Ultra-high discharged energy density capacitor using high aspect ratio Na 0.5 Bi 0.5 TiO 3 nano ﬁ bers † is © The Royal Society of

Ceramic/polymer nanocomposites are attractive for energy storage applications due to their ability to exploit the high permittivity of ceramic ﬁ llers and high breakdown strength of the polymer matrix. One challenge for the development of high performance nanocomposites based on ceramic particulates or ﬁ bers in a polymer matrix is that they often require a high volume fraction (>50%) to achieve a high permittivity, which is often at the expense of a reduction in dielectric strength and mechanical ﬂ exibility. In this paper we demonstrate by both experiment and ﬁ nite element simulation that high aspect ratio nano ﬁ ber ﬁ llers o ﬀ er an e ﬀ ective approach to achieve high energy density and dielectric strength. Lead-free ferroelectric Na 0.5 Bi 0.5 TiO 3 (BNT) nano ﬁ bers with a high aspect ratio (>200) are synthesized by a hydrothermal method and dispersed in a poly(vinylidene di ﬂ uoride- co -hexa ﬂ uoropropylene) (P(VDF-HFP)) matrix. The increased fraction of b -phase and the alignment of BNT nano ﬁ bers perpendicular to the direction of the applied electric ﬁ eld lead to an enhanced dielectric strength, compared to spherical BNT/P(VDF-FHP) nanoparticles and pure P(VDF-HFP), and experimental measurements are compared with numerical simulations. The results demonstrate that the nano ﬁ ber nanocomposites exhibited an ultra-high discharged energy density (12.7 J cm (cid:1) 3 ) and provide an innovative approach to produce high-energy storage density materials. ﬀ usion and thermal conductivity enhancement of the BNT NF/P(VDF-HFP) nanocomposites; simulation of the distribution of of the nanocomposites with BNT nanoparticles or BNT nano  bers; D – E of the BNT nano  ber/P(VDF-HFP) nanocomposites with various  ller loadings at the largest electric  eld. NFs/P(VDF-HFP)


Introduction
High power capacitors are widely applied in electronic devices with pulsed power such as radar, electric vehicles, mobile electronics, power electronics, lasers, and rail guns. [1][2][3][4][5][6][7][8] However, these capacitors usually suffer from low energy density, hence they can only be applied in high cost and bulky electronic devices. 9,10 The maximum discharged energy density (U) of linear dielectric materials is dened as: where 3 0 and 3 r are the permittivity of vacuum and the material, respectively, and E b is the breakdown electric eld of the material. It is clear that the energy density is determined by the E b and 3 r of the dielectric material, and the E b is a critical factor since U has a quadratic dependence on the E b . [11][12][13][14] In this regard, ceramic/polymer nanocomposites have been investigated since they have the potential to simultaneously optimize the two factors that determine the energy density by exploiting the high permittivity of ceramic llers and the high breakdown strength of the polymer matrix. [15][16][17] It has been shown that the microstructural morphology and concentration of the ceramic llers have a signicant inuence on the energy storage density of dielectric nanocomposites. [18][19][20][21] In our previous work, 0-3 nanocomposites (0-dimensionally spherical nanoparticles dispersed in a 3-dimensionally connected polymer matrix) containing BaTiO 3 and Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 nanoparticles (NPs) dispersed in a poly(vinylidene diuoride-co-hexauoropropylene), P(VDF-HFP), polymer matrix exhibited a signicantly higher permittivity than pure P(VDF-HFP); however, the increased permittivity of the nanocomposite was at the expense of a decreased breakdown strength compared to the pure polymer matrix phase. 9,19 The high volume fraction (>50 vol%) of ceramic nanoparticle llers that is needed to signicantly increase the permittivity can also lead to the formation of defects, such as voids and cracks, in the 0-3 nanocomposite, as well as reduce the mechanical exibility of the composites.
The complex balance between permittivity and breakdown strength is attributed to the presence of high local electric eld concentrations, which are caused by the large contrast in permittivity between the ceramic and polymer matrix phase. 22 Recently, it was demonstrated that the use of high aspect ratio one-dimensional nanober llers could be an effective approach to overcome the challenge of increasing the permittivity without leading to a corresponding decrease of breakdown strength and thereby improve the energy density of the nanocomposite. 9,18,21,23,24 The improvement is thought to be due to the increased permittivity of the high aspect ratio llers, as demonstrated by theoretical models such as the Maxwell-Garnett model. 18,25 The nature of the distribution of nanobers in the polymer matrix and their orientation in perpendicular, parallel and random directions relative to the direction of the electric eld signicantly affects the electric eld distribution in the nanocomposite. However, the inuence of the morphology of the ceramic nanobers or nanoparticles in the polymer matrix on the electric eld distribution and the effective capacitance of the composites remains unclear. Most ceramic nanobers/polymer composites in previous reports 11,13 exhibited an increase in discharged energy density with an increase in the fraction of nanobers; however the manufacture of high aspect ratio nanobers continues to be a challenge. 18 Thus, it is of interest that dielectric nanocomposites possessing an ultrahigh discharged energy density are formed using a relatively small fraction of nanobers. Na 0.5 Bi 0.5 TiO 3 (BNT) is considered to be an excellent leadfree ferroelectric ceramic with a d 33 piezoelectric coefficient of approximately 80 pC N À1 and a high relative permittivity of approximately 500 at 1 kHz, which has attracted signicant interest because of its potential to replace lead based piezoelectric materials. 26,27 However, research on BNT/polymer composites, especially using the BNT nanobers to create new nanocomposites for energy storage applications, remains limited.
In this paper, high aspect ratio BNT nanobers and BNT nanoparticles are synthesized by a simple hydrothermal method by controlling the temperature and NaOH concentration of the reaction. BNT nanobers and nanoparticles will be examined as a ller introduced into a (P(VDF-HFP)) polymer matrix. To investigate the inuence of BNT ller morphology on the permittivity and breakdown strength of the nanocomposites, the localised electric eld distribution and capacitance of P(VDF-HFP) nanocomposites with BNT nanobers and BNT nanoparticles for energy storage applications have also been simulated using a nite element approach (ANSYS).
To enhance the adhesion between the llers and matrix, the ceramic llers were initially modied using dopamine, and FT-IR results indicate that the dopamine has led to modication of the BNT by condensation polymerization; the content of dopamine is 2.9 wt%, which is related to the amount of BNT NFs, as shown in Fig. S1 (ESI). † 20,28 The dielectric performance, discharged energy storage density and thermal management of the samples were investigated. This paper will show that the use of high-aspect-ratio BNT nanobers led to an increased permittivity and high thermal conductivity. Of particular interest is that the discharged energy density of the nanocomposites increased signicantly by introducing a low content of BNT nanobers (2.37 vol%), and the maximum energy density increased to 12.7 J cm À3 . This work therefore provides a practical route to achieve ultra-high energy storage density with a low level of BNT nanober loading.

Synthesis of BNT nanobers and BNT particles
BNT nanobers and BNT particles were obtained by controlling the hydrothermal reaction temperature and NaOH concentration, as reported in our previous study. 29 Specically, 0.005 mol of Bi(NO 3 ) 3 $5H 2 O, 0.01 mol of NaNO 3 and 0.005 mol of Ti(OC 4 H 9 ) 4 were dissolved in 7.5 mL of CH 3 COOH, 2.5 mL of distilled water, and 10 mL of CH 3 CH 2 OH. The Bi(NO 3 ) 3 $5H 2 O and NaNO 3 solutions were then mixed with Ti(OC 4 H 9 ) 4 solution, which subsequently formed a suspension with the addition of 10 M of NaOH solution and stirred for 1 h. The BNT nanobers and particles were synthesized at 150 C for 48 h with a NaOH concentration of 10 M and 170 C for 48 h with a NaOH concentration of 10 M, respectively. The products were washed with distilled water several times and dried at 80 C in an oven.

Surface functionalization of BNT llers using dopamine
Dopamine modied BNT was prepared using a method reported previously. 20 In a typical reaction, 2 g of BNT powder was dispersed in 20 mL of a mixture of 95 : 5 (v/v) ethanol/H 2 O using an ultrasonic processor to increase the hydroxyl groups on the surface of the BNT. The hydroxylated BNT was recovered by centrifugation and dried under vacuum at 60 C for 12 h, and was dispersed in 0.01 M dopamine hydrochloride aqueous solution, while stirring for 10 h at 60 C. The functionalized BNT was subsequently separated by centrifugation and rinsed repeatedly with excess deionized water, and nally dried overnight under vacuum at 60 C.

Preparation of BNT/P(VDF-HFP) nanocomposites
Surface functionalized BNT llers were dispersed in a 70 : 30 (v/v) acetone/DMF hybrid solvent by sonication and stirring and then mixed with P(VDF-HFP) particles for further stirring and sonication for 48 h. The resulting suspension was then cast onto a clean glass surface, and dried at 80 C for 12 h under vacuum. The thickness of the nal composite lm was approximately 10-20 mm. Gold electrodes were sputtered on both sides of the lm using a mask with 2 mm diameter eyelets. Fig. 1 shows an illustration of the preparation approach of the exible BNT nanober/P(VDF-HFP). The functionalized BNT NFs were dispersed in the P(VDF-HFP) nanocomposite lm and gold electrodes were sputtered on both sides of the lm to characterize the electrical properties for storage applications.

Characterization
The crystal structure of the nanocomposites was examined in q-2q mode by X-ray diffraction (XRD, Rigaku D-Max/2550VB + ) utilizing Cu K a radiation (l ¼ 1.5418Å). Transmission electron microscopy (TEM) images were obtained from a JEOL JEM-2100 instrument operating at an accelerating voltage at 200 kV. The samples were prepared by dropping the sample solutions onto carbon coated copper grids and air-drying before measurement. Fourier-transform infrared (FT-IR) spectroscopy was performed with a Nicolet 6700 instrument over the range of 4000-450 cm À1 to determine the functionalization of the samples. Thermogravimetric analysis (TGA, NETZSCH STA 449) was conducted at a heating rate of 10 C min À1 in a nitrogen ow (20 mL min À1 ). Characterization of the morphology of the composites was performed by scanning electron microscopy (SEM, JSM-6390). Frequency-dependent permittivity and dielectric loss were measured using an Agilent 4294A LCR meter over a frequency range of 1 kHz to 10 MHz. Leakage current density, endurance testing, electric displacement-electric eld (D-E) loops and leakage current were measured using a Precision Premier II ferroelectric polarization tester (Radiant, Inc.) and Delta 9023 furnace. The thermal diffusivity and conductivity of the nanocomposites were measured by a laser ash technique using a thermal constant analyzer (LFA427, Netzsch, Selb, Germany).

Characterisation of BNT nanobers and particles
Scanning electron microscopy (SEM) images of the BNT nano-bers and nanoparticles that were hydrothermally prepared are shown in Fig. 2a and b, respectively. The majority of the nanobers exhibit a high aspect ratio (>200) with an average diameter of approximately 67 nm and average length of 17.78 mm; this was measured from 50 randomly selected nanobers in an SEM image using ImageJ ( Fig. 2d and e). The average diameter of the nanoparticles was measured using a laser particle size analyser and was found to be approximately 800 nm. The XRD pattern of BNT nanobers and BNT nanoparticles is shown in Fig. 2c

Characterisation of the nanocomposites
It has been demonstrated that the presence of the polar b-phase in ferroelectric polymers such as P(VDF-HFP) is benecial for increasing the permittivity and the piezoelectric/ferroelectric  properties of the composite due to the large dipolar moment of this particular polar phase. [30][31][32] The introduction of ceramic llers into the P(VDF-HFP) matrix led to the formation of a higher fraction of the b-phase by modication of the aphase. 33 Fig. 4a shows the XRD pattern of pure P(VDF-HFP), BNT NPs/P(VDF-HFP) and BNT NFs/P(VDF-HFP) nanocomposites. It can be seen that the pure (unlled) P(VDF-HFP) exhibited peaks at 2q ¼ 18.38 , 19.96 and 26.6 , which correspond to the a-phase 30,32 with no b-phase detected. For the BNT nanoparticle/P(VDF-HFP) composite system, the peak of the aphase at 2q ¼ 19.56 is weakened, and the a-phase peaks at 2q ¼ 18.38 and 26.6 both disappear aer the introduction of the BNT nanoparticles, which is thought to be due to the addition of the crystalline BNT ceramic changing the crystallinity of the P(VDF-HFP) polymer.
It is notable that the peak at 2q ¼ 20.74 that corresponds to the b-phase is observed in the XRD pattern of the BNT nano-ber/P(VDF-HFP) nanocomposite in Fig. 4a. Therefore, the introduction of one-dimensional ceramic llers to P(VDF-HFP) appears to facilitate the formation of the polar b-phase, which can also be observed from the FT-IR results of the P(VDF-HFP) nanocomposites in Fig. S3a. † This is in contrast to zerodimensional nanoparticle llers, and indicates that onedimensional high aspect ratio ceramic llers may be more effective in increasing the permittivity of nanocomposites due to the formation of the polar b-phase. In addition, one-dimensional ceramic llers with a high aspect ratio have a larger dipole moment and lower surface energy compared to zerodimensional particulates, which favours polarization and dispersion. 17,34 To further investigate the inuence of the introduction of the ceramic nanobers on the crystallization of the polymer matrix, differential scanning calorimetry (DSC) curves of the BNT nanober/P(VDF-HFP) composites during the second heating circles are shown in Fig. 4b. The melting point (T m ) and crystallinity (c c ) of the samples were obtained from DSC results, and the corresponding results are summarized in Table 1. It can be seen that the T m is initially slightly increased then decreased and the c c is decreased from 28.7% to 21.6% as the content of BNT NFs increased. The results can be explained by the following reasons. Firstly, the BNT nanobers act as a new nucleation center, which can decrease the nucleation energy and increase the degree of crystallization of the P(VDF-HFP) matrix on the surface of the BNT nanobers. Secondly, the introduction of BNT nanobers decreases the degree of order of the P(VDF-HFP) matrix. Thus, the crystallinity and melting point of the nanocomposites increase with small amounts of BNT nanobers, however they decrease as the ller loading is increased. Fig. 5a-c show SEM images of the surface morphology of the BNT nanober/P(VDF-HFP) composite, with increasing loading levels of 2.37 vol%, 5.19 vol% and 12.73 vol% respectively. Fig. 5d shows a cross-section of the nanocomposite with 5.19 vol% of BNT nanoparticles. The high aspect ratio BNT nano-bers are observed in Fig. 5a-c, which are homogeneously dispersed and embedded in the polymer matrix. The formation of agglomerates, voids and cracks is not observed even when the BNT nanober loading is increased to 12.73 vol%, as is shown in Fig. 5c. A similar view is shown in Fig. 5d, where the BNT nanoparticles are uniformly dispersed throughout the composite and tightly adhered to the surrounding matrix. Since all the llers are modied using dopamine (Fig. S1a †) before being incorporated into P(VDF-HFP), the hydroxyl groups in dopamine form strong dipole-dipole interactions with the -F atoms from P(VDF-HFP). In addition, due to the strong electronegative nature of the -F atoms, hydrogen bonding (-F/ OH-) can be easily formed. 30 Therefore, the BNT nanobers exhibit excellent dispersion and compatibility in the polymer matrix.
To assess the dielectric properties of the nanocomposites formed using BNT nanobers and BNT nanoparticles, the frequency dependent permittivity, dielectric loss and electric conductivity of the nanocomposites with various loading levels   of BNT nanobers and BNT nanoparticles are shown over a frequency range of 500 Hz to 10 MHz in Fig. 6. It can be seen that the permittivity of the nanocomposite increased with increasing loading level of either BNT nanobers or nanoparticles, as shown in Fig. 6a and c, respectively. It is also observed that the permittivity of the nanocomposite with BNT nanobers is higher than the nanocomposite with BNT nanoparticles at the same volume fraction. This phenomenon is clearly observed in Fig. 6f; for example, at a ller loading level of 5.19 vol% the permittivity of the BNT nanober composite is 15% higher than that of the BNT nanoparticle composite. In addition to the increased fraction of the b-phase (Fig. 4a), the increased permittivity of the nanocomposites also arises from the Maxwell-Wagner-Sillars (MWS) interfacial effect, where the phase dependent permittivity (k(r)) is dened as given below: 11 where a, b, g and h are the BNT nanober, BNT nanoparticles, P(VDF-HFP) matrix phases and the interfacial phase. The BNT nanoparticles have an average diameter of 869 nm, as shown in Fig. 2, and are therefore signicantly larger than the BNT nanobers (an average diameter of less than 100 nm), so that the BNT nanobers have more interface area and interface polarization than the BNT nanoparticles for the same ller volume fraction. In addition, the permittivity of the nanocomposites gradually decreased with increasing frequency, and this trend is more obvious as the ller loading level increases; for example, the permittivity of the nanocomposite with 12.73 vol% BNT nanobers is 21.7 at 1 kHz and 13.0 at 1 MHz (Fig. 6a). A decrease in permittivity with increasing frequency has been observed to result from the existence of electrical conductivity in the material, which has been simulated using resistor-capacitor networks. 36 The properties are relatively independent of the magnitude of the applied electrical eld, see Fig. 6e. The nanocomposites also exhibited improved thermal conductivity (Fig. S2 †) and increased tensile strength (Fig. S3b †) compared to the pure matrix phase. Fig. 7a shows the frequency dependence of electrical conductivity of the BNT NF nanocomposites with various ller loadings. It can be seen that the electrical conductivity increases with increasing frequency and ller loading; this indicates that the nanocomposites behave in a capacitative manner and all exhibit a relatively low electrical conductivity that is less than 6.8 Â 10 À7 S m À1 . The temperature dependence of the electric conductivity and permittivity of nanocomposites with 12.73 vol% BNT nanobers at various frequencies is shown in Fig. 7b and c, respectively. The electric conductivity and permittivity of the nanocomposite were stable with a change in temperature, e.g. the electric conductivity was 5.3 Â 10 À5 S m À1 at 100 kHz at  room temperature and 5.2 Â 10 À5 S m À1 when the temperature was increased to 120 C. The permittivity showed a similar phenomenon, which was 18.7 and 21.8 at room temperature and 120 C at 1 kHz respectively. These results demonstrate the excellent temperature stability of BNT NFs/P(VDF-HFP) composites in terms of electric conductivity and permittivity.
A high fatigue endurance is necessary for long-term stability during the capacitor charge-discharge cycling process. 37,38 Thus, the residual polarization (P r ) of P(VDF-HFP) nanocomposites with various BNT NF loading levels was investigated as a function of the charge-discharge cycles up to 10 6 cycles with pulse heights of 40 kV mm À1 and pulse frequency xed at 1 kHz. It can be seen in Fig. 7d that the P r of the nanocomposites with 2.37 vol% BNT nanobers increased by only 6.1% aer 10 6 switching cycles. However, the P r was increased by 85.7% when the BNT nanober content was increased to 12.73 vol% under the same cycling conditions. These results indicate that the P(VDF-HFP) nanocomposites with a low BNT nanober content possess superior cycling stability compared with the nanocomposites with a high BNT NF content, which are likely to exhibit a relatively high leakage current density due to the increased oxygen vacancies in ABO 3 -type perovskite structures. 39 The characteristic leakage current density-electric eld curves with various BNT nanober contents, temperature and electric eld were investigated and are shown in Fig. 8. The nanocomposite with a low BNT nanober content (2.37 vol%) was an excellent insulating material for practical applications due to the low leakage current density of 1.47 Â 10 À7 A cm À2 under 40 kV mm À1 at room temperature (Fig. 8a), which increased by more than two orders of magnitude (2.83 Â 10 À5 A cm À2 ) when the BNT nanober content was increased to 12.73 vol% (Fig. 8c). These results were consistent with the fatigue endurance test shown in Fig. 7d. However, the leakage current showed an obvious temperature diffusion phenomenon, especially when the ller content was low, e.g. the leakage current density of the nanocomposite with 2.37 vol% BNT nanobers was 1.47 Â 10 À7 A cm À2 , which was continuously increased to 3.20 Â 10 À6 A cm À2 as the temperature increased from room temperature to 120 C under 40 kV mm À1 (Fig. 8a). These results may originate from the relatively low oxygen vacancy concentration and rapid free electron migration with temperature. 37,39,40 The leakage current density of the three samples showed an increase with an increase of the applied electric eld (Fig. 8a-c). In the lower eld region (<5 kV mm À1 ), the current density rapidly increased with the applied electric eld, whereas the current density showed a lower dependency on the eld at higher applied elds. In addition, the nanocomposites exhibited an increased leakage current density as the loading level of the BNT nanobers increased; for example, the leakage current densities of the nanocomposites with increasing nanober contents are 3.94 Â 10 À7 A cm À2 (2.37 vol%), 6.81 Â 10 À6 A cm À2 (5.19 vol%), 4.28 Â 10 À5 A cm À2 (12.73 vol%) at 40 C under 40 kV mm À1 . This is attributed to the high leakage current density of BNT and the defects and space charge introduced by the BNT nanober inclusions. 41 According to eqn (1) the breakdown strength is the key parameter to achieve a high discharge energy density for the composite. The breakdown strength of the BNT nanober/ P(VDF-HFP) composites with various volume fractions of llers is shown in Fig. 9, which is analyzed with a two-parameter Weibull distribution function (Fig. 9a), using the equation: The characteristic breakdown strength (E 0 ) is obtained when the cumulative probability of electric failure (P(E)) equaled 63.2% and b is the shape parameter, as shown in Table S1. † 42 As Fig. 7 (a) Frequency dependence of the electric conductivity; temperature dependence of (b) electric conductivity, (c) relative permittivity of the nanocomposites with 12.73 vol% BNT nanofiber at various frequencies; (d) endurance test of the nanocomposites with various BNT nanofibers with the electric field cycling and pulse field amplitude of 40 kV mm À1 . shown in Fig. 9a, the characteristic breakdown strength is determined from a t of eqn (3) to at least eight individual breakdown measurements. As can be seen from Fig. 9a and b, the sample with 2.37 vol% BNT nanobers exhibited the highest breakdown strength of 458 kV mm À1 , which is higher than that of the pure (unlled) P(VDF-HFP) polymer (398 kV mm À1 ), a result that has also been reported elsewhere. 33 The breakdown strength decreases to 302 kV mm À1 when the ller loading is increased to 12.73 vol%. As shown by Liu et al., 12 a low concentration of nanobers improves the breakdown strength due to a number of reasons. Firstly, the homogeneous dispersion and strong adhesion of the high aspect ratio nanobers aer surface modication in the nanocomposite can reduce charge transfer and prevent the polymer chain from moving freely. 11 Secondly, the high aspect ratio nanobers orientated parallel to the lm surface direction during the solution casting process can endure a higher electric eld vertical to the lm surface direction (see Fig. S4 †). 12,43 Finally, the nanobers also inuence the crystallization of the polymer, as seen in Fig. 4. The defects, such as the accumulation and voids in the nanocomposite, inevitably increased when the BNT nanober loading increased. The accumulated nanobers in the nanocomposites can readily form a connected path for the free charge, and the voids will encapsulate the air, therefore, the breakdown strength was decreased. These results indicate that incorporation of a small loading level of BNT NF to the polymer matrix (2.37 vol%) may be an effective method to achieve high energy densities.
The discharged energy density of the samples can be calculated from the electric displacement-electric eld (D-E) loops. Fig. 10a shows the D-E loops of the nanocomposites with various loading levels of BNT at an electric eld of 300 kV mm À1 , and the maximum D-E loops are shown in Fig. S5 (ESI). † As can be seen from Fig. 10a, the electric displacement of the nanocomposites increased with the loading level of BNT nanobers at the same electric eld, while the remnant displacement greatly increased. As a result, the nanocomposites with 12.73 vol% BNT nanobers showed a low energy density, which is shown in Fig. 10b. The nanocomposite with 2.37 vol% BNT nanobers have the largest discharged energy densities of 12.7 J cm À3 , which is more than three times that of the pure (unlled) P(VDF-HFP). The signicant increase in energy density is mainly due to the high breakdown strength and the high effective electric displacement shown in Fig. S6 (ESI). † Table 2 summarizes the previously reported dielectric nanocomposites with different ceramic nanobers. The discharged energy density achieved in this work using a low content of Na 0.5 Bi 0.5 TiO 3 nanobers is superior to the performance of nanocomposites reported elsewhere.

Modelling of composite dielectric materials
Finite element modelling of a single high permittivity inclusion in a low permittivity matrix was used to further understand the energy storage properties of the BNT/P(VDF-HFP) nanocomposites investigated experimentally. Rather than model a complex three-dimensional system, a series of simplied two dimensional models were created to examine the effect of the ceramic lling fraction, aspect ratio and angle of the high permittivity inclusion to the applied electric eld direction on both the permittivity and breakdown strength of the nanocomposite. An additional model will be discussed which introduces a polar b-P(VDF-HFP) as an 'interphase' between the matrix and the high permittivity inclusion. The modelling soware used was ANSYS v15.0 using a two dimensional fournode element type (PLANE13) for electrostatic analysis. In all cases the matrix phase (a-P(VDF-HFP)) was modelled with a relative permittivity, 3 r ¼ 10, and the inclusion was assigned the dielectric properties of BNT (3 r ¼ 377). It should be noted at this point that units and scales of length are in effect arbitrary in all the analyses so electrical loads applied to the models were selected so that the applied eld in each case was unity.
The effective permittivity of the modelled composites was calculated by summing the electrostatic energy of each element and calculating the capacitance, and from this permittivity, using the relationship C ¼ Q/V, where C is the capacitance, Q is the charge and V is the voltage. Electrical breakdown strength was not modelled directly but instead the maximum local electric eld (E max f ) within the composite due to the applied eld for each geometry was recorded. The maximum applicable eld for a single phase capacitive material, as discussed previously, is the breakdown strength, E b ; above this eld the material will no longer store charge as it becomes electrically conductive. When high permittivity phases are introduced into a composite system, the electric eld concentrates in the low permittivity phase 16,17,33 , which is oen the high breakdown strength phase;  in the BNT/P(VDF-HFP) composite system explored here the low permittivity polymer phase has a higher breakdown strength.
If it is assumed that there is no change in the breakdown strength of the constituent phases in the creation of the composite, a concentration of electric eld within the material is likely to lead to electrical breakdown at applied elds below E b , such that the maximum eld applied to the composite material must be modied by a 'concentration' factor of 1/ E max f so as to ensure the local eld does not exceed the breakdown strength at any point within the composite. The effective breakdown strength of the composite can therefore be dened by the relationship: Our initial model was designed to investigate the effect of lling fraction of the high permittivity BNT phase into the P(VDF-HFP) matrix. A circular BNT inclusion of varying radius (r ¼ 1, 2, 3, 4, 5, 6,7,8,9) was modelled in the center of a square P(VDF-HFP) matrix (20 Â 20). A ne triangular nite element mesh was used that satisfactorily mapped the inclusion geometry and electrical loads were applied to the model at boundary lines to simulate electrodes in a parallel plate capacitor, thus generating an electric eld across the geometry. An example of such a model can be seen in Fig. 11a which shows that the applied electric eld tends to concentrate in the low permittivity matrix phase and is signicantly smaller in the high permittivity inclusion. The results from this model for composite permittivity and the inverse of the maximum eld (i.e. the factor by which the breakdown strength is modied in eqn (4)) are shown in Fig. 11b. The data have been normalized with respect to the single phase matrix material to demonstrate clearly the effect of the high permittivity inclusions on the effective properties of the composites. It can be seen in Fig. 11b that introducing a high permittivity second phase increases the composite permittivity, however signicant increases are not realized until the ll fraction exceeds $0.3 (30 vol%) when the modelled permittivity is doubled compared with single phase P(VDF-HFP). 36 As the electric eld concentrates in the low permittivity phase to such an extent that the eld in the high permittivity inclusion is close to zero, it appears that the increase in permittivity is linked to the concentration of the eld in the low permittivity polymer phase, meaning that more charge, Q, is  stored, as V in the relationship Q ¼ CV is effectively increased for the same overall volume. However, while there is an increase in permittivity, there is also a rapid increase in the maximum electric eld at very low volume fraction of the high permittivity second phase, which is likely to lead to a reduction in the effective breakdown strength of the material. The highest elds are observed at the tips of the inclusion parallel to the applied eld, as shown in Fig. 11a. The model above clearly indicates that the inclusion of high permittivity particles can increase the effective permittivity but also increase the maximum electric eld and therefore reduce the breakdown strength, which is an important factor from eqn (1). The model is now adapted to investigate how the effective composite permittivity is affected by the aspect ratio of the high permittivity second phase and its orientation/angle relative to the applied electric eld. The BNT inclusion was modelled as an ellipse with the aspect ratio dened as the ratio of the radii of the major and minor axes, with an aspect ratio of one being a circular inclusion. Fig. 12a shows example geometries of angle and aspect ratio; aspect ratios ranging from one to 10 have been investigated in this model. The inclusion was modelled in the center of a 20 Â 20 P(VDF-HFP) matrix and the angle rotated from 0 (i.e. parallel to the applied eld) to 90 (perpendicular to the applied eld) in steps of 11.25 . In all cases the ll fraction of the BNT phase was constant at 0.00785. Electric eld contour plots of ber composites (aspect ratio 10) are shown in Fig. 12b and c for angles with respect to a eld of 0 and 90 , respectively, and demonstrate that the highest eld concentrations occur in the polymer matrix in the vicinity of the high permittivity inclusion, parallel to the eld direction. The effect of aspect ratio and angle with respect to the eld on the effective permittivity of the composite and the maximum local electric eld is shown in Fig. 12d and e. The highest increase in the composite permittivity was found when high aspect ratio inclusions were aligned parallel to the applied eld (Fig. 12d), however, this also caused signicant increases in the local electric eld at the sharp tips of the high permittivity inclusion (Fig. 12e). The normalized energy density for each case was calculated using the relationship u norm e ¼ 3 norm /(E max f ) 2 , where 3 norm is the composite permittivity normalized with respect to the permittivity of the single phase material, and is plotted in Fig. 12f as a function of angle for varying aspect ratios. The composite with high aspect ratio BNT NFs in the direction of perpendicular to the applied eld is predicted possessing the highest energy density, however, due to the reduction in 1/ E max f with the addition of a high permittivity second phase no composite geometry improves on the energy density of the single phase material, shown as a dashed black line in Fig. 12f. Clearly for these composite systems, the introduction of the high permittivity phase increases the local electric eld which increases the effective permittivity (Fig. 12d) but also increases the local electric eld (Fig. 12e), leading to reduced energy density (Fig. 12e).
In the models discussed to this point the nanoparticle composites (AR ¼ 1) are predicted to have higher permittivity than high aspect ratio nanober composites (AR ¼ 10 at 90 ) aligned perpendicular to the eld direction, which was not the case observed experimentally where the nanober composites had superior permittivity to the nanoparticle composites at the same volume fraction of BNT. To understand the reasons behind these results it was necessary to develop a third nite element model whereby a rectangular ber of varying aspect ratio (aspect ratio ¼ 12.5, 50, 200) and constant lling fraction (0.004) was contained in a rectangular matrix and a polar b-P(VDF-HFP) 'interphase' with varying thickness was modelled between the matrix and the high permittivity inclusion. This is Fig. 12 (a) Example geometries investigated via a finite element approach and their corresponding aspect ratios and angles with respect to the applied electric field; (b) and (c) electric field contour plots of fibers modelled parallel and perpendicular to the applied field, respectively, showing that field concentration occurs at sharp tips of the high permittivity phase but in the low permittivity matrix; (d), (e) and (f) effect of aspect ratio and angle on permittivity, field concentration factor (1/E max f ) and energy density, respectively, normalized to the single phase material shown in all plots with a dashed black line.
included due to the observation that the BNT nanober llers in P(VDF-HFP) facilitate the formation of the polar b-phase, Fig. 4.
The rectangular model had dimensions of 100 Â 500 and was meshed with square elements of equal size; Fig. 13a shows a close up image of the mesh surrounding the ber. The size of the matrix was selected in this case to ensure that boundary effects did not inuence the results as the ber aspect ratio was increased. Three thicknesses of interphase layer on the surface of the ber were investigated (element thickness ¼ 0, 1, 2, where t ¼ 0 has no interlayer) for the effect on electric eld distribution in the composite and permittivity. The b-P(VDF-HFP) interphase was modelled with a relative permittivity of 15, 49 compared to a relative permittivity of 10 for the bulk matrix. Electric elds were applied perpendicular to the ber direction as this was shown to be the best conguration for energy storage, as in Fig. 12c. Reported relative permittivity values for b-P(VDF-HFP) vary between 10 and 60, 50 which has an effect on the results of this model in terms of the composite permittivity, electric eld concentration factor (1/ E max f ) and the normalized energy density, such that increasing the interphase permittivity leads to an increase in the overall permittivity but also increases the maximum local electric eld concentration in the matrix, leading to a reduction in the normalized energy density compared to an interphase relative permittivity of 15, see Fig. S7. † A contour plot of the electric eld distribution within a composite with an interphase thickness of one element and a relative permittivity of 15 is shown in Fig. 13b. The presence of the interphase was found to increase the permittivity for all aspect ratios and permittivity was found to increase with increasing interphase thickness. High aspect ratio llers yield the best improvements in permittivity, see Fig. 13c. This is due to the increase in the surface area of the ber with aspect ratio and explains why the nanoparticle composites were found experimentally to exhibit a lower permittivity compared to the nanober composites at the same BNT volume fraction (see Fig. 6); the use of high aspect nanobers simply led to a higher volume of the interphase compared to the nanoparticles, which experimentally had a signicantly larger diameter than the bers: 800 nm compared to 67 nm.
The presence of the higher permittivity b-P(VDF-HFP) interphase reduced the eld concentration in the P(VDF-HFP) matrix compared to when there was no interphase, which can be seen from the data in Fig. 13d where the solid lines (1/E max f in the matrix, colors denote varying aspect ratios) approach unity (i.e. no eld concentration) as the interphase thickness is increased. It was also found that increasing the thickness of the b-P(VDF-HFP) layer reduced the eld concentration within this phase and higher aspect ratios were also benecial in this respect, this is indicated by the dashed lines in Fig. 13d. The effect of introducing an interphase on the electric eld distribution of the composites may partially explain why experimentally an increase in breakdown strength was observed at low volume fractions of BNT nanobers, see Fig. 9b, as the eld concentrations are reduced due to the more gradual change in permittivity around the high permittivity inclusion. At higher BNT volume fractions the close proximity of neighboring nanobers is likely to lead to eld concentrations that negate the benets of the nucleation of the interphase, hence the decline in breakdown strength observed experimentally above 2.37 vol% volume fraction of BNT nanobers. The increase in permittivity and reduction in eld concentration with the addition of the interphase leads to higher predicted energy densities than for the composites in all cases, with the best results seen for high aspect ratio bers with a thick interphase, as shown in Fig. 13e.

Conclusions
This paper demonstrates that the use of a small volume fraction of high aspect ratio nanober llers is an effective approach to achieve a nanocomposite architecture capable of achieving a high energy density and high dielectric strength. Lead-free high aspect ratio ferroelectric Na 0.5 Bi 0.5 TiO 3 (BNT) nanobers and particles were synthesized by a hydrothermal method. The P(VDF-HFP) nanocomposite lms with a variety of BNT nano-bers and nanoparticle loading levels (2.37, 5.19 and 12.73 vol%) were obtained by casting and hot pressing. The relative permittivity of the nanocomposite continuously increased with the level of BNT nanober loading, while also maintaining a relatively low dielectric loss (<0.11). A small amount (2.37 vol%) of BNT nanobers introduced to the polymer matrix increased the fraction of the polar b-phase in the nanocomposite, which led to an increase of the permittivity. Due to the partial perpendicular distribution of BNT nanobers to the applied electric eld direction, the local electric eld concentration was reduced, which was investigated in detail by nite element analysis (ANSYS). The presence of high aspect ratio nanobers with the treatment of surface modication and the alignment of nanobers perpendicular to the applied electric eld led to a high breakdown strength of 458 kV mm À1 for the nanocomposite with 2.37 vol% BNT nanobers with a corresponding large energy storage density of 12.7 J cm À3 . The thermal conductivity also increased to 0.67 W m À1 K À1 compared to the pure P(VDF-HFP) polymer (0.2 W m À1 K À1 ). This research provides a novel nanocomposite approach to produce high energy storage density dielectric materials for advanced electronic and electrical power system applications.