ε value of the Au-TNR/PVDF-6 composite was~226 at 1 kHz, which is~20 times larger than that of a pure PVDF polymer (ε ≈ 10.78). The increase in ε for the three-phase Au-TNR/PVDF nanocomposites can be ascribed to the formation of Au-TNR hybrid nanoparticles. A large amount of blocked charges at the interface between TNR-PVDF and Au-PVDF can enhance interfacial polarization, which is known as Maxwell-Wagner-Sillars (MWS) polarization [6,46]. Therefore, in an electric field, the enhanced interfacial polarization enhances the ε of the Au-TNR/PVDF nanocomposites. Another factor is the semiconductor nature of the TNR nanoparticles, which can produce interfacial polarization over a wide range of frequencies. Moreover, the ε behavior of each sample exhibits a similar trend in the 10 2 -10 6 Hz range. Meanwhile, the tanδ values of the Au-TNR/PVDF nanocomposites decreased as the frequency was increased to approximately 10 4 kHz and gradually increased at higher frequencies, as shown in Figure 7b. This increase in tanδ is generally consistent with the dielectric relaxation of the pure PVDF polymer [6]. Considering a low-frequency range, tanδ of the Au-TNR/PVDF nanocomposites increased with increasing f Au-TNRs . The increased tanδ value as a result of increased filler loading is attributed to the conduction of free charge carriers [6,47], which corresponds to the increase in f Au-TNRs . Furthermore, for the composites with high filler loading, it is observed that tanδ continuously increases with decreasing frequency from 10 3 to 10 2 Hz. This observation was resulted from the conduction of free charge carriers, which is more prominent in a low-frequency range. The increase in tanδ in the high-frequency range is attributed to the α a relaxation from the glass transition in the PVDF polymer [6,48]. Th tanδ of the nanocomposite increases slowly with increasing Au-TNR content. Interestingly, tanδ is exceptionally low for all nanocomposites at 1 kHz. The maximum value of tanδ is less than 0.08 at a frequency of 1 kHz. The tanδ value of Au-TNR/PVDF-6 is 0.05, which is much lower than values obtained in other work (tanδ > 0.1) that used Ag@TiO 2 as fillers [34,35,37,49]. As shown in Figure 7c, the σ ac value of the Au-TNR/PVDF nanocomposite increased slightly with increasing Au-TNR content. At f Au-TNRs = 0.624, the σ ac value of the nanocomposite was only 6.58 × 10 −9 S·cm −1 at 1 kHz, which is lower than that of the other three-phase composite systems (>10 −7 S·cm −1 ) [34,35]. These results confirm that no conducting network is formed, indicating that the Au-TNR-PVDF nanocomposites exhibit good insulation properties.  [34,35,37,49]. As shown in Figure 7c, the σac value of the Au-TNR/PVDF nanocomposite increased slightly with increasing Au-TNR content. At fAu-TNRs = 0.624, the σac value of the nanocomposite was only 6.58 × 10 −9 S·cm −1 at 1 kHz, which is lower than that of the other three-phase composite systems (>10 −7 S·cm −1 ) [34,35]. These results confirm that no conducting network is formed, indicating that the Au-TNR-PVDF nanocomposites exhibit good insulation properties.  Figure 8 shows the ε′ and tanδ of Au-TNR/PVDF at 1 kHz as functions of temperature. As shown in Figure 8a, steady values of ε′ were observed for almost all nanocomposites with increasing temperature. Only Au-TNR/PVDF-5 and Au-TNR/PVDF-6 exhibited ε′ values that were slightly temperature dependent. Figure 8b shows the tanδ relaxation peaks in the pure PVDF polymer. The first relaxation was observed between −40 and 0 °C, which can be attributed to the β-relaxation of PVDF. The second relaxation was observed at a temperature above 40 °C, which can be attributed to the α-relaxation [50].  Figure 8 shows the ε and tanδ of Au-TNR/PVDF at 1 kHz as functions of temperature. As shown in Figure 8a, steady values of ε were observed for almost all nanocomposites with increasing temperature. Only Au-TNR/PVDF-5 and Au-TNR/PVDF-6 exhibited ε values that were slightly temperature dependent. Figure 8b shows the tanδ relaxation peaks in the pure PVDF polymer. The first relaxation was observed between −40 and 0 • C, which can be attributed to the β-relaxation of PVDF. The second relaxation was observed at a temperature above 40 • C, which can be attributed to the α-relaxation [50]. Figure 8 shows the ε′ and tanδ of Au-TNR/PVDF at 1 kHz as functions of temperature. As shown in Figure 8a, steady values of ε′ were observed for almost all nanocomposites with increasing temperature. Only Au-TNR/PVDF-5 and Au-TNR/PVDF-6 exhibited ε′ values that were slightly temperature dependent. Figure 8b shows the tanδ relaxation peaks in the pure PVDF polymer. The first relaxation was observed between −40 and 0 °C, which can be attributed to the β-relaxation of PVDF. The second relaxation was observed at a temperature above 40 °C, which can be attributed to the α-relaxation [50].  Figure 9a shows the ε′ values of TNR/PVDF and Au-TNR/PVDF-5 as a function of frequency. The ε′ value of the three-phase nanocomposite (Au-TNR/PVDF-5) was found to be much higher than that of the two-phase nanocomposite (TNR/PVDF) (with nearly the same total volume fraction of filler) in the 10 2 -10 6 Hz frequency range, which indicates that the addition of a small amount of Au nanoparticles can result in a significant enhancement in the ε′ of a polymer composite. Interestingly, the tanδ value of the Au-TNR/PVDF-5 nanocomposite at 1 kHz was 0.048. These excellent dielectric properties of Au-TNR/PVDF are not only due to the introduction of the Au-TNR hybrid nanoparticles, but also due to the increasing polar β-phase in the PVDF matrix, which was confirmed by FTIR spectroscopy (Figure 4). The large interfacial area of the semiconducting TNRs is one of the most important factors that significantly increases the dielectric response in the nanocomposite. As shown in Figure 9b, although tanδ of the Au-TNR/PVDF-5 nanocomposite was increased over the measured frequency range compared to that of the twophase TNR/PVDF nanocomposite, the obtained tanδ value was lower than 0.08 in the frequency range of 10 2 -10 6 Hz.  Figure 9a shows the ε values of TNR/PVDF and Au-TNR/PVDF-5 as a function of frequency. The ε value of the three-phase nanocomposite (Au-TNR/PVDF-5) was found to be much higher than that of the two-phase nanocomposite (TNR/PVDF) (with nearly the same total volume fraction of filler) in the 10 2 -10 6 Hz frequency range, which indicates that the addition of a small amount of Au nanoparticles can result in a significant enhancement in the ε of a polymer composite. Interestingly, the tanδ value of the Au-TNR/PVDF-5 nanocomposite at 1 kHz was 0.048. These excellent dielectric properties of Au-TNR/PVDF are not only due to the introduction of the Au-TNR hybrid nanoparticles, but also due to the increasing polar β-phase in the PVDF matrix, which was confirmed by FTIR spectroscopy (Figure 4). The large interfacial area of the semiconducting TNRs is one of the most important factors that significantly increases the dielectric response in the nanocomposite. As shown in Figure 9b, although tanδ of the Au-TNR/PVDF-5 nanocomposite was increased over the measured frequency range compared to that of the two-phase TNR/PVDF nanocomposite, the obtained tanδ value was lower than 0.08 in the frequency range of 10 2 -10 6 Hz. The ε′ values of the Au-TNR/PVDF nanocomposites could not be fitted to two-phase composite models consisting of a ceramic and a polymer (e.g., effective medium theory (EMT), Maxwell-Garnett, Yamada, logarithmic [5,51]) with high Au-TNR contents, as demonstrated in the inset of Figure 10. This is due to interfacial polarization at the interface between fillers and PVDF polymer matrix. Moreover, the ε′ values of the Au-TNR/PVDF nanocomposites could not be fitted to the percolation model, which is employed for metal/polymer dual phases. As shown in Figure 10, the dielectric behavior of the Au- The ε values of the Au-TNR/PVDF nanocomposites could not be fitted to two-phase composite models consisting of a ceramic and a polymer (e.g., effective medium theory (EMT), Maxwell-Garnett, Yamada, logarithmic [5,51]) with high Au-TNR contents, as

Conclusions
This study presented a novel method for successfully achieving high ε′ and low tanδ in three-phase PVDF polymer-matrix nanocomposites. The dielectric properties of a PVDF polymer improved significantly by incorporating conductive Au nanoparticles and semiconductive TNRs with enlarged interfacial areas. The Au nanoparticles were discretely attached to the TNR surfaces to enhance interfacial polarization and simultaneously prevent the formation of conducting pathways in the insulative PVDF matrix. As a Figure 10. Experimental data of ε for the Au-TNR/PVDF nanocomposites at 1 kHz and 20 • C fitted by the effective medium theory (EMPT) model; inset is the experimental data of ε for the Au-TNR/PVDF nanocomposites fitted by two-phase various theoretical models.

Conclusions
This study presented a novel method for successfully achieving high ε and low tanδ in three-phase PVDF polymer-matrix nanocomposites. The dielectric properties of a PVDF polymer improved significantly by incorporating conductive Au nanoparticles and semiconductive TNRs with enlarged interfacial areas. The Au nanoparticles were discretely attached to the TNR surfaces to enhance interfacial polarization and simultaneously prevent the formation of conducting pathways in the insulative PVDF matrix. As a result, a high ε (~157) and low tanδ (~0.05) were obtained in the three-phase nanocomposite filled with 1.8 vol% Au and 47.4 vol% TNRs. The dielectric response in the two-phase TNR/PVDF composite increased by more than a factor of two after introducing small amounts of Au nanoparticles. This dielectric behavior is described using the EMPT model. The results indicate that Au nanoparticles significantly contribute to enhancing interfacial polarization and creating a more polar β-PVDF phase, which increases ε . In contrast, due to the small amount of Au nanoparticles used and their discrete growth on the TNRs, the value of tanδ remained low. To further investigate the possible use of the Au-TNR/PVDF nanocomposites in capacitor applications, fabrication conditions that produce nanocomposite thin films need be studied.

Data Availability Statement:
The data presented in this study are available in article.