Enhancement investigations on dielectric and electrical properties of niobium pentoxide (Nb2O5) reinforced poly(vinylidene fluoride) (PVDF)- graphene oxide (GO) nanocomposite films

ABSTRACT An ultra high dielectric constant nanocomposites comprising of poly(vinylidene fluoride) (PVDF) as a polymer matrix and niobium pentoxide (Nb2O5)-reinforced graphene oxide (GO) have been successfully developed using solution casting technique. Scanning electron microscopy (SEM) demonstrates that the homogeneous dispersion of Nb2O5 and GO within the PVDF matrix was realized. The dielectric and electrical properties of the resulting PVDF-GO-Nb2O5 nanocomposite films as a function of frequency were studied. The dielectric constant of the nanocomposites system reached a value of about ≈140 at 100 Hz, with a relatively low dielectric loss factor (≈ 1.4). The enhanced dielectric performance of the PVDF-GO-Nb2O5 nanocomposites was ascribed to the presence of Nb2O5 onto the GO, which exhibits strong interaction between GO and PVDF matrix through hydrogen bonding. Moreover, the experimental results fit well with percolation theory and near the percolation threshold (fc < 2 wt %) with high dielectric constant was achieved for PVDF-GO-Nb2O5 nanocomposites. Furthermore, the AC electrical conductivity was also noticeably enhanced. Our strategy provides a facile method to prepare high dielectric constant and relatively low dielectric loss PVDF-GO-Nb2O5 nanocomposite films that might be suitable for energy storage applications.


Introduction
Polymeric nanocomposites containing selected inorganic fillers with elevated dielectric constant and low dielectric loss have brought about considerable attention in the field of energy storage devices [1], sensors [2], and flexible electronics, due to their inherent advantages of high break down strength, easy process ability, mechanical flexibility, and economical efficiency [3,4]. In order to meet the miniaturization and inexpensive requirements of energy storage devices, dielectric nanocomposites with relatively high dielectric constant, high break down strength, and low loss materials are strongly desired. Great efforts have been made to prepare flexible nanocomposite films using polymers and highly conductive fillers for justifying the candidature of dielectric and electrical behavior of material [4]. In recent few years, many research groups are trying to develop high dielectric constant polymer nanocomposites for embedded capacitor applications [5]. However, Graphene is a class of smart material with sp 2 hybridized monolayer carbon atoms arranged in two-dimensional honey comb lattice-like structure. Graphene is reported to have an extraordinary property, which includes high surface area, high electronic conductivity, young's modulus, and thermal conductivity, respectively [6,7]. In order to improve the thermal, dielectric and electric performance of the polymer nanocomposites, graphene makes it suitable for use as inorganic filler-based materials. The bulk amount of graphene can be formed by the chemical reduction of graphene oxide (GO) by graphite as precursor [8]. Using this chemical technique, huge scale manufacture of graphene is expected to be the simplest and most useful technique as graphite is cheap and easily available. On the other hand, GO are two-dimensional carbon-based materials with different oxygen containing functional groups including hydroxyl, carbonyl, and epoxide [9]. The presence of these functional groups of GO is strongly hydrophilic in nature and also the individual sheets of GO is well dispersed in water. Moreover, it has been reported that the improvement of thermal stability, mechanical, and electrical properties of GO-reinforced polymers is due to their huge aspect ratio, high strength, and the strong attachment with polymer matrix [10].
Niobium pentoxide (Nb 2 O 5 ), one of the most important transition metal oxides has immense interest due to their potential applications in gas sensors, catalysts, micro-electronics, and optoelectronic industries [11]. However, the Nb 2 O 5 is an n-type semiconductor with a band gap of about 3.4 eV, low in comparison with other oxide [12]. This niobium pentoxide has several advantageous characteristics including surface area enables for easy modification by intercalation, superficial modification and formation of nanosheets or nanoscrolls [13][14][15]. Moreover, it is also used as promising doping agent for tailoring nanostructured composites materials for potential applicability in the various fields. Niobium pentoxide is biocompatible as well as it enhances bioactivity and corrosion resistance of the respective nanocomposites [16][17][18]. In this study, the niobium pentoxide-reinforced grapheneoxide-based polymer nanocomposites have achieved significant increase in dielectric constant with improved conductivity and suppressed loss. Besides, polymers are most normally used as dielectric materials with high mechanical flexibility, good process ability, low cost, and high dielectric strength [19]. Especially, the ferroelectric polymers such as poly(vinylidene fluoride) (PVDF) and its co-polymers poly(vinylidene fluoride co-hexa fluoropropylene) (PVDF-HFP), which is a semi-crystalline thermoplastic polymeric materials with extraordinary high piezo and pyro electric coefficient, better thermal stability, chemical resistance, high dielectric constant (≈10) and high break down strength [20][21][22].
In the present investigation, the flexible polymeric nanocomposite films with high dielectric constant and suppressed dielectric loss by using graphene oxide (GO), niobium pentoxide (Nb 2 O 5 ) as the fillers and poly(vinylidene fluoride) (PVDF) as the matrix was prepared by solution casting techniques. A study concerning niobium pentoxide reinforced graphene-oxidebased materials has not been previously reported in the literature so far. Keeping in mind, we have fabricated PVDF-GO-Nb 2 O 5 nanocomposite films with enhanced dielectric and electrical properties. The current work is focused on preparation of nanocomposites which optimizes the dispersion level of GO and Nb 2 O 5 particles within the polymeric matrix to get improved dielectric properties (dielectric constant and dielectric loss) and electrical performance (AC conductivity) of the nanocomposites than the neat polymer. Besides, the dielectric and electrical performance of the PVDF-GO-Nb 2 O 5 nanocomposite films were analyzed by using impedance analyzer in a wide range of frequency from 100 Hz to 1 MHz at room temperature. We believed that this study may provide a perspective utility of Nb 2 O 5 for the development of ultra high dielectric and electrical performance of the nanocomposites for energy storage applications.

Chemicals and materials
Poly(vinylidene fluoride) (PVDF) powder (M w = 180, 000 g/mol) was purchased from Sigma-Aldrich, India, and used as polymeric matrix. Natural flake graphite was purchased from mK NANO, USA. Potassium permanganate (KMnO 4 ), sulfuric acid (H 2 SO 4 ), sodium nitrate (NaNO 3 ), hydrogen peroxide (H 2 O 2 ) (30 wt %), and hydrochloric acid (HCl) were purchased from Merck, India. The niobium pentoxide (Nb 2 O 5 ) powder was supplied by Spectrochem. Pvt. Ltd., India. The N, N-dimethylformamide (DMF) was obtained from Himedia Laboratories Pvt. Ltd, India and used as solvent for the preparation of PVDF-GO-Nb 2 O 5 nanocomposite films. All the chemicals were of analytical grade and used without further purification.

Synthesis of graphene oxide (GO)
Graphene oxide (GO) was synthesized according to some previously reported modified Hummer's method [23,24]. In this synthesis method, graphite powder, NaNO 3, and KMnO 4 were added to a H 2 SO 4 solution under continuous stirring for 1 h in a round-bottom flask. The reaction mixture was stirred and maintained temperature at 35°C for 1 h. Then, 90 ml of deionized water was added, while keeping the temperature at 98° C for 15 min and warm water was poured slowly followed by a drop wise addition of 30% H 2 O 2 with continuous stirring for 2 h until the color of the solution changed to golden yellow. As a result, the reaction mixture was filtered and washed several times with distilled water, until the pH of the supernatant was reaches 7 using centrifugation at 8500 rpm for 45 min. The product was dried at 45°C in a vacuum oven until completely dried and finally to get the purified graphene oxide.

Preparation of PVDF-graphene oxide (GO)-Nb 2 O 5 nanocomposites
The PVDF-GO-Nb 2 O 5 nanocomposite films with different weigh percentage of Nb 2 O 5 contents were prepared by solution casting technique. Firstly, poly (vinylidene fluoride) (PVDF) was dissolved in N, N-dimethylformamide (DMF) and stirred for 1 h to ensure homogeneity of the solution. Then, previously synthesized GO was dispersed into the mixture of DMF and PVDF under ultra-sonication bath for 30 min and further continuously stirred for 30 min at room temperature. Predetermined amounts of Nb 2 O 5 particles were dispersed in DMF by using an ultrasonic bath for 30 min and then suspension was added into the PVDF solution. The resulting mixture was stirred vigorously for several hours to improve the dispersion of the Nb 2 O 5 , GO and simultaneously to remove the air bubbles to form a stable suspension. Subsequently, the resultant solution was casted into a piece of clean glass petri dish and dried in a vacuum oven at 80°C for 4 h to evaporate DMF solvent to produce the PVDF-GO-Nb 2 O 5 nanocomposite films. All the resultant nacomposite films were measured to be ~72 µm thickness of various compositions were prepared by solution casting technique. For making a comparison, the PVDF-GO nanocomposite containing 10 wt% of GO was also prepared by the same processing method in the absence of Nb 2 O 5 . The schematic diagram of the synthesis process of PVDF-GO-Nb 2 O 5 nanocomposite films was shown in scheme 1.

Characterization techniques
The TEM measurement of graphene oxide (GO) was carried out in the transmission electron microscope (JEOL 2100) operating at 200 kV. SEM observations were performed to analyze the detailed microstructure of the Nb 2 O 5 reinforced graphene oxide (GO) nanocomposite films by using a scanning electron microscopy (SEM, ZEISS EVO-18). The UV-Visible absorption spectrum of well dispersed GO were recorded on a Shimadzu UV-2450 UV-visible spectrophotometer. The Fourier-transform infrared (FTIR) spectrum of the graphene oxide was measured on a spectrometer (5700 FTIR, Nicolet) by using KBR pellet. The dielectric and electrical responses of the PVDF-GO-Nb 2 O 5 nanocomposite films in the frequency range from 100 Hz to 1 MHz were measured using an impedance analyzer (HIOKI 3570 Impedance analyzer).

Results and discussion
The schematic illustration of the bonding interaction between GO, Nb 2 O 5 and PVDF nanocomposites is shown in Scheme 2. The niobium pentoxide (Nb 2 O 5 )reinforced GO and PVDF matrix exhibits improvement of dielectric and electrical performance of the nanocomposites. This may be due to the strong interfacial interaction between Nb 2 O 5 , GO and PVDF matrix. Moreover, there is a strong interaction between hydrogen ion of GO with O atoms of Nb 2 O 5 and fluorine groups in the polymer chain through hydrogen bonding [25,26]. This hydrogen bonding helps GO dispersion in the PVDF matrix and also significantly improves the compatibility of the nanocomposites [25][26][27][28].

Morphology analysis
The surface studies on morphology properties of prepared graphene oxide were examined by TEM micrographs as shown in Figure 1(a). The TEM image of the sample of graphene oxide was emerged as semitransparent, which describes the material is not stable under high energy beam [29,30]. The morphology of graphene oxide is also signifying the presence of wrinkled structure, which suggests that it may be randomly aggregated particles with non uniform size. However, the GO revealed a thick flake layers, irregular shape, and having multilayer structures at edges with no removal of oxygen atoms, which may cause cracking of structure, occurred during oxidation process [30][31][32]. Moreover, the higher transparency area signifies much thinner films of a few layers of graphene oxide resulting from stacking nanostructure exfoliation [33,34]. On the other hand, the morphology of the niobium pentoxide reinforced PVDF composite films was studied using scanning electron microscopy (SEM). As shown in Figure 1(b,c), it is observed that the increment of filler niobium-reinforced GO gives better dispersion of 2.5 wt% of filler content, which is a strong interfacial interaction between the Nb 2 O 5, GO and the polymer matrix [35]. From the SEM images of Scheme 1. Schematic illustration for preparation of PVDF-GO-Nb 2 O 5 nanocomposite films. 0.5 wt% and 2.5 wt% of Nb 2 O 5 -reinforced GO-PVDF composite films (Figure 1(b,c)), GO plays a vital role in the nucleation and growth of Nb 2 O 5 which is dispersed uniformly in the PVDF matrix without apparent agglomeration. In the presence of Nb 2 O 5 and graphene oxide (GO), the polymer matrix acquire reinforcement and consequently plastic constraint may occur [36]. This leads to the formation of spherical structure of GO within which Nb 2 O 5 particles get embedded and dispersed within the polymer matrix. This may be due to the improved interfacial interaction between Nb 2 O 5 -GO and the PVDF matrix through polar groups of Nb 2 O 5, which promotes the effectiveness of filler particles [37]. In addition, the graphene oxide sheets are readily  dispersed into the polymer matrix, due to the existence of hydrophilic oxygen containing functional groups on their surface. Moreover, the incorporation of Nb 2 O 5 and GO into PVDF matrix has led to increased interfacial area of attachment and also contribute to the improvement in dielectric constant of the PVDF-GO-Nb 2 O 5 nanocomposites. The formation of these Nb 2 O 5 -reinforced GO sheets in a local area is helpful for the improvement of electrical conductivity and dielectric properties of the nanocomposites [37,38]. Figure 2(a) shows the UV-Visible absorption spectrum of graphene oxide. According to the absorption spectra, the spectrum of graphene oxide has a strong absorption peak at about 230 nm related to π-π* transition of the C-C aromatic bond and weak absorption (a small shoulder) at 300 nm due to n-π* transitions of C = O bond [39][40][41]. The FTIR spectrum of GO in Figure 2(b) shows a broad peak appeared at 3444 cm −1 is responsible for stretching mode of -OH bond, reveals the presence of hydroxyl groups in graphene oxide. It shows characteristic absorption peak at 1721 cm −1 and 1376 cm −1 corresponds to the C = O and -C-O stretching of carboxylic groups, aromatic -C = C (1639 cm −1 ), epoxy -C-O (1241 cm −1 ), and alkoxy -C-O (1069 cm −1 ) indicating the existence of oxygen containing functional groups on the graphene oxide [41][42][43][44][45]. Figure 3 represents the dielectric constant (ԑ r ) and AC electrical conductivity for neat PVDF and PVDF-GO nanocomposites comprising 10 wt% of GO contents as a function of frequency at room temperature. As shown in Figure 3(a,b), it is observed that both the value of dielectric constant and ac electrical conductivity is larger than that of the PVDF matrix, which can be attributed to the hopping conduction mechanism of GO in the PVDF matrix [46]. The value of the dielectric constant decreases with increase in frequency for PVDF-GO composite (Figure 3(a)), which is a general feature of polar dielectrics. The low dielectric constant at high-frequency region and high dielectric constant at low-frequency region is the typical characteristic of space charge relaxation effect. But in case of neat  PVDF, the dielectric constant becomes saturated at frequency region (10 3 to 10 5 Hz) due to dipolar polarization and interfacial polarization [47][48][49][50]. Moreover, at low-frequency region, slight increase in the dielectric constant is noticed, which may be due to the contribution of all the types of polarizations (electronic, atomic, dipolar, interfacial) [49][50][51]. Furthermore with 10 wt% of GO, the dielectric constant is decreasing with increase in frequency may be ascribed to the failure of the interfacial polarization process to keep up with the changing step of the external applied electric field. Thus, at a high-frequency range, these properties of the composites are dominated by the relaxation process of PVDF matrix [49,50]. The AC conductivity (Figure 3(b)) increases with increase in frequency because the conduction may be due to increase in the hopping of charge carriers with increase in frequency [52,53]. However, the PVDF-GO composites the value of the AC electrical conductivity gradually increased with increase in frequency and higher than that of neat PVDF over the whole frequency range, which may be due to the better dispersion of conductive GO in the PVDF matrix resulting easy passage of the charge carriers through the material [54]. It is interesting to note that in case of neat PVDF the whole conductivity spectrum consists of two different regimes: (1) the frequency-independent plateau regime (2) frequency-dependent regime corresponding to AC conductivity. The plateau regime detected in the low-frequency region shifts toward high-frequency [55]. On increasing the frequency, the electrical conductivity transmutes from frequency-independent DC conductivity to frequency-dependent AC conductivity. The low-frequency plateau signifies the migration of charge carrier through defects by hopping like motion. On the other hand, at high frequencies the conduction may be due to hopping of electron and conductivity increases due to increase in the hopping frequency [52,53]. In addition, with the presence of conductive GO may improve the electrical conductivity of the PVDF composites, favorable for the enhancement of dielectric constant of the PVDF composites. Moreover, the dielectric constant of neat PVDF is ≈ 6.0 at 100 Hz, but the dielectric constant for two phase PVDF-GO nanocomposite is ≈ 35, which is moderately low, although nearly six times larger than that of the neat polymer matrix. Previously, it has been reported that a high weight percentage of filler loading (> 60 wt %) is essential to achieve high dielectric constant polymerbased nanocomposites [56], but it may also have some adverse effect on prepared nanocomposites in terms of the crystallinity and flexibility.

Dielectric properties of the PVDF-GO-Nb 2 O 5 nanocomposites
To achieve excellent dielectric properties of the PVDF-GO-Nb 2 O 5 nanocomposites, the effect of different weight percentage of Nb 2 O 5 particles on the electrical performances was investigated. Figure 4 shows the dependence of dielectric constant of PVDF-GO-Nb 2 O 5 nanocomposite films with different weight percentage of Nb 2 O 5 contents in the room temperature frequency range (100 Hz to 1 MHz). As shown in Figure 4(a), it is observed that the dielectric constant value of the nanocomposites exhibit significant development with the increase of Nb 2 O 5 content over the entire frequency range. For instance, the value of the dielectric constant increases from ≈ 30 to 140 (100 Hz), when the filler content increased from 0.5 to 2.5 wt%, which is about 24 times larger than that of pristine PVDF film. However, the dielectric constant of neat PVDF and PVDF-GO-Nb 2 O 5 nanocomposites decreases with increase in frequency. Also with gradual increase in the weight percentage of Nb 2 O 5, the dielectric constant goes on increasing especially at low-frequency region. This reveals, by incorporating conductive filler (Nb 2 O 5 ) into the polymer matrix results enhancement of the dielectric constant, which is owing to the effect of interfacial or Maxwell-Wagner-Sillars (MWS) polarization [57][58][59][60]. The interfacial polarization is associated with the entrapment of free charges generated at the interface of Nb 2 O 5 , GO and the polymer matrix due to their unusual dielectric constant and conductivity of the nanocomposites. Moreover, with the increase in frequency, the interfacial polarization cannot follow the external electric field change, thus there is a sharp reduction of space charge polarization and slow down dielectric relaxation of the matrix of the nanocomposites. This also leads to the decrease in the dielectric constant at higher frequency region [60,61]. Figure 4(b) shows the dependence of dielectric loss of PVDF-GO-Nb 2 O 5 nanocomposites as a function of frequency at room temperature. The dielectric loss relates to the measurement of the energy dissipation in a dielectric material through application of alternating electric field. As shown in Figure 4(b), it is observed that the entire nanocomposites show improved dielectric loss due to the incorporation of conductive Nb 2 O 5reinforced GO into PVDF matrix. In the low-frequency region, the polarization in the nanocomposite is less due to non alignment of dipoles in the direction of the electric field, which causes less dissipation of energy resulting decrease in the dielectric loss. On the other hand, when the frequency increases (>10 3 Hz), polarization is increased due to more dipole alignment in the direction of the applied electric field, which enhances the conductivity in the nanocomposite [62,63]. Consequently, more energy dissipation takes place causing increase in the dielectric loss values. The nanocomposite with 2.5 wt% of Nb 2 O 5 exhibits the dielectric loss value (≈ 1.4) at a frequency of 100 Hz. Such loss is the inevitable consequence of the considerably improved conductivity of the nanocomposites and can be considered as main aspect of the percolative nanocomposites [64]. However, the GO are isolated by the Nb 2 O 5 layers composed of GO and polymer matrix, which results in the formation of conductive networks and these conductive networks can give rise to leakage current in the nanocomposites. The higher weight percentage of filler loading may provide more conductive pathway and thus the dielectric loss values is increased [48].
The variation of the dielectric constant and dielectric loss with Nb 2 O 5 loading at two particular frequencies from 10 2 Hz and 10 3 Hz is presented in Figure 5. It is observed from the Figure 5(a), the value of the dielectric constant increases with increase in frequency and also increases with increasing weight percentage of filler loadings. However, the Nb 2 O 5 -reinforced GO-PVDF nanocomposites reveal a superior dielectric constant than that of the neat PVDF and PVDF-GO nanocomposites. However, the nanocomposite shows higher dielectric constant in lower frequency regions may be due to the increase in the interfacial polarization [58][59][60]. For the weight percentage of Nb 2 O 5 content lower than 2.5 wt%, the dielectric constant of the nanocomposites increases gradually and found to be 25, 45, 65, and 120, respectively, for 0.5 wt% to 1.5 wt% of filler loading. The improvement of dielectric constant (<10 2 Hz) may be due to the rise of frequency explained on the basis of the movement of polymer chain segments does not have sufficient time to catch up with the application of electric field. Furthermore, the tunneling resistance among the GO strongly sensitive to thermal fluctuation is reduced with increase of frequency [65]. As a result, the conductivity of the nanocomposites is improved; this favors the enhancement of the dielectric constant. The dielectric loss of the nanocomposites is another crucial parameter for dielectric application of the prepared PVDF-GO-Nb 2 O 5 nanocomposites. As shown in Figure 5(b), the value of the dielectric loss (≈ 1.4 at 100 Hz) steadily increases with increase in the weight percentage of Nb 2 O 5 contents; which may be the outcome of the conductive paths within the nanocomposite system. Meanwhile, these conductive paths may give rise to high electrical conductivity and increase in the current leakage therefore the value of the dielectric loss increased at higher filler loading [66]. Figure 6 shows the variation of dielectric constant (ԑ r ) of PVDF-GO-Nb 2 O 5 nanocomposites as a function of different weight percentage of the Nb 2 O 5 at 100 Hz and room temperature. The dielectric constant of the nanocomposites increases gradually with increase in the filler loading, but increases considerably when the Nb 2 O 5 filler content comes closer to 1.5 wt%. At this stage, parallel micro-capacitors were hard, due to the presence of large distance between two neighboring sites of GO and Nb 2 O 5 . As weight percentage of Nb 2 O 5 increases above 1.5 wt% and reached percolation threshold, the dielectric constant values increased noticeably. Interestingly, it is observed that the dielectric constant was enhanced from ≈140 to 144 when content of Nb 2 O 5 increased from 1.5 wt% to 2.5 wt%, which suggests the incorporation of Nb 2 O 5 . Even at low concentration of Nb 2 O 5 appreciably improved the dielectric constant of the resultant PVDF-GO-Nb 2 O 5 nanocomposites. This progress of dielectric constant near the percolation threshold can be explained by the presence of microcapacitor networks [56,66]. So the vicinity of percolation threshold, a large number of conductive Nb 2 O 5 networks were separated by thin dielectric layer composed of PVDF matrix and graphene oxide, consequence upon this result in the formation of small capacitors throughout the PVDF-GO-Nb 2 O 5 nanocomposites. Thus, the PVDF-GO-Nb 2 O 5 nanocomposite films near the percolation threshold can be considered as a large electrode area and high charge storage capability, which encourage the rapid increase of capacitance. Moreover, the nanocomposites with 2.5 wt% of Nb 2 O 5 achieve a maximum dielectric constant value ≈140, which is nearly about 22 times higher than that of the pure PVDF. The variation of the dielectric constant (ԑ r ) near the percolation threshold is given by the power law [66,67], ε ¼ε m fc À f ð Þ=fc À s forf < fc (1) where ε and ε m is the dielectric constant (ԑ r ) of the PVDF-GO-Nb 2 O 5 nanocomposites and the neat PVDF matrix, respectively. f is the weight percentage of Nb 2 O 5 contents of the nanocomposites, fc is the percolation threshold, and s is the critical exponent. Figure 6 shows that experimental data fit well to the log-log plots of the power law on linear scale using Equation (1) gives fc = 2.0 wt% with the critical exponent of s = 0.997. In addition, the critical exponent nearly agrees well with that in the universal percolation theory (s ≈ 1). Besides, this result is not always observed in practical continuum system [68]. Figure 7 shows the dependence of AC electrical conductivity (σ Ac ) of the PVDF-GO-Nb 2 O 5 nanocomposites with different weight percentage of Nb 2 O 5 content as a function of frequency. For the nanocomposites with low weight percentage of Nb 2 O 5 contents (≤ 1.5 wt %), the conductivity curves exhibit a frequency independence character in low-frequency range, which suggests an insulator to conductor transition owing to the presence of some conductive paths in the nanocomposites. However, the conductivity of all said nanocomposites increases linearly with increase in frequency for all loaded weight percentage of filler content and is larger than that of the neat PVDF. When fNb 2 O 5 approaches fc, the percolation threshold and uphold the power laws [33,69] as described below:

AC electrical conductivity study
σ / ω μ as f Nb 2 O 5 ! fc (2) In Equation (2), ω is the angular frequency (equal to 2πν), ν is the frequency and μ is the corresponding critical exponent, always between 0 and 1. The experimental data of the PVDF-GO-Nb 2 O 5 nanocomposites with fc = 1.5 wt% (near fc) give µ = 0.99 (See Figure 7 (b)). Moreover, this result is slightly larger than that of the common value (µ uni = 0.70) from the percolation theory [29].

Conclusions
In summary, the Nb 2 O 5 -reinforced GO-PVDF nanocomposite films were prepared successfully by using solution casting technique. The PVDF-GO-Nb 2 O 5 nanocomposites were carefully analyzed by SEM analysis and experimental results showed homogeneous dispersion of the GO and Nb 2 O 5 particles into the polymer matrix. The strong interfacial interactions were observed between Nb 2 O 5 , GO and PVDF matrix. The dielectric and electrical performance of the PVDF-GO-Nb 2 O 5 nanocomposites were measured in a wide range of frequencies from 10 2 Hz to 10 6 Hz. The PVDF-GO-Nb 2 O 5 nanocomposites exhibited considerable increment in the dielectric constant, which is associated with homogeneous dispersion of GO and Nb 2 O 5 particles within the polymer matrix may be attributed to the interfacial or Maxwell-Wagner-Sillars (MWS) polarization effect [46,47]. At the filler content 2.5 wt%, the value of dielectric constant reaches ≈140 and a minimized dielectric loss (1.4) was noticed at the frequency of 100 Hz. The dielectric constant of PVDF-GO-Nb 2 O 5 nanocomposites was 24 times greater than pristine PVDF films on the other hand it is fou times greater than two-phase PVDF-GO nanocomposites.
Besides, the dielectric constant of PVDF-GO-Nb 2 O 5 nanocomposite follows the percolation theory and showed percolation threshold of fc = 2 wt%. These findings put forward the PVDF-GO-Nb 2 O 5 nanocomposite films might be suitable candidates for the development of high-performance dielectric composite materials for energy storage applications.