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Electron structure in modified BaTiO 3 / poly(vinylidene fluoride) nanocomposite with high dielectric property and energy density

: It's significantly urgent to develop the polymer film capacitor with large energy density and high charge-discharge efficiency for the applications of portable electronics and power hybrid system. In this study, poly(vinylidene fluoride) (PVDF) nanocomposite film incorporated with tetradecylphosphonic acid modified BaTiO 3 was prepared via solution casting to achieve high dielectric property and large energy density. The strong interactions were formed between modifier and polymer segments, which was characterised by X-ray absorption near edge structure of synchrotron radiation. The decrease of activation energy indicates that the functionalisation of BaTiO 3 weakens the heterogeneous nucleation of nanoparticle. The dielectric constant of 30 vol.% nanocomposite film achieves 50.1 with low loss of 0.02 at 100 Hz, which is attributed to the strong interaction between the phosphonic acid and fluoride atoms of PVDF segments. The energy density of 20 vol.% nanocomposite is 4.4 J/cm 3 with charge-discharge efficiency of 78% at 120 MV/m due to the large interfacial polarisation. The functionalisation strategy of high- k nanofillers enhances the compatibility in polymer nanocomposite, which contributes to the flexible polymer capacitor with large energy density and high charge-discharge efficiency.


Introduction
Dielectric polymer film is especially suitable for the applications in energy storage and transformation because of its remarkable electrical and mechanical properties, and becomes the research focus in past 20 years [1][2][3][4][5]. The electrostatic storage capability of insulated film is determined by the dielectric constant and the electric breakdown, which indicates that next generation of dielectric films not only exhibit high permittivity, also retain high dielectric strength with low energy dissipation [2,4]. It is urgent to develop insulated dielectrics with large electric recoverable capacity because the current dielectrics either have high electric breakdown for common polymers or high permittivity for ferroelectric ceramics. Thus, it is suggested that the polymer composite strategy should be explored to obtain dielectric film with high energy density by the comprehending of the physical phenomena, such as inorganic-organic interactions, spatial dispersion of nanofillers, the interfacial layers, and electrical properties [6][7][8].
Recently, ferroelectric ceramic nanoparticles with high dielectric constant have been incorporated into polymer matrix to improve the energy density for advanced applications in up-to-date electronics and power system [9][10][11][12][13]. The technology of ferroelectric ceramic/polymer hybrid, which is an effective method to obtain nanocomposite with high dielectric constant, however, encounters the compatibility issue between the inorganic nanoparticles and organic polymer. Generally, high-volume fractional nanofillers are essential to achieve relatively large dielectric constant, which leads to poor processability and void defects of the nanocomposite film. This would decrease the applied electric strength and eventually reduce the energy density of polymer nanocomposite. The increase of the effective dielectric constant should be accompanied without the sacrifice of efficiency for energy storage cycle. Hence, the functionalisation of nanofillers is suggested as an effective solution to improve the compatibility and thus enhance the electrical capability in the polymer nanocomposite [14]. Pentafluorobenzyl phosphonic acid (PFBPA) surface-modified BaTiO 3 (BT) nanoparticles were added in P(VDF-HFP) nanocomposite to achieve high dielectric constant and breakdown strength of nanocomposite [12,15]. The measured energy density of 3.2 J/cm 3 in 50 vol% nanocomposite at 164 MV/m was due to the depression of porosity based on the statistical particle packing simulation and effective medium theory. The gradient distribution structure was designed in P(VDF-HFP) nanocomposite embedding with core-shell BT@TiO 2 nanoparticle to obtain high energy density due to large interfacial polarisation [16]. High dielectric property and breakdown strength were obtained in cross-linked poly(vinylidene fluoridechlorotrifluoroethylene) (P(VDF-CTFE-DB)) nanocomposite incorporated with 3-aminpropyltriethoxysilane (KH-550) modified SiC particles. The permittivity and mechanical property were wellbalanced in the resultant nanocomposite because of the improved compatibility and the interfacial effect [17]. Furthermore, the crystal structure in PVDF-based polymer was conversed after the addition of nanoparticles, which was attributed to different crystallisation behaviour of polymer induced by the nanofillers [6].
It is essential to investigate the crystallisation of dielectric nanocomposite and further comprehend the relationship between the structure and the property of bulk polymer since the dielectric property of PVDF-based polymer is related to the electroactive phase and crystal structure [6,7,18,19]. The isothermal crystallisation of the α-PVDF in the scope of Avrami equation was evaluated with two different methods involving the traditional double logarithmic properties and the non-linear least squares [20]. The temperature dependence of the kinetics parameters varied greatly from the different statistical weight of composing parts in the classical expression. The crystal structure of PVDF, which depends on the fabrication conditions and is strongly affected by the presence of inorganic nanoparticles, is determined by the crystallisation behaviour [21][22][23]. The incorporation of nanoparticles decreases the size of polymer spherulite, leading to the shift of crystallisation peak towards the high temperature. Also, the nucleating effect of nanoparticles accelerated the crystallisation rate of PVDF [24]. Several kinds of nanofillers, such as carbon nanotubes, CoFe 2 O 4, and NiFe 2 O 4 nanoparticles, were added into polymer host by solution blending to feature the crystallisation of polymer nanocomposite [25][26][27][28]. It is illustrated that the nucleation kinetics was greatly altered by the presence of nanoparticles due to  [20,25].
In order to improve the compatibility and obtain high dielectric property in PVDF nanocomposite, tetradecylphosphonic acid (TDPA) modified BT (m-BT) was introduced into matrix, and the evolution of different crystal structures in PVDF was induced by modified nanoparticle [9,29]. The effect of functionalisation of nanoparticles on the interface and subsequently polarisation of the modified nanocomposite should be further outlined to explore the mechanism of enhancement for dielectric property. In this work, Xray absorption near edge structure (XANES) was applied to perceive the differences of electron structure for carbon atom in PVDF with the presence of functionalised nanoparticles. The effect of modified nanoparticle on the crystallisation behaviour and dielectric property of PVDF nanocomposite film was investigated systematically. The m-BT/PVDF nanocomposite with large dielectric constant, high energy density, and high charge-discharge efficiency was obtained due to the improved interfacial polarisation induced by functionalisation of nanoparticles. This strategy of functionalised dielectric nanocomposite sheds a light on the mechanism of interfacial improvement and paves the path for polymer film capacitor with promising electrical storage capability.

Preparation of m-BT/PVDF nanocomposite
The free-standing nanocomposite film with thickness of ∼60 µm was prepared by simple solution casting. Typically, 0.5 g of PVDF powder was initially dissolved in 10 mL of DMAc, and then TDPA-BT nanoparticles were added in the glass vessel. The mixed solution was stirred for 25 min at room temperature to obtain homogenous mixture solution. The extra gas bubble was removed before pouring on glass plate. Finally, the mixture was dried at 80°C for 120 min and peeled off as the resultant nanocomposite film. The PVDF nanocomposite with modified BT was labelled as m-BT/PVDF. The comparative sample with 30 vol% original BT was prepared and simplified as BT/PVDF here.

Characterisations
In order to illustrate the differences of electron structure induced by the modified nanoparticles, XANES was employed to examine the fine structure of carbon element in PVDF matrix. The XANES spectra measurements were performed from energy range of 100 to 1000 eV with scanning step of 0.2 eV on the U18 beam line of Hefei National Synchrotron Radiation Laboratory, China. Crystallisation of PVDF nanocomposite film was estimated by differential scanning calorimetry (DSC, TA Q2000). Dry highpurity nitrogen gas was sent into DSC cell through the whole experiment with a flow rate of 50 mL/min. The thermal history of PVDF nanocomposite film was erased by heating at 180°C for 3 min, and the sample was then cooled down till room temperature to accomplish the crystallisation thoroughly.
Dielectric property of PVDF nanocomposite film was obtained under room temperature by the Agilent 4294A LCR meter from 100 Hz to 0.1 MHz at 0.5 Vrms. The polarisation hysteresis loops were measured using the TREK 609B-3-K-CE ferroelectric test system (Radiant Technologies) at 10 Hz. The disc-shaped specimen with the diameter of 3 mm was spray-coated with gold electrodes prior to polarisation characterisation. The conductivity of nanocomposite was performed on the RTS-8 four-probe tester with ZC-90 high resistivity meter (Taiou Electronics). The circular sample was prepared with thickness of ∼0.20 mm and diameter of ∼8.0 mm.

Electron structure of nanocomposite
It is reported that the different crystallisation behaviour of the polymer nanocomposite after the addition of nanofillers is due to nucleating effect of nanoparticles [25,27,29]. The effect of functionalisation of BaTiO 3 nanoparticle on the interface and crystallisation of nanocomposite film needs to be investigated to yield large enhancement of dielectric property. The BaTiO 3 nanoparticles of ∼70 nm were purchased from Aldrich, and incorporated into PVDF to obtain nanocomposite with high dielectric constant. The functionalisation of nanoparticle and the preparation of PVDF nanocomposite film are schematically shown in Fig. 1. It is well-known that the functionalisation of BaTiO 3 surface would improve the compatibility between polymer matrix and nanofillers, which also induce the conversion of different crystal structures of polymer host [6,7]. The modification of nanoparticles exhibits a huge effect on the dispersion of nanofillers and improvement of PVDF nanocomposite with high quality by solution casting.
The electron structure of carbon atom in PVDF was characterised by XANES to examine the interaction between the modified nanofillers and PVDF matrix. The normalised X-ray absorption spectrum of carbon element is displayed in Fig. 2. The intensity of spectrum indicates the transition probability of electron at the core excited state from inner shell into unoccupied. The absorption of carbon atom at 284.8 eV is corresponding to π* excitation, meanwhile the peaks at 287.2, 288.2, 292.6, and 294.5 eV are assigned to σ* excitations. The relatively weak peak around 287.2 eV belongs to the transition from C1s to σ* C-H in -CH 3 groups in accordance with previous assignments for similar species [30]. Also, the absorption at 288.2 eV is suggested as the transition from C1s to σ* C-H in -CH 2 CH 2 -groups. Among all peaks, the absorption at 288.2 eV corresponding to C-H bond exhibits the huge depression of intensity, which verifies the entanglement interaction between the modifier and the matrix. Quantitative comparison, there is a decrease of 23% in the transition of intensity for σ* C-H in -CH 2 CH 2 -groups. It is suggested that the activity of hydrogen couplings in alkyl radicals ranges from near zero to high value, which depends on the orientation of the C-H bond with respect to the unpaired electron orbital. The decrease of σ* C-H intensity evidences that strong physical interaction is generated between the PVDF segments and organic modifier, which enables the modified nanoparticles to disperse homogeneously in the nanocomposite film [7,14]. This strong interaction between nanofillers and matrix is consistent with Tanaka's model, which suggests that the interface of polymer nanocomposite is composed with bonded layer, bound layer, and loose layer [6]. The conformation, crystallinity as well as mobility in the region adjacent to nanoparticle, is far different from the bulk, which may lead to dipole orientation of polar segments. This probably clarifies the enhancement of dielectric response and polarisation in the modified nanofillers/polymer nanocomposite.

Crystallisation behaviour
The crystallisation was performed on every sample in the hermetic Al pan of the chamber during the whole experiment. The DSC curves of non-isothermal crystallisation for PVDF nanocomposites are displayed in Fig. 3. The maximum exothermal peak of PVDF shifts towards lower temperature with the increasing crystallisation cooling rate, and the similar trend is also surfaced in the crystallisation of nanocomposite film (Figs. 3b-e). There are distinct shoulder peaks in the crystallisation of 30 vol% nanocomposite with pristine nanoparticles, which is not observed in the functionalised sample. This phenomenon may be generated from the compatibility between organic host and inorganic nanofillers. Also, the high loading of nanoparticles yields the steric hindrance more than the nucleation effect in the nanocomposite. High super cooling is essential since extra energy is required for polymer segments to propagate into the regular crystal structure. A bimodal melting peak is observed in the unmodified BT/PVDF nanocomposite, which is attributed to the feature of lamellar thickness with temperature-dependent bimodal distribution. The higher peak corresponds to melting of big crystals and the lower one is the rearrangement of macromolecular chains in small sizes. The crystallisation parameters of PVDF nanocomposite films, e.g. peak temperature (T p ), end temperature (T e ), half time of crystallisation (t 1/2 ) and crystallisation enthalpy (ΔH), are obtained from Fig. 3 and summarised in Table 1. The value of t 1/2 decreases with increasing concentration of nanofillers, which strengthens that the nucleation is the primary step during the crystallisation of PVDF nanocomposite. Under low loading, the nucleation effect of m-BT nanoparticles accelerates the crystallisation, whereas the crystallisation enthalpy ΔH increased slightly, which is analogous to the multi-walled carbon nanotube/PVDF nanocomposites [31]. The enthalpy of PVDF decreases as the content of m-BT nanoparticles increases, which is related to the limit mobility of PVDF segments. This would lead to the low crystallinity of PVDF under high volume fraction, which is also consistent with the isothermal crystallisation of poly(vinyl methyl ether) aqueous system [32]. These nanoparticles with constrained polymer layer as nucleating agents participates the crystallisation kinetics instead of heterogeneous agents [33].
Crystallisation kinetics of the polymer nanocomposite is determined by various kinds of factors, e.g. the nucleation of polymer chains, the interaction of composing parts, and the presence of different crystalline phases induced by varied nucleation and crystal growth rates [34,35]. Assuming that the crystallisation is activated by thermal and the effect of cooling rate on peak temperature of crystallisation is concerned, activation energy is estimated by the following equation [29]: where ΔE represents the ability of crystallisation and is usually determined by the slope coefficients of plots of ln(ϕ/T p 2 ) as a function of 1/T p . The activation energy of the non-isothermal crystallisation for PVDF nanocomposite is shown in Fig. 4. The value of activation energy for PVDF nanocomposite is lower than neat PVDF, which indicates great ability on crystallisation. There is a decrease in the free energy of nucleation with increasing content of nanofillers in the nanocomposite [36]. When the content of nanofillers reaches 20 vol%, the nucleation effect of nanoparticles plays an important role in the crystallisation of nanocomposite. Under high loading, the presence of nanoparticles leads to steric hindrance instead of nucleation effect, which confines the mobility of PVDF segments during the crystallisation. The activation energy of 20 vol% unmodified BT/PVDF nanocomposite is 43.1 kJ/mol, which is a little higher than that of functionalised film. Due to strong interaction between the polymer segments and functional groups, the thermal property of PVDF nanocomposite is also affected by the modifier on the surface of BT nanoparticles [37].

Electric property
The high-k ceramic nanoparticle was introduced into polymer matrix to yield 0-3 type of nanocomposite film with high dielectric property. The improved permittivity of nanocomposite film is due to the dipolar interaction of spherical fillers and polymer host. The dielectric property of PVDF nanocomposite film was characterised by dielectric spectroscopy with the frequency range of 100 Hz to 0.1 M Hz at room temperature and displayed in Fig. 5. The dielectric constant ε′ of PVDF is 10.7 at 100 Hz, which is much higher than other polymer dielectrics [2,6]. The ε′ for 30 vol% m-BT nanocomposite film is 50.1 at 100 Hz (Fig. 5a). The dielectric constant of 30 vol% pristine BT/PVDF nanocomposite film, however, is 29.1 at 100 Hz, which is much lower than it of modified nanocomposite. The dielectric loss is small at low frequency in nanocomposite film and then increase under high frequency (Fig. 5b). The loss of modified nanocomposite is lower than the nanocomposite with pristine BT, which may result from the significant reduction of resonance of host polymer after the addition of functionalised nanoparticles. The dielectric loss of 30 vol% m-BT/PVDF nanocomposite is about 0.02, preventing high loss induced by the residual free modifier in nanocomposite system. The permittivity of ferroelectric material depends on the polarity and activity of dipoles in the polymer accompanied with the mobility of macromolecular segments, which relies on the interaction between inorganic nanofillers and organic host [6,38,39]. The organic TDPA on BT surface improves the compatibility between the nanofillers and matrix. The addition of m-BT nanoparticles induces the transition of crystal structure from the αphase to β-phase in PVDF [20]. Moreover, the non-polar TDPA leads to physical absorption between those two phases rather than chemical bond. The mobility of dipoles is not restricted under the external field and finally generates the high permittivity compared with other modifiers [9,15]. Although the dielectric constant decreases slightly at the initial test, it becomes quite stable with increasing frequency, e.g. ε′ = 37.2 at 2 kHz for 30 vol% m-BT/ PVDF, and ε′ = 32.8 at 100 kHz. The dielectric property of functionalised nanocomposite film is found to be insensitive to test frequency. Under low frequency, the segments in m-BT/PVDF nanocomposite film are restrained by the entanglement, and thus the dielectric constant is independence on frequency [14]. The bonding between the grafting organics and PVDF segments contributes to weak frequency dependence of modified nanocomposite, which allows dielectric nanocomposite as a promising candidate in the applications of wide-range frequency. The variation of the weak-field dielectric property at 1 kHz for PVDF nanocomposite is plotted in Fig. 6. The dielectric constant of sample steadily increases and reaches 43.2 in 30 vol% PVDF nanocomposite, which is three times higher than that of pristine film. The effective dielectric constant of the nanocomposite is estimated based on the Lichtenecker logarithmic rule, which is commonly applied in two-phase composite system [6,7,15]: where y 1 and y 2 represent the volume fractions of ceramic fillers and polymer matrix which have dielectric constant of ɛ 1 and ɛ 2 , respectively. As shown in Fig. 6, the calculated results derivate with the experimental data. Under high loading, the Lichtenecker logarithmic law overpredicts those measured values. Such derivation probably is induced by the insufficient macromolecular chains left to shelter the nanofillers and thus the increase of porosity in the nanocomposite [40]. The surface-modified BaTiO 3 nanoparticles with TDPA yielded well-dispersed and high-quality nanocomposite thick film in the PVDF host, which provides fundamental structure for improvement of dielectric property. The conductivity of m-BT/PVDF nanocomposite film is displayed in Fig. 7. The conductivity σ increases after the introduction of m-BT, such as σ = 2.0 × 10 −12 S/cm for pristine PVDF, while σ = 4.6 × 10 −11 S/cm is obtained in 30 vol% m-BT/PVDF nanocomposite. The nanocomposite retains relatively low conductivity, which is attributed to the functionalisation of nanofiller surface and subsequent interfacial improvement. The P-E loops of PVDF and 20 vol% m-BT/PVDF nanocomposite were obtained at 10 Hz under room temperature and plotted in Fig. 8. The polarisation of nanocomposite is enhanced after the addition of modified nanofillers with low hysteresis, which is reasoned to the improved compatibility and subsequently interfacial polarisation. The discharged energy density (U) of the PVDF nanocomposite film is derived from P-E loop according to the following equation: where E is the electric field and D is the electric displacement. The comparison of electrical energy storage in PVDF-based nanocomposite developed in this work with those in the literature is listed in Table 2. The energy density of pure PVDF film is 2.7 J/cm 3 at 120 MV/m, while U = 4.4 J/cm 3 at 120 MV/m in 20 vol% m-BT/PVDF nanocomposite film. The charge-discharge efficiency in modified nanocomposite retains as high as 78% at ΔE = 120 MV/m, which indicates low energy loss in the electric storage for the long-term operation of polymer film capacitor. The enhancement of polarisation results from the combination of large-fraction electroactive phase and Maxwell-Wagner-Sillars (MWS) polarisation for heterogeneous system [6,7,15]. It is acknowledged that the addition of nanofiller, e.g. magnetic oxides, montmorillonite clay, and carbon nanotubes, into PVDF-based polymer induces the conversion from non-polar phase to electroactive phases and thus improves the polarity [44,45]. The hydrogen bond is yielded between the phosphate modifier and -CF 2 -as schematically shown in Fig. 9. The interaction between nanofillers and PVDF segments contributes to the all-trans conformation in crystal growth. Furthermore, the addition of nanofillers decreases activated energy of crystallisation and advances the growth of electroactive phase. It is suggested that the MWS polarisation is related to the free charges entrapped in the interfaces, which may contribute to the interfacial polarisation [46]. The PVDF film prepared by the common solution casting is comprised of transgauches and all-trans with some degree of correlations. A high degree of regular structure in the ferroelectric phase of PVDF with modified nanofillers are obtained due to the strong interaction between F atoms of polymer chain and phosphonic modifier of BT surface. The increase of regular dense structure induces the improvement of dielectric constant and the depression of loss. The strong interaction between nanofillers and PVDF segments would converse the crystalline structure of ferroelectric polymer and improve the relaxation and orientation of dipoles, and further lead to the enhancement of dielectric response in nanocomposite [24].

Conclusions
In summary, the modified BaTiO 3 /PVDF nanocomposite film with high dielectric property and large energy density was developed. The electron structure and dielectric property as well as crystallisation behaviour of PVDF nanocomposites were investigated systematically. The compatibility between modified BaTiO 3 nanoparticles and organic matrix is improved due to the strong interconnection between the modifier of nanoparticle surface and the PVDF matrix. The nanocomposite film exhibits relative high dielectric constant and low loss after functionalisation of nanoparticle surface. The energy density is 4.4 J/cm 3 with charge-discharge efficiency of 78% at 120 MV/m in 20 vol% nanocomposite, which is attributed to the interfacial polarisation induced by the improved compatibility. This study outlines new insight to optimise the dielectric property by the functionalisation of nanofillers, and sheds a light on the mechanism of enhancement for the dielectric performance in the polymer nanocomposite.

Acknowledgments
The financial support from the National Natural Science Foundation of China (21474091, 51707175) and Natural Science Foundation of Zhejiang Province of China (LY18B040005) is greatly appreciated. This work is also supported by China Postdoctoral Science Foundation (2018M640572). The authors also thank Mr W.S. Yan at Hefei National Synchrotron Radiation Laboratory for XANES characterisation.