Dielectric Properties of Graphene/Titania/Polyvinylidene Fluoride (G/TiO2/PVDF) Nanocomposites

Flexible electronics have gained eminent importance in recent years due to their high mechanical strength and resistance to environmental conditions, along with their effective energy storage and energy generating abilities. In this work, graphene/ceramic/polymer based flexible dielectric nanocomposites have been prepared and their dielectric properties were characterized. The composite was formulated by combining graphene with rutile and anatase titania, and polyvinylidene fluoride in different weight ratios to achieve optimized dielectric properties and flexibility. After preparation, composites were characterized for their morphologies, structures, functional groups, thermal stability and dielectric characterizations by using scanning electron microscopy, X-ray diffraction, Raman spectroscopy, Fourier transform infrared spectroscopy, thermal gravimetric analysis and impedance spectroscopy. Dielectric results showed that prepared flexible composite exhibited dielectric constant of 70.4 with minor leakage current (tanδ) i.e., 0.39 at 100 Hz. These results were further confirmed by calculating alternating current (AC) conductivity and electric modulus which ensured that prepared material is efficient dielectric material which may be employed in electronic industry for development of next generation flexible energy storage devices.


Introduction
Flexible electronics are attracting increased attention in the electronic industry day by day due to their compact nature and ease of handling. Along with other electronics, flexible dielectric materials are also getting popular for many applications like in field effect transistors (FET), gate dielectrics, pulse power systems, sensors and energy storage devices, etc [1][2][3][4]. Polymers are attractive to synthesize flexible materials but they have limitations of low capacitance and low dielectric constants [4]. In last few years efforts have been made to enhance dielectric constant (ε ) of polymers either by using dielectric or conducting fillers [5,6].
Conducting fillers can elevate ε to a much higher value, but the amount of conducting filler plays a critical role in this increase. The dielectric response of conducting filler/polymer composites depends upon the percolation phenomenon. In such composites if the concentration of conducting filler is persulphate (K 2 S 2 O 8 ) was purchased from Scharlau (Germany). Phosphorus pentoxide (P 2 O 5 ) and titanium(IV) oxide (purity > 99.5% having specific surface area of 9.6 m 2 g −1 ) were taken from Riedel-de Haen (Germany). All reagents were used without any treatment and purification.

Preparation of Graphene/Titania/Polyvinylidene Fluoride Nanocomposite Films
Graphite powder was oxidized to graphene oxide (GO) by a previously reported method [19]. Graphene was synthesized by reduction of GO by using hydrazine hydrate [20]. Firstly, 1 g of PVDF was completely mixed in N,N-dimethylforamide (DMF, 20 mL) while heating and stirring at 80 • C. Specific amounts of TiO 2 and graphene were dispersed separately in 10 mL of DMF by using a probe sonicator (Branson Digital Sonifier 450, Branson Ultrasonics Corporation, Danbury, CT, USA). Both solutions were mixed while stirring at 80 • C for 45 min. Film of G/TiO 2 /PVDF composite was casted on petri dish by drying the solution at 60 • C. Firstly few composite films of G/TiO 2 /PVDF were prepared by varying amounts of graphene while amounts of other components were kept constant. After measuring their ε , graphene concentration giving maximum ε was fixed while few more films were fabricated with varying amounts of TiO 2 . G x T y PVDF, G 2x T y PVDF, G 3x T y PVDF, G 4x T y PVDF, G 5x T y PVDF, G 4x T 2y PVDF and G 4x T 3y PVDF (where x = 0.01, y = 0.1) were symbolized as G1T10PVDF, G2T10PVDF, G3T10PVDF-, G4T10PVDF, G5T10PVDF, G4T20PVDF and G4T30PVDF, respectively. Amount of PVDF in all samples was fixed i.e., 1 g. A scheme of the preparation of the films is shown in Figure 1. titanium(IV) oxide (purity > 99.5% having specific surface area of 9.6 m 2 g −1 ) were taken from Riedelde Haen (Germany). All reagents were used without any treatment and purification.

Preparation of Graphene/Titania/Polyvinylidene Fluoride Nanocomposite Films
Graphite powder was oxidized to graphene oxide (GO) by a previously reported method [19]. Graphene was synthesized by reduction of GO by using hydrazine hydrate [20]. Firstly, 1 g of PVDF was completely mixed in N,N-dimethylforamide (DMF, 20 mL) while heating and stirring at 80 °C. Specific amounts of TiO2 and graphene were dispersed separately in 10 mL of DMF by using a probe sonicator (Branson Digital Sonifier 450, Branson Ultrasonics Corporation, Danbury, CT, USA). Both solutions were mixed while stirring at 80 °C for 45 min. Film of G/TiO2/PVDF composite was casted on petri dish by drying the solution at 60 °C. Firstly few composite films of G/TiO2/PVDF were prepared by varying amounts of graphene while amounts of other components were kept constant. After measuring their ε′, graphene concentration giving maximum ε′ was fixed while few more films were fabricated with varying amounts of TiO2. GxTyPVDF, G2xTyPVDF, G3xTyPVDF, G4xTyPVDF, G5xTyPVDF, G4xT2yPVDF and G4xT3yPVDF (where x = 0.01, y = 0.1) were symbolized as G1T10PVDF, G2T10PVDF, G3T10PVDF-, G4T10PVDF, G5T10PVDF, G4T20PVDF and G4T30PVDF, respectively. Amount of PVDF in all samples was fixed i.e., 1 g. A scheme of the preparation of the films is shown in Figure 1.

Characterization of Graphene/Titania/Polyvinylidene Fluoride Nanocomposite Films
The FESEM images of nanocomposites shown in Figure 2 were recorded to study their morphology. In the FESEM images graphene sheets, TiO 2 particles and PVDF are clearly visible. Both fillers are evenly distributed in the polymer. It is evident that graphene sheets are segregated rather than being aligned due to occurrence of TiO 2 and PVDF. Nanoparticles of TiO 2 lie on graphene layers and the polymer. With increase in weight of TiO 2 , big aggregates start to form which affect dielectric properties of the nanocomposites which would be discussed in detail later in dielectric plots.

Characterization of Graphene/Titania/Polyvinylidene Fluoride Nanocomposite Films
The FESEM images of nanocomposites shown in Figure 2 were recorded to study their morphology. In the FESEM images graphene sheets, TiO2 particles and PVDF are clearly visible. Both fillers are evenly distributed in the polymer. It is evident that graphene sheets are segregated rather than being aligned due to occurrence of TiO2 and PVDF. Nanoparticles of TiO2 lie on graphene layers and the polymer. With increase in weight of TiO2, big aggregates start to form which affect dielectric properties of the nanocomposites which would be discussed in detail later in dielectric plots. XRD patterns of neat polymer and nanocomposite are shown in Figure 3A. In XRD pattern of pure PVDF, peaks at 20.4° and 29.7° are indicative of the beta (β) and alpha (α) phases of PVDF, respectively [21]. In XRD patterns of nanocomposites, the peaks located at 25 [22]. Intensity of peak of α- XRD patterns of neat polymer and nanocomposite are shown in Figure 3A. In XRD pattern of pure PVDF, peaks at 20.4 • and 29.7 • are indicative of the beta (β) and alpha (α) phases of PVDF, respectively [21]. In XRD patterns of nanocomposites, the peaks located at 25.  [22]. Intensity of peak of α-PVDF at 29.7 • decreases due to interaction of fillers with PVDF. Peak for graphene is not visible in XRD peaks of nanocomposites. It may be due to presence of peak for anatase TiO 2 which lie at 25.7 • and also due to the reason that graphene is exfoliated and segregated during sonication process. This isolation of graphene layers is also shown in FESEM images in Figure 2. Raman spectra further elucidating the structure of pure PVDF and two selected nanocomposites i.e., G4T10PVDF and G4T20PVDF are shown in Figure 3B.

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PVDF at 29.7° decreases due to interaction of fillers with PVDF. Peak for graphene is not visible in XRD peaks of nanocomposites. It may be due to presence of peak for anatase TiO2 which lie at 25.7° and also due to the reason that graphene is exfoliated and segregated during sonication process. This isolation of graphene layers is also shown in FESEM images in Figure 2. Raman spectra further elucidating the structure of pure PVDF and two selected nanocomposites i.e., G4T10PVDF and G4T20PVDF are shown in Figure 3B.  The band at 839 cm −1 is indicative of β-PVDF. Bands at 397 and 630 cm −1 in the composites correspond to anatase TiO 2 . Bands at 1352 and 1338 cm −1 in nanocomposites belong to D band and 1574 cm −1 correspond to G band of graphene [21,23].
FTIR spectra of pure polymer and it's all synthesized nanocomposite are shown in Figure 3C. Peaks at 1077, 1156 and 1406 cm −1 confirm α-PVDF. Peaks at 827, 879 and 1234 cm −1 show presence of β-PVDF [24]. Peaks for graphene at 1077 and 1156 cm −1 are merged with peaks of PVDF. N-H stretching peak at 1406 cm -1 is due to DMF residues in the nanocomposites [21]. Peak for stretching vibrations of Ti-O-Ti bonds of anatase TiO 2 is visible at 472 cm −1 [25]. TG curves of graphene, TiO 2 , pure polymer, and two selected samples i.e., G4T10PVDF and G4T20PVDF nanocomposites recoded at 30-900 • C are shown in Figure 3D. TG curve of graphene show that degradation of graphene starts at 380 • C and at 590 • C it completely degrades. TiO 2 does not degrade even at high temperature of 900 • C. At 380 • C degradation of PVDF starts and at 565 • C, 96% of it degrades. G4T10PVDF and G4T20PVDF starts to degrade at 327 • C and 334 • C, and lose about 93% and 82% of their weights at 510 • C and 500 • C, respectively. More TiO 2 in G4T20PDMS is responsible for increased thermally stability.

Dielectric Studies of Graphene/Titania/Polyvinylidene Fluoride Nanocomposite Films
A Wayer Kerr 6500B precision impedance analyzer was used at 20 Hz-2 MHz to study the dielectric properties of the samples. Films were placed between copper electrodes and measurements were made. Dielectric constant of films was measured by using relation; ε = Ct/ε o A where C, t, ε o and A represent capacitance, thickness of film, vaccum permittivity and area of the film. ε vs log f plots of pure PVDF and G/TiO 2 /PVDF nanocomposites are shown in Figure 4A. ε is high at lower frequencies due to fact that induced and permanent dipoles can accommodate themselves in proper alignment in this region, a phenomenon called the Maxwell Wagner Sillar (MWS) effect, also termed as interfacial polarization (IP). However, when frequency is increased, dipoles have less time to line up themselves in proper orientations, thus decreasing MWS and IP. This process is called polarization relaxation phenomenon [26]. At very high frequency range, ε becomes constant being frequency independent, a phenomenon called microcapacitor structure model [27]. ε increases when w/w of graphene is raised till G4T10PVDF which has value of 42.1 at 20 Hz. ε decreases with rising frequency and reaches and maintains to 11.6 at 2 MHz. But still it is greater than that of pure PVDF. Increase of ε with amount of graphene is due to reason that graphene is conductive and when its amount is increased it causes rise of IP. As conducting graphene is increased in the nanocomposite, more and more free charges accumulate at interfaces of the components thus forming more dipoles. Both increased interfacial area and homogeneous distribution of fillers contribute in rise of IP [26,28]. It was reported earlier that when conducting and non-conducting additives are embedded in the composites simultaneously, microcapacitors are formed where conducting part act as electrodes and non-conducting part acts as dielectric medium. In presently prepared nanocomposites, graphene sheets acts as electrodes while ceramic and polymers act as dielectric medium of the microcapacitors. As the amount of graphene is increased the number of microcapacitors also multiplies till G4T10PVDF. However after G4T10PVDF when the graphene concentration is further raised in G5T10PVDF, ε starts to decline. It is due to the fact that graphene sheets become associated to make flow of charges possible, thus the leakage current is raised to depress ε [29]. To further enhance ε of the nanocomposites the amount of ceramic was raised by keeping all other concentrations constant. ε again raised till the percolation level of ceramic was reached in G4T20PVDF. G4T20PVDF possesses highest ε among all nanocomposites i.e., 159.8 at 20 Hz which declined and was maintained to 34.8 at 2 MHz. The rise in ε after increasing amounts of ceramic is attributed to expansion of effective charge transport network to improve the conductivity within the nanocomposites [30,31]. However after reaching the percolation level when the amount of ceramic was further raised ε was decreased as rising amounts of ceramic result in aggregation of ceramic nanoparticles which not only effects the morphology, but also the efficiency of the charge transport network and the dielectric properties as well.
Upon application of an electrical field current starts to flow through the conducting graphene as result of which electrical energy is converted into thermal energy [29]. At 20 Hz, tanδ of G4T10PVDF is 0.5 which reduces to 0.25 at 2 MHz. Tanδ decreases even more with addition of TiO2 and G4T20PVDF has tanδ of 0.5 at 20 Hz which further reduces o 0.03 at 2 MHz. Comparative plots of ε′ and tanδ of pure polymer and nanocomposites at various frequencies are shown in Figure 5a-d. AC conductivity (σac) of films calculated by using the relation σac = ɛoε′ωtanδ (angular frequency = ω = 2πf) σac of pure PVDF and nanocomposites plotted against frequency are shown in Figure 6A. σac rises when amount of conducting graphene is raised due to formation of conducting routes. σac is further raised when the ceramic concentration is raised. Among all nanocomposites, G4T20PVDF has the highest σac. Ceramic addition improves σac due to formation of a charge transport network within the nanocomposites. The results are in complete harmony with previously literature findings [31]. Comparative values of ε′, tanδ and σac of pure polymer, G4T10PVDF and G4T20PVDF nanocomposites at diverse frequencies are shown in Table 1. Electric modulus is used to explain transport of electrical charges within the dielectric medium. Real (M′) and imaginary parts (M″) of electric modulus were calculated by using relations; M′ = ε′/(ε″ 2 + ε′ 2 ) and M″ = ε″/(ε′ 2 + ε″ 2 ), respectively. M′ and M″ of pure polymer and all ternary nanocomposites plotted against log f are shown in Figure 6B,C. Figure 6B exhibits that M′ rises with rise in frequency till it acquires its maximum value, known as asymptotic value (M∞). Achieving M∞ is indicative of the capacitive nature of the ternary nanocomposites. It is also indicative of a relaxation process which extends over a long frequency range. Figure 6C shows that M″ also rises and reaches a maximum value, M″max, after which it starts to decline with rise in high frequency range [32]. At low frequency range charges and charge carriers are able to move freely according to applied electric field and may travel long distance Energy dissipation of pure polymer and all nanocomposites was calculated in the form of tanδ by using formula: Tanδ = ε"/ε where ε" and ε represent the dielectric loss and dielectric constant, respectively. Plots of tanδ of PVDF and all nanocomposites against frequency are shown in Figure 4B. It is clear that tanδ decreases with raised frequency. The effect of different amounts of fillers on tanδ was also studied. It was found that when the amount of graphene is increased, tanδ also increases as well aligned conducting graphene sheets cause an increase of the leakage current density. Upon application of an electrical field current starts to flow through the conducting graphene as result of which electrical energy is converted into thermal energy [29]. At 20 Hz, tanδ of G4T10PVDF is 0.5 which reduces to 0.25 at 2 MHz. Tanδ decreases even more with addition of TiO 2 and G4T20PVDF has tanδ of 0.5 at 20 Hz which further reduces o 0.03 at 2 MHz. Comparative plots of ε and tanδ of pure polymer and nanocomposites at various frequencies are shown in Figure 5a-d.
AC conductivity (σ ac ) of films calculated by using the relation σ ac = ε o ε ωtanδ (angular frequency = ω = 2πf) σ ac of pure PVDF and nanocomposites plotted against frequency are shown in Figure 6A. σ ac rises when amount of conducting graphene is raised due to formation of conducting routes. σ ac is further raised when the ceramic concentration is raised. Among all nanocomposites, G4T20PVDF has the highest σ ac . Ceramic addition improves σ ac due to formation of a charge transport network within the nanocomposites. The results are in complete harmony with previously literature findings [31]. Comparative values of ε , tanδ and σ ac of pure polymer, G4T10PVDF and G4T20PVDF nanocomposites at diverse frequencies are shown in Table 1. Electric modulus is used to explain transport of electrical charges within the dielectric medium. Real (M ) and imaginary parts (M") of electric modulus were calculated by using relations; M = ε /(ε" 2 + ε 2 ) and M" = ε"/(ε 2 + ε" 2 ), respectively. M and M" of pure polymer and all ternary nanocomposites plotted against log f are shown in Figure 6B,C. Figure 6B exhibits that M rises with rise in frequency till it acquires its maximum value, known as asymptotic value (M ∞ ). Achieving M ∞ is indicative of the capacitive nature of the ternary nanocomposites. It is also indicative of a relaxation process which extends over a long frequency range. Figure 6C shows that M" also rises and reaches a maximum value, M"max, after which it starts to decline with rise in high frequency range [32]. At low frequency range charges and charge carriers are able to move freely according to applied electric field and may travel long distance till M"max is achieved. However at high frequencies, charges or charge carriers may move to small course only as they do not have sufficient time for alliance as there electric field is rapidly changing [33,34].

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till M″max is achieved. However at high frequencies, charges or charge carriers may move to small course only as they do not have sufficient time for alliance as there electric field is rapidly changing [33,34].

Conclusions
In summary, in this research work, we have demonstrated the successful fabrication of new flexible ternary nanocomposite films by combination of PVDF polymer used as base matrix and to achieve flexibility with titania and graphene additives providing their specific properties. The comprehensive characterization of prepared composites with different ratios of these three components was performed to confirm their morphologies, structures, functional groups, thermal stability and their dielectric properties. Results showed that nanocomposite G4T20PVDF (G:TiO2:PVDF = 4:20:100) exhibited a dielectric constant and energy loss of 70.4 and 0.39 at 100 Hz. Calculation of AC conductivity and electric modulus further confirmed that prepared nanocomposite films are effective dielectric materials which are proposed for use in the electronics industry for development of next generation flexible energy storage devices.

Conclusions
In summary, in this research work, we have demonstrated the successful fabrication of new flexible ternary nanocomposite films by combination of PVDF polymer used as base matrix and to achieve flexibility with titania and graphene additives providing their specific properties. The comprehensive characterization of prepared composites with different ratios of these three components was performed to confirm their morphologies, structures, functional groups, thermal stability and their dielectric properties. Results showed that nanocomposite G4T20PVDF (G:TiO 2 :PVDF = 4:20:100) exhibited a dielectric constant and energy loss of 70.4 and 0.39 at 100 Hz. Calculation of AC conductivity and electric modulus further confirmed that prepared nanocomposite films are effective dielectric materials which are proposed for use in the electronics industry for development of next generation flexible energy storage devices.