**3. Results and Discussion**

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 1.** TEM images of (**a**) Au, (**b**) TNRs, and (**c**) Au-TNR hybrid nanoparticles.

Figure 2 shows XPS spectra of the Au-TNR powder. As shown in Figure 2a, Au 4*f* peaks were observed at 83.33 and 86.98 eV, which are assigned to Au 4*f* 7/2 and Au 4*f* 5/2, respectively [41,42]. This confirmed the existence of Au in the prepared Au-TNR powder. As shown in Figure 2b, small Ti 2*p* peaks were observed at binding energies of 457.69 and 461.34 eV, respectively, corresponding to the presence of Ti3+. Ti 2*p* signals was observed at binding energies of 458.75 and 464.41 eV, indicating the presence of Ti4+ [43]. The Ti3+/Ti4+ ratio was found to be 7.52%. Figure 2c shows three of O 1*s* 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 Ti3+ in the Au-TNR powder is likely to have originated from oxygen vacancies, which can be explained by Equations (1) and (2).

$$O\_O^{\infty} \to \frac{1}{2}O\_2 + V\_O^{\bullet\bullet} + 2e^- \tag{1}$$

$$Ti^{4+} + e^- \to Ti^{3+} \tag{2}$$

The presence of the Ti3+ ions can cause a significant increase in conductivity, thereby leading to electron hopping between the Ti3+ and Ti4+ ions under an applied electric field. The XPS results confirmed the existence of Au, Ti3+, and oxygen vacancies, which affected ε enhancement in the Au-TNR/PVDF nanocomposites.

**Figure 2.** XPS spectra of Au-TNR hybrid nanoparticles; (**a**) Au 4*f*, (**b**) Ti 2*p*, and (**c**)O1*s*.

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.

**Figure 3.** XRD patterns of the Au standard data Au standard (JCPDS 00-00-1172), TNRs, fabricated Au-TNR hybrid nanoparticles, and Au-TNR/PVDF-4 nanocomposite.

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−<sup>1</sup> are attributed to the nonpolar α-phase [4], consistent with the XRD result (Figure 3). As the characteristic bands of the β- and γ-phase overlapped at 840 cm<sup>−</sup>1, they were difficult to distinguish. However, the characteristic band at 1279 cm−<sup>1</sup> 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<sup>−</sup>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:

$$\mathbf{F}(\boldsymbol{\beta}) = \frac{\mathbf{A}\_{\beta}}{(\mathbf{K}\_{\beta}/\mathbf{K}\_{\alpha})\mathbf{A}\_{\alpha} + \mathbf{A}\_{\beta}} \tag{3}$$

where A<sup>α</sup> and A<sup>β</sup> are the absorption bands at 766 and 840 cm<sup>−</sup>1, respectively, and K<sup>α</sup> and K<sup>β</sup> are the absorption coefficients of the respective bands (K<sup>α</sup> = 6.1 × 10<sup>4</sup> and K<sup>β</sup> = 7.7 × 104 cm2·mol<sup>−</sup>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.

**Figure 4.** FTIR spectra of the TNR/PVDF and Au-TNR/PVDF-5 nanocomposites.

**Figure 5.** SEM cross-section images of (**a**) PVDF, (**b**) Au-TNR/PVDF-2, (**c**) Au-TNR/PVDF-4, and (**d**) Au-TNR/PVDF-6.

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.

**Figure 6.** Element mapping and EDS-FESEM characterization of Au-TNR/PVDF-4.

The frequency dependences of ε , tanδ, and σac 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 102–106 Hz range. Meanwhile, the tanδ values of the Au-TNR/PVDF nanocomposites decreased as the frequency was increased to approximately 10<sup>4</sup> 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<sup>3</sup> to 10<sup>2</sup> 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<sup>a</sup> 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 [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 *f* Au-TNRs = 0.624, the σac value of the nanocomposite was only 6.58 × 10−<sup>9</sup> S·cm−<sup>1</sup> at 1 kHz, which is lower than that of the other three-phase composite systems (>10−<sup>7</sup> S·cm<sup>−</sup>1) [34,35]. These results confirm that no conducting network is formed, indicating that the Au-TNR-PVDF nanocomposites exhibit good insulation properties.

**Figure 7.** Frequency dependence of (**a**) ε , (**b**) tanδ, and (**c**) σ for nanocomposites with varying amounts of Au-TNRs.

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.** Temperature dependence of (**a**) ε and (**b**) tanδ for nanocomposites with varying amounts of Au-TNRs.

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 102–106 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 102–106 Hz.

**Figure 9.** Frequency dependence of (**a**) ε and (**b**) tanδ for TNR/PVDF and Au-TNR/PVDF-5 at 20 ◦C; the different ε values (green area) resulted from the Au nanoparticles.

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-TNR/PVDF nanocomposites is in good agreement with the EMPT model [35,52], which combines the EMT model with percolation theory, as shown in Equation (4):

$$\varepsilon\_{\rm eff} = \varepsilon\_{\rm PVDF} \left[ 1 + \frac{f\_{\rm TNRS} (\varepsilon\_{\rm TNRS} - \varepsilon\_{\rm PVDF})}{\varepsilon\_{\rm PVDF} + \mathbf{n} (1 - f\_{\rm TNRS}) (\varepsilon\_{\rm TNRS} - \varepsilon\_{\rm PVDF})} \right] \left| \frac{f\_{\rm \rm f} - f}{f} \right|^{-q} \tag{4}$$

where εeff is the effective ε of the Au-TNR/PVDF composite, *f* TNRs is the volume fraction of the TNRs, *f* <sup>c</sup> is the percolation threshold, εPVDF is the ε of PVDF (εPVDF = 10.78), εTNRs is the ε of TNRs (εTNRs = 150), n is the morphology fitting factor, and *q* is the critical exponent. Due to the semiconducting nature of TNRs and conducting nature of Au nanoparticles, *f* is assigned as the volume fraction of Au-TNR hybrid particles, which can influence the percolation behavior of the composites. For the curve fitted using the EMPT model, the optimum fitting parameters were determined to be: n = 0.11, *q* = 1.0, and *f* <sup>c</sup> = 0.8. It is worth noting that n and *q* are very close to those reported for the Ag-BaTiO3/PVDF (n = 0.11) [52] and the Ni-BaTiO3/PVDF (*q* = 1.0) [23], respectively. The percolation threshold is expected to occur at a high filler loading (*f* c = 0.8), which is much higher than the maximum filler loading used in this current study, and is due to the small amount of conductive Au nanoparticles used and the hybrid structure of the Au-TNR particles. Therefore, the percolation network (or conduction pathway) would not be formed in the Au-TNR/PVDF composite because the hybrid structures of the Au-TNRs prevent the formation of conducting pathways because the randomly grown Au nanoparticles do not continuously coat the TNR surface. The large increase in the ε value is primarily attributed to interfacial polarization between the Au–PVDF, Au–TNR, and TNR–PVDF interfaces.

**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.
