Effect of γ-PVDF on enhanced thermal conductivity and dielectric property of Fe-rGO incorporated PVDF based flexible nanocomposite film for efficient thermal management and energy storage applications

Abstract

Here, we investigate the effect of thermal conductivity of γ-crystallites of PVDF in Fe-rGO/PVDF nanocomposite, which are of potential use as actuators and temperature sensors for thermal management applications. The formation of γ-crystallites help to increase the thermal conductivity of the nanocomposite up to 0.89 W mK⁻¹ at low level of filler loading (3 wt%) and we showed that the thermal conductivity depends on the amount of crystalline polar γ-phase in addition to filler concentration. Although thermal conductivity depends on the crystallinity of the nanocomposite, here enhancement of thermal conductivity is not related only to crystallinity, as the crystallinity is decreased compared to neat PVDF. However the thermal conductivity increases because of the generation of a higher number of γ-crystallites of small size. Furthermore, the nanocomposite at low filler loading also shows high dielectric constant with low dielectric loss of the order of ≈57 and ≈0.13, respectively, at 1 kHz. Moreover, the energy storage property and its dependence on γ-crystallite size reveals that the material can also exhibit superior released energy density (1.45 J cm⁻³) as compared to pure PVDF.

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1. Introduction

Recently, polymer nanocomposite having large thermal conductivity and high dielectric constant are highly necessary due to their diverse applications in electric and electronic industries^1,2 including stress control, sensors, actuators, embedded capacitors, electromagnetic shielding, and most latest energy storage devices.^2–4 The enhancement of thermal conductivity of the polymer nanocomposite is still a most urgent challenge for the dissipation of heat from micro/nano electronic devices during operation. We thus need to enhance the thermal conductivity to a certain limit for easy dissipation of heat from the system. Although polymer composites exhibit a wide variety of applications from generators to automobile parts, including in heat exchangers and power generation, they also have a great potential application in micro/nano electronic devices. Polymer composites have advantages for practical application compared to other systems due to their easy processability.⁴ Poly(vinylidene fluoride) (PVDF) is a promising piezoelectric and ferroelectric polymer for the preparation of polymer based embedded capacitors owing to its valuable properties, such as high energy storage, high dielectric constant, high heat resistance and sustainability in high electric field range due to the presence of spontaneous arrangement of –C(F)– dipoles in the crystalline phases (α, β, γ, δ and ε).^3,5–7 Although several research groups have prepared PVDF-based nanocomposite having high dielectric constant, only a few reports^4,8–11 on the investigation of thermal conductivity, as well as dielectric properties of the polymer nanocomposite, have been reported so far. Moreover, low thermal conductivity of these polymer nanocomposite restricts the heat dissipation and thereby leads to a decrease in dielectric strength of the materials.¹² Rapid and efficient dissipation of heat generated from electronic materials is essential to maintain the operating temperature at the desired level. Recently, conducting nanofillers such as, CNT,¹³ exfoliated graphite¹² and graphene¹⁴ have been of great interest due to their ability to form conducting network at very low filler loading in polymer nanocomposite, which significantly improves thermal conductivity by easy dissipation of heat. Among these, graphene is believed to be the most ideal nanofiller due to its light weight, excellent corrosion resistance, large surface area, high aspect ratio, low manufacturing cost, high electrical conductivity¹⁵ and excellent thermal conductivity (≈4000–5000 W mK⁻¹).¹⁶ However, reports on the studies of thermal and electrical conductivity of PVDF/graphene nanocomposite are relatively rare.^17–19 This provides the scope for further investigation on development of high thermal conductive, high dielectric constant/low dielectric loss PVDF/graphene nanocomposite. Several research groups have worked on PVDF matrix based polymer nanocomposite to increase the dielectric constant by adding various inorganic and organic fillers such as ZnO,²⁰ BaTiO₃,⁸ BaTiO₃–SiC,²¹ PZT,²² BCZT,²³ AlN/SiC,²⁴ Al,²⁵ Al–SiC,²⁶ Ag,⁴ MWCNT,²⁷ graphite,⁵ and recently graphene.²⁸ However, most of these fillers are used at considerably high volume to achieve high dielectric constant in the nanocomposite. This results in brittleness, low flexibility, poor mechanical performance, toxicity, and low breakdown strength (mainly for ceramic fillers) in the nanocomposite.² Good thermal conductivity and high dielectric constant are essential material properties when a high amount of heat is released during operation.⁹ A flexible dielectric material possessing a high thermal conductivity and high dielectric constant with low dielectric loss is highly desirable for enhancing the lifetime of polymer nanocomposite materials by the dissipation of heat, required in energy sectors.¹⁰ In our previous study,⁷ we found that Fe-rGO acts as an efficient filler to stabilize the γ-phase of PVDF polymer, improving the piezoelectric energy harvesting behavior of the nanocomposite. During harvesting of energy, the applied mechanical force and generated electrical power subsequently produces heat; but this necessarily has to be removed from the system. For this particular purpose, we have further investigated the heat dissipation behavior of Fe-rGO/PVDF nanocomposite by measuring the thermal conductivity of the stabilized γ-PVDF component of the nanocomposite. Though the thermal conductivity of PVDF based graphene composite^17,18 depends on the nature of the filler (such as filler conductivity, distribution of filler, size of filler etc.) as has been thoroughly reported elsewhere, to the best of our knowledge, an investigation on the dependence of phase of the base polymer has not yet been reported. Earlier literature^2,3 reports that the thermal conductivity depends on the degree of crystallinity, where, Zhang et al. only comment about the dependence of thermal conductivity on crystalline phase without elaboration of the effect of phase.²⁹ As yet, there is no report on dependence of thermal conductivity on the crystalline phases of polymer. In the present work, we investigate how the characteristic behavior of the γ-phase of PVDF affects the thermal conductivity of the nanocomposite.

Here, we demonstrate the thermal conducting behavior is strongly dependent on stabilized γ-PVDF, as a low cost light-weight component of a flexible (see inset in Fig. 1) Fe-rGO/PVDF nanocomposite. The nanocomposite displays excellent thermal conductivity (0.89 W mK⁻¹) and released energy density (1.45 J cm⁻³) at significantly low loading (3 wt%) of Fe-rGO, as compared to those (0.13 W mK⁻¹ and 0.27 J cm⁻³, respectively) of the pristine polymer. In addition, the nanocomposite reveals substantial improvement in dielectric constant (ε′ ≈ 57 at 1 kHz) with very low dielectric loss (ε′′ ≈ 0.13 at 1 kHz) at 3 wt% filler loading. As far the literature is concerned no previous work has been done which shows the dependence of thermal conductivity on phase of PVDF.

Fig. 1 Schematic of the fabrication process of the nanocomposite films studied in this work.

2. Experimental section

2.1. Materials

Graphite, sodium nitrate (NaNO₃), potassium permanganate (KMnO₄) and iron powder were purchased from Loba Chemie, India. Graphene oxide (GO) and iron oxide doped reduced graphene oxide (Fe-rGO) were synthesized in our laboratory by a previous method⁷ and characterization details are given in ESI (Experimental section and Fig. S1†). Poly(vinylidene fluoride) (PVDF) was purchased from Alfa Aesar. N,N-Dimethyl formamide (DMF), hydrogen peroxide (H₂O₂), sulfuric acid (H₂SO₄) and ethanol were supplied from Merck Chemicals, India. All solvents used were of analytical grade and were used without further purification.

2.2. Preparation of the nanocomposite

The synthesized Fe-rGO was first dispersed in DMF (1 mg ml⁻¹) solution by ultrasonication for about 50 min and mixed with the (1 g/10 ml) PVDF solution in DMF at 90 °C under magnetic stirring. Next, the solution mixture of Fe-rGO/PVDF/DMF was homogenized by ultrasonication for 50 min for good distribution of Fe-rGO in the mixture. For complete removal of DMF, the resulting mixture was kept for 4 days in a vacuum oven at 120 °C. After drying, flexible nanocomposite films were obtained, as shown schematically in Fig. 1. The fabricated materials with different Fe-rGO loadings (0.0, 0.3, 0.6, 1.5 and 3.0 wt%) were denoted PVDF, 0.3Fe-rGO/PVDF, 0.6Fe-rGO/PVDF, 1.5Fe-rGO/PVDF and 3.0Fe-rGO/PVDF, respectively.

2.3. Characterization

The thermal conductivity of the nanocomposite films with almost equal area (5 ± 0.045) cm² with thickness 0.2 ± 0.012 mm was measured by a HOT Disk thermal analyzer (TPS 2500, Sweden, sensor 5465). The characteristic vibrational peaks were analyzed by Fourier-transform infrared spectroscopy (NEXUS-870). The thermal properties of the nanocomposite were studied by thermogravimetric analysis (TGA) (TGA-209NETZSCH, Germany) and differential scanning calorimetry (DSC) (TA instrument, Q20). Morphological studies were performed using field emission scanning electron microscope (FESEM) ​ (Carl Zeiss-SUPRA40) and transmission electron microscopy (TEM) (JEM-2100, JEOL, Japan). X-Ray diffraction (XRD) patterns of the samples were measured using an X′ Pert PRO diffractometer (PANalytical, Netherland). Elemental analysis was measured by a PHI 5000 Versa Probe II scanning X-ray photoelectron spectrometer (XPS). The dielectric and AC conductivity study of the nanocomposite films (gold as upper and lower electrodes) were performed by impedance analysis (Agilent 4294A, frequency range of 40 to 3 × 10⁶ Hz) and ferroelectric properties of the nanocomposite films (similar thickness) were studied using a Precision Premier II tester (Radiant Technologies, Inc.).

3. Results and discussion

3.1. Thermal conductivity

Significant enhancement of thermal conductivity of the prepared PVDF nanocomposite (schematically described in Fig. 1) is observed at low filler loading, as shown in Fig. 2A. It has been shown that the thermal conductivity gradually increases and reaches up to 0.89 W mK⁻¹, at as low as 3 wt% filler loading, which is ≈7 times greater than that (0.13 W mK⁻¹) of pure PVDF. At the same time the thermal diffusivity also gradually increases up to 0.40 mm² s⁻¹ at the same filler loading, as shown in Fig. 2B. Incorporation of conducting Fe-rGOs into the PVDF matrix significantly increases the thermal conductivity due to the stabilization of γ-PVDF and formation of conducting network of Fe-rGO throughout the nanocomposite. Our prepared nanocomposite exhibits superior thermal conductivity than reported for graphene based PVDF nanocomposite at this filler loading level (3 wt%), as given in ESI, Table S1.†

Fig. 2 Variation of (A) thermal conductivity and (B) thermal diffusivity of PVDF nanocomposite at different filler loadings.

Possibly, there are three major points that can accelerate the thermal conductivity of the nanocomposite. First, Fe-rGO is a strong conducting nanofiller which increases the thermal conductivity by transferring heat through the rGO continuous conducting network structure. Thus Fe-rGO acts as a bridge between the α/γ-spherulites of PVDF, which facilitates the heat transfer from one spherulite to another through the Fe-rGO nanosheets. Secondly, the presence of crystalline zones in the nanocomposite, as crystalline zones have greater heat transfer property than amorphous zones.²⁸ Finally, we observed that the thermal conductivity also depends on the amount of crystalline γ phase which increases the thermal conductivity of the final nanocomposite. However, in our present study, as the crystallinity (discussed later) of the PVDF is found not to show any significant changes with filler loading, we assume that enhancement of the thermal conductivity in the Fe-rGO/PVDF nanocomposite is mainly attributed to the conducting nanofillers and existence of crystalline γ phase. One can argue that the enhancement of the thermal conductivity is not only due to γ-phase, but also due to the increase of conducting network structure which increases with the increasing of filler loading. To verify this, we have measured the thermal conductivity of differently treated nanocomposite films at constant (3.0 wt% Fe-rGO) filler loading (similar network structure in nanocomposite). The rationale behind choosing this particular filler loading is that 3 wt% of Fe-rGO can stabilize ≈99% (relative proportion) of crystalline γ-phase of PVDF in the nanocomposite, as shown in ESI, Fig. S5A.†

Dependence of thermal conductivity with amount of crystalline γ-phases can be better understood by heat treatment of the 3.0Fe-rGO/PVDF nanocomposite film. We kept three pieces of the same film sample with fixed dimensions (within the error limit) in hot air ovens (same type of hot ovens) at 180 °C for 1 h. After that, cut pieces of film samples were cooled at different cooling rates such as 5, 10, 20 and 30 °C h⁻¹, respectively, and phase composition was monitored by FTIR, as shown in Fig. 3A. As can be seen, the peak corresponding to the β-phase (1277 cm⁻¹) of PVDF appeared in all three samples to a different extent (%) with the conversion of γ-phase after thermal treatment at different cooling rates. The β-phase formation in 3.0Fe-rGO/PVDF nanocomposite occurred less when the film was cooled at a faster cooling rate. The underlying reason behind the transformation of the γ- to β-phase is not fully known to us at this stage of investigation, and we are working on it to explore the possible causes. However earlier literature reports that the phase conversion should occur at different heating and cooling conditions.³⁰ Further investigation is needed to understand the exact phenomena behind this phase conversion of PVDF in the presence of nanofiller. FTIR study (Fig. 3A) shows that the intensity of crystalline γ-phase decreases with the increase in β-phase formation. Due to the γ- to β-phase conversion of PVDF the thermal conductivity of nanocomposite film changes with different cooling rates as shown in Fig. 3B. The increasing thermal conductivity with increased cooling rate is linked to lower conversion of the γ- to the β-phase in the nanocomposite. Here, the increasing rate of thermal conductivity is not related to crystallinity as the crystallinity only marginally changes (discussed later) with an increase of cooling rate. Hence, we can unambiguously predict that the thermal conductivity of the nanocomposite mostly depends on the amount of crystalline polar γ-phase. The explanation regarding the influence of crystalline γ-phases on thermal conductivity according to primary heat conduction mechanism is related to the polar form, via phonons and phonon vibrations in the polymer which can be influenced by many factors.³¹ We assume that polar crystalline PVDF phase is associated with the various lamellar stackings and different molecular chain conformations which play a greater role to influence the thermal conductivity.

Fig. 3 (A) AT-FTIR spectra and (B) thermal conductivity of 3.0Fe-rGO/PVDF nanocomposite at different cooling rates. (C) AT-FTIR spectra and (D) thermal conductivity of pure PVDF at different casting temperatures.

For further confirmation, we have also examined the thermal conductivity of PVDF at different fabrication temperatures without adding any nanofiller. The stabilization of the γ-phase in pure PVDF can be controlled by slow fabrication cooling rate, as already mentioned in earlier literature.³² Hence, we have prepared PVDF films at different fabrication temperatures such as 70, 80, 90, 100 and 120 °C and measured FTIR (Fig. 3C) and thermal conductivity (Fig. 3D) of the pure PVDF films. The intensity corresponding to the γ-phase gradually increases with the decreasing of fabrication temperature, as shown in Fig. 3C. We also observed that the crystallinity of PVDF slightly decreases (42 to 41%) with lowering fabrication temperature (measured from DSC). The thermal conductivity increases with decreasing fabrication temperature (Fig. 3D) as the γ-phase content increases with decreasing fabrication temperature (Fig. 3C) for pure PVDF (measured three times for clarification within the error bar limit). This finding leads us to conclude that the thermal conductivity directly depends on the amount of crystalline γ-phase of PVDF. In other words, we can state that enhancement of thermal conductivity of the nanocomposite is mainly related to the Fe-rGO networks throughout the PVDF matrix and the amount of γ-crystallites. Moreover, the thermal conductivity of the nanocomposite may also depend on the morphology, porosity, size, shape, and dispersion of the fillers.²⁸

We have proposed a probable schematic illustration in Fig. 4 for understanding the mechanism of thermal conductivity of the prepared nanocomposite. Due to the significant thermal interface resistance in the boundary between the semi-crystalline and amorphous regions, pure PVDF exhibits low thermal conductivity. Due to the presence of more α and less amount of γ-crystals in PVDF the heat is transferred only through spherulites in the pure PVDF. However, with the addition of Fe-rGO in the PVDF matrix, the heat transfer property increases due to the formation of γ-crystals as well as conducting Fe-rGO network. At higher filler loading (3 wt%), Fe-rGO nanosheets lie very close to each other and form a dense conducting network structure and stabilize a higher relative proportion of γ-phase in the nanocomposite. The Fe-rGO is a high thermally conducting material and thus formation of spherulite–Fe-rGO–spherulite bridges along with the conductive continuous Fe-rGO network at higher filler loading helps to conduct the heat from one surface to another surface of the nanocomposite film. Furthermore, decreasing in size (10.02, 8.71, 5.05, 4.60 and 4.29 nm) of γ-crystallites (calculated from XRD study as given in ESI, Fig. S6†) with increasing filler loading increases the surface area that can transfer the heat easily from one γ-spherilite to other γ-spherulites.

Fig. 4 Schematic illustration of transformation of heat by both γ-crystallites (size of the γ-crystallites decreases with increased loading) and Fe-rGO networks.

3.2. Thermal study

Although the thermal conductivity and energy density of the nanocomposite strongly depends on the crystalline behavior^2,3 of the materials, here we found that thermal conductivity does not depend on increased crystallinity since the crystallinity is decreased (as given in ESI, Table S2†) with filler loading. With the increase in Fe-rGO loading the melting temperature (T_m) (as shown in Fig. 5A) and crystalline temperature (T_c) (ESI, Fig. S7†) of the nanocomposite also increases.

Fig. 5 (A) DSC curves (1^st heating) of PVDF and Fe-rGO/PVDF nanocomposite at different filler loadings. (B) DSC patterns of 3.0Fe-rGO/PVDF nanocomposite and (C) pure PVDF at different cooling rate and different fabrication temperature, respectively. (D) TGA curves of PVDF, Fe-rGO and Fe-rGO/PVDF nanocomposite at different Fe-rGO loadings, respectively. The inset of Fig. 5D shows a zoomed portion in the region of 400–500 °C temperature.

Due to very large surface area of the nanofiller, it can easily induce heterogeneous nucleation and adsorbs PVDF chains that restrict the movement of polymer chain (i.e. formation of γ-phase) segments, leading to an increase in the T_m and T_c values of the nanocomposite.^7,33 Hence, due to the formation of γ-phase, the melting temperature increases which affects the thermal conductivity of the nanocomposite. To illustrate the crystalline nature of the nanocomposite the percentage crystallinity (χ_c) was also calculated from DSC 1^st heating scan using the following equation:

where, ΔH_m is the enthalpy of the nanocomposite and ΔH⁰_m is the enthalpy of 100% crystalline neat PVDF (103.40 J g⁻¹).^7,33 The χ_c value of PVDF is almost unaffected with increasing of Fe-rGO loading in the nanocomposite, 42% in pure PVDF cf. 41% in 0.6Fe-rGO/PVDF and 40% in 3.0Fe-rGO/PVDF nanocomposite (ESI, Table S2†). Apparently, we can state that in our nanocomposite the thermal conductivity does not depend on crystallinity, rather it depends on filler content and amount of crystalline γ-form of the PVDF. For further clarification we also studied the transition temperature (melting) of heat-treated 3.0Fe-rGO/PVDF nanocomposite (as given above) and pure PVDF at different fabrication temperatures as discussed above. For heat treated samples of 3.0Fe-rGO/PVDF nanocomposite, the crystallinity is more or less the same (42, 42, 41, 41%) with the increasing cooling rate, while T_m of PVDF slightly decreases with increasing cooling rate (as shown in Fig. 5B). In the case of pure PVDF (fabricated at different temperatures) an increasing melting temperature (Fig. 5C) was observed with lower fabrication temperature, indicating the formation of more crystalline γ-phase of PVDF. The fabrication temperature does not have much effect on the crystallinity of the pure PVDF. These results are also supported by the FTIR study, as shown in Fig. 3A and C.

A marginal weight loss occurs in Fe-rGO at a temperature of 100 °C due to release of absorbed water and ≈20% loss in mass occurs gradually up to 800 °C as shown in Fig. 5D. The thermal stability of the Fe-rGO/PVDF nanocomposite gradually increases with increase in Fe-rGO loading. Here, mainly a two-step degradation was observed in Fe-rGO/PVDF nanocomposite. In the 1^st step, a slight weight loss occurring between 200 to 450 °C is attributed to the loss of adsorbed water molecules from the surface of the nanocomposite and probable degradation of the carbon backbone in the Fe-rGO. In the 2^nd step, a major weight loss occurs in the range of 450 °C to 800 °C, which can be ascribed to degradation of the PVDF matrix. In the case of 0.6Fe-rGO/PVDF nanocomposite, the characteristic of the curve is different in the temperature range of 200 to 450 °C compared to 1.5 and 3.0Fe-rGO/PVDF nanocomposite, possibly due to the good compatibility between the oxygen functionalities present in Fe-rGO and the –CF₂–/–CH₂– groups of PVDF leading to enhanced cohesive energy of the nanocomposite.³⁴ The enhancement of degradation temperature of the nanocomposite compared to pristine PVDF can be explained by considering the onset degradation temperature, T_o (temperature at 5 wt% loss, indicated by green dotted line) and the temperature corresponding to 50% weight loss (T₅₀, indicated by green dotted line) of PVDF and Fe-rGO/PVDF nanocomposite. Both the T_o (451 °C) and T₅₀ (475 °C) values of pure PVDF were found to increase with increase in Fe-rGO loading such as 0.6Fe-rGO/PVDF (T_o = 457 °C, T₅₀ = 481 °C), 1.5Fe-rGO/PVDF (T_o = 461 °C, T₅₀ = 487 °C) and 3.0Fe-rGO/PVDF (T_o = 471 °C, T₅₀ = 497 °C), as can be seen in the inset represented in Fig. 5D. 3 wt% of Fe-rGO loading can increase the T_o and T₅₀ values up to 471 and 497 °C which is ≈20 and ≈22° greater than for pure PVDF. Introduction of Fe-rGO restricts the thermal motion of the polymer chain, enhancing the thermal stability of the polymer matrix, and improved interfacial adhesion between Fe-rGO and PVDF matrix also provides thermal stability to the Fe-rGO/PVDF nanocomposite.^28,34 This anomalous phenomenon also suggests that Fe-rGO acts as an effective thermal barrier which inhibits the degradation of pristine PVDF polymer.

3.3. Morphology

The surface morphology of the nanocomposite reveals the formation of a conducting network by the dispersed conducting nanofillers in the polymer matrix, supporting the improved electrical and thermal conducting property of the polymer nanocomposite as shown in Fig. 6A and B. The increase in dielectric constant at lower frequency region can be explained considering the concept of a micro-capacitor. When the conducting particle is surrounded by an insulating material in a composite, the free electrons of the conducting particle move with the applied field and thereby creates a strong dipole in the direction of applied field. The electrons of this micro-capacitor are unable to switch between one another. This is due to the extremely high electrical resistance between the interlayer’s polymer molecules. With the increase of the filler loading in the composite, the number of micro-capacitors also increases and this is reflected as an increase in dielectric constant of the nanocomposite. The main reason behind this is the increase of the highly strong dipoles in the nanocomposite. Usually, this type of nanocomposite shows lowering of dielectric constant after a certain level of loading of the filler. Beyond this critical filler loading, the filler concentration becomes sufficiently high that electrons partially shuttle between one filler to the other by tunneling and hopping mechanisms through the polymer or by direct contact. This reduces the dipole strength and overall dielectric constant of the nanocomposite.³⁵ In the present work, the filler loading was kept below the dielectric percolation limit, which was reflected by the AC conductivity that reached up to a maximum of 10⁻⁶ S cm⁻¹ at 3 wt% filler loading (discussed later). This type of conductivity is mainly due to the polarization effect of material, and not connected to the electron transfer through the material.

Fig. 6 Fracture surface FESEM images (A and B) of the nanocomposite shows the presence of Fe-oxides particles (red circular dotted line) and formation of the Fe-rGO network. The HRTEM images (C and D) of nanocomposite show the existence of Fe-oxides particles on the surface of rGO and formation of the Fe-rGO network. The inset shows the signature of SAED patterns of Fe-rGO in the as-prepared nanocomposite.

Hence, the increasing number of micro/nano capacitors can affect the dielectric and energy density properties of the Fe-rGO/PVDF nanocomposite. The presence and distribution of carbon, oxygen, fluorine and Fe atoms can be confirmed by X-ray mapping, as shown in ESI, Fig. S8.† The presence of Fe-oxides particles in the Fe-rGO/PVDF nanocomposite on the surface of the rGOs is clearly visible, which is indicated by red dotted circles as shown in Fig. 6. The wrinkled, crumbled and even folded morphology of rGO (ESI, Fig. S2A†) is also retained in the nanocomposite (Fig. 6). This type of phenomenon implies that there may be occurrence of interconnection of Fe-rGO nanosheets with the polymer matrix due to strong bonding interaction between the filler and polymer matrix. The presence of rGO layer and Fe-oxide particles in the nanocomposite was also studied by HRTEM analysis as shown in Fig. 6C and D. The rGO is composed of sheets of few layered type of structure near the edges due to the re-stacking of the layers during reduction, as observed in Fig. 6C and D. This may happen due to the π–π interaction of Fe-rGO nanosheets which forces them to re-stack. In contrast, the nanocomposite shows the distribution of filler and presence of few layer type of morphology (folding style) which impacts on the thermal conducting property of the nanocomposite. Fe-rGO nanosheet can be encapsulated by PVDF matrix with the formation of a conducting network structure of Fe-rGO in the Fe-rGO/PVDF nanocomposite (Fig. 6D). The presence of Fe-oxides particles in the nanocomposite was also confirmed by SAED (Fig. 6D), EDX analysis (ESI, Fig. S9†) and X-ray mapping (ESI, Fig. S8†), respectively.

3.4. Dielectric and energy storage property

The frequency dependent dielectric (ε′) constant remarkably increases with the increasing of Fe-rGO loading at a lower frequency but decreases at higher frequency, as shown in Fig. 7A. Due to the conductivity difference of polymer and filler the overall charge increases with loading which leads to an increase in overall capacitance. At a low frequency region, various micro/nano-capacitors of Fe-rGO nanosheets are generated which are separated by dielectric PVDF thin film and lead to a high dielectric value.³⁶ The dielectric constant value for pure PVDF is nearly 8 at 1 kHz. This value was increased to 12 at 0.3 wt% filler loading and further increased to 57 when the nanocomposite was prepared with 3.0 wt% of Fe-rGO loading. At higher frequency region, relaxation of polymer nanocomposite occurred which plays a key role to decrease the dielectric constant. This type of phenomenon of dielectric response was also reported earlier in a polymer composite system.³⁷ We assume that this type of behavior is probably due to presence of Fe-rGOs and crystalline γ-phase in the nanocomposite. The dependence of dielectric constant on γ-crystalline phase can also be explained by measuring the dielectric constant of PVDF with different frequencies at different fabrication temperatures, as shown in Fig. 7E. As can be seen, the dielectric constant of PVDF marginally increases with slow cooling rate. This can be possibly due to the formation of a higher number of γ-crystals in the system which enhanced the dielectric constant value. It can be stated that the dielectric property strongly depends on γ-crystallites of PVDF. However, we can provide no comprehensive explanation on the direct relationship of γ-crystals with dielectric constant property, and this needs further investigation.

Fig. 7 Frequency dependence of (A) dielectric constant (ε′), (B) dielectric loss (ε′′) and (C) AC electrical conductivity of PVDF and the nanocomposite at different Fe-rGO loadings. (D) Variation of dielectric constant and dielectric loss with Fe-rGO loading (wt%) at different frequencies of 10³, 10⁴, 10⁵and 10⁶, respectively. (E) Frequency dependent dielectric constant of pure PVDF cast at different temperatures. (F) The dependence of dielectric relaxation time of the nanocomposite with various filler loadings.

Moreover, at higher frequency region (1 MHz) the dielectric constant of the nanocomposite is also higher than for neat PVDF, suggesting possible use of the nanocomposite as a superior energy storage material in a broad frequency range. The phenomenon at low frequency region can be explained by interfacial polarization occurring due to the Maxwell–Wagner–Sillars effect.^2,3 Significant amount of charges were accumulated at the interface of conducting nano-fillers and insulating polymer by surface polarization due to their different conductivity values. Furthermore, large number of micro/nano-capacitors were generated in the nanocomposite due to the presence of multilayered Fe-rGO nanosheets.

The frequency dependent dielectric loss (ε′′) of pure PVDF and the nanocomposite are shown in Fig. 7B. As observed, the dielectric loss goes through a minimum (dielectric relaxation) and then increases with increasing frequency. It is interesting that the dielectric loss for all the nanocomposite films is less compared to pure PVDF film at higher frequency region (>10³ Hz) (Fig. 7D). However, the dielectric loss of the nanocomposite is almost equal to that of pure PVDF at lower frequency region (from 10² to 10³ Hz) although the loss is significantly less with respect to its high dielectric constant (Fig. 7D), especially if we compare with the available literature reports as given in ESI, Table S3.† From Fig. 7D, it is clearly observed that the material shows relatively high dielectric constant with relatively low loss at lower frequency region (10³ to 10⁴ Hz), which is an essential criterion for energy storage materials, as reported elsewhere.³⁸ With the incorporation of nanofillers in the PVDF matrix, the crystallite size (10.02 to 4.29 nm) of the PVDF also decreases (ESI, Fig. S6†), which plays a crucial role to reduce the dielectric loss by reversible dipoles.³⁹ We also calculated relaxation times (τ_rel) of the nanocomposite using the relation, τ_rel = 1/f_min, where f_min is the frequency at the lowest dielectric loss. The relaxation time gradually decreases with the increasing of filler loading, from 113 to 42 μs, as shown in Fig. 7F. This is an indication of dipolar polarization which is dominant in this process.⁶ It is of note that the temperature dependent dielectric loss shows a maximum due to ferroelectric relaxor behavior. This occurred at lower frequency area (∼1 kHz) at lower temperature (below room temperature) and is shifted towards higher frequency regions at higher temperatures. This type of performance can be clarified through Vogel–Tammann–Fulcher (VTF) formalism.⁴⁰

The AC conductivity of pure PVDF showed linear dependence on the frequency which is the common tendency of insulating polymers as shown in Fig. 7C. The AC conductivity of the nanocomposite gradually increases with increase of filler loading (0.3 to 3.0 wt%). Depending on the filler loading, the AC conductivity of the nanocomposite remains almost similar up to a given frequency region, known as critical frequency (f_c). For any dielectric material, at low frequency (below f_c) the AC electrical conductivity (σ_AC) depends mainly on DC conductivity (σ_DC), dielectric loss factor (ε′′) and angular frequency (ω, where ω = 2πf) i.e. the two-phase conductive behavior can be represented by the following equation:⁴¹

σ_AC = σ_DC + ωε′′ (2)

The second component (ωε′′) strongly depends on the polarization of dipoles which arises from permanent and induced dipoles and accumulated interfacial polarization, which is commonly known as Maxwell–Wagner–Sillars (MWS) effect, due to the heterogeneous conductivity of Fe-rGO and PVDF.^2,3 Below the critical frequency (f_c) the interfacial polarization effect becomes more prominent because the dipoles or induced dipoles have enough time to orient themselves along the direction of the external applied electric field, which is called relaxation phenomena. The frequency independent electrical conductivity up to the critical frequency (f_c) for various disordered dielectric materials has been reported earlier.⁴² However, above the critical frequency (f_c) (at high frequency) the polarization effect is insufficient because the dipoles have less relaxation time to orient them along the direction of applied electric field. Above f_c, the applied electric field tends to reduce the space charge accumulation. So the dipole dispersion in the applied field direction decreases in proportion to polarization. Hence, the AC electric conductivity depends only upon excitation charge particles and also the electron flow through the conductive network pathway.

The nanocomposite films possess high dielectric constant with low dielectric loss, which are basically requirements of a material for use as energy storage devices. The energy storage density (U) has been calculated from electric displacement–electric field (D–E) loops (ESI, Fig. S10†) by the following equation:³

U = ∫ E dD (3)

where, E is the applied electric field and D is the electric displacement. In our discussion, the released energy density is referred to as the energy density. The energy storage density gradually increases with increasing of Fe-rGO loading under a given electric field as shown in Fig. 8A due to strong interaction between the filler and polymer matrix, as supported by FTIR and Raman spectra (ESI, Fig. S4A and S5B†). The nanocomposite has high dielectric constant and can store more energy to display high energy density. The 3.0Fe-rGO/PVDF film achieves higher amount of γ-phase (≈99% relative proportion) as well as energy density of 1.45 J cm⁻³ which is five times greater than for pure PVDF (0.280 J cm⁻³). The γ-phase containing PVDF has more energy density compared to PVDF containing other phases, due to the maximum polarization, lower remnant polarization, larger breakdown strength and absence of early D saturation.⁴³

Fig. 8 (A) Variation of the released and loss energy density at different Fe-rGO loadings. (B) Variation of energy density and γ-crystallites size with filler loadings.

The loss energy density marginally decreases with respect to the released energy density (Fig. 8A) which indicates that the nanocomposite is suitable for high capacity storage materials applicable in the rechargeable battery industry. According to Frohlich theory, the dielectric strength (energy storage) is related not only to molecular structure but also depends on crystallinity and crystallite size (here γ-crystallites) of the nanocomposite.² The crystallinity of the nanocomposite at different filler loadings is nearly same compared with pure PVDF and crystallite size of the γ-crystallites gradually decreases with the increasing of Fe-rGO loading: 10.02, 8.71, 5.05, 4.60 and 4.29 nm for PVDF, 0.3Fe-rGO/PVDF, 0.6Fe-rGO/PVDF, 1.5Fe-rGO/PVDF and 3.0Fe-rGO/PVDF nanocomposite, respectively. Fe-rGO/PVDF nanocomposite favors an increase of crystal boundaries which can accelerate the energy storage density up to 1.45 J cm⁻³ in the nanocomposite at relatively low loading (3 wt% Fe-rGO). The released energy density of PVDF gradually increases with decreasing crystallite size of the γ-crystallites in PVDF with the increasing of filler loadings as shown in Fig. 8B. This signifies that a higher number of micro/nano-capacitors and charges were generated, which produces more energy storage capabilities. Moreover, the conducting filler also helps to accelerate the energy storage density of the nanocomposite, which can be explained on the basis of the micro-capacitor/nano-capacitor model.³ In the nanocomposite, the conducting fillers are separated by a dielectric polymer layer which forms a heterogeneous system that can serve as a good dielectric material with great energy storage capability. Namely, two conducting particles are separated by a very thin layer of host polymer (treated as a local capacitor) as dielectric material. Local capacitor networks are increased and expanded between the two virtual electrodes with the increasing of filler loading. Each micro-capacitor contributes an abnormally high capacitance. When the conducting fillers are very close to each other the intensity of the local electric field is significantly increased. This increasing tendency of electric field intensity promotes the migration and accumulation of the charge carriers of the filler–matrix interfaces. This interfacial polarization (MWS effect) is responsible for increasing dielectric constant (at lower frequency) and energy storage density.³ Thus, our prepared lightweight nanocomposite satisfies the requirements for the development of next-generation high-performance flexible energy storage devices having sufficient thermal conductivity. Due to the presence of interaction between the Fe-rGOs and dipoles of PVDF, this affects the thermal conductivity and energy density properties. We see that the efficiency (ESI, Table S4†) is marginally increased compared to PVDF. In addition, the nanocomposite contains low remnant polarization (0.26 μC cm⁻²), which enhanced the energy density and efficiency of the nanocomposite.

4. Conclusions

In conclusion, the prepared nanocomposite show that the thermal conductivity strongly depends on crystalline γ-phase in addition with filler concentration. The presence of nanofiller slightly decreases the crystallinity of PVDF but results in an increase in the amount of γ-crystallites in the nanocomposite. The unfavorable decreasing crystallinity for enhancing thermal conductivity is more than compensated by the increasing polar γ-crystallites which favor shifting of the thermal conductivity to a higher value. From our study, we can conclude that the enhancement of thermal conductivity is related to synergistic effect of crystalline γ-PVDF and conducting filler. Morphological studies indicate good dispersion of Fe-rGO nanosheets and the formation of a conducting network structure in the nanocomposite. Furthermore, the dielectric constant also depends on the crystalline γ-form of PVDF. The present investigation reveals a new finding where one can observe that the thermal conductivity is directly related to crystalline γ-crystallites of PVDF. The improvement of thermal conductivity as well as dielectric constant in PVDF based nanocomposites is a significant finding, which may strengthen the application of such nanocomposite in sensors, actuators, energy storage devices, embedded capacitors, and stress control areas. Our current research work may open up a new platform to obtain high thermal conductivity in PVDF based nanocomposite with a great potential application in many electric and electronic industries.

Acknowledgements

The authors are grateful for the financial support from the DST, Govt. of India providing the INSPIRE fellowship (IF130632). We are also grateful to Nilesh Kumar Shrivastava for help in different experimental areas.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra04365h

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