Ultrahigh β-phase content poly(vinylidene fluoride) with relaxor-like ferroelectricity for high energy density capacitors

Poly(vinylidene fluoride)-based dielectric materials are prospective candidates for high power density electric storage applications because of their ferroelectric nature, high dielectric breakdown strength and superior processability. However, obtaining a polar phase with relaxor-like behavior in poly(vinylidene fluoride), as required for high energy storage density, is a major challenge. To date, this has been achieved using complex and expensive synthesis of copolymers and terpolymers or via irradiation with high-energy electron-beam or γ-ray radiations. Herein, a facile process of pressing-and-folding is proposed to produce β-poly(vinylidene fluoride) (β-phase content: ~98%) with relaxor-like behavior observed in poly(vinylidene fluoride) with high molecular weight > 534 kg mol−1, without the need of any hazardous gases, solvents, electrical or chemical treatments. An ultra-high energy density (35 J cm−3) with a high efficiency (74%) is achieved in a pressed-and-folded poly(vinylidene fluoride) (670-700 kg mol−1), which is higher than that of other reported polymer-based dielectric capacitors to the best of our knowledge.

T he demands of reducing both CO 2 emissions and the consumption of fossil fuels require an enhancement of the efficiency of energy usage and the long-term pursuit of renewable and sustainable energy sources (such as solar, wind, wave, etc.). These energy sources are intermittent, and it is therefore of paramount importance to develop efficient, low-cost and environmentally friendly electric energy storage systems. Currently, there are three main options: batteries, electrochemical capacitors and dielectric capacitors 1 . Batteries, with their high energy density (lead-acid battery: 200-400 J cm −3 and lithium ion: 900-2500 J cm −3 ) and low power density (<500 W kg −1 ), are usually used in applications that require relatively slow release of energy (>100 s), while capacitors, with their high power density (electrochemical capacitors: 10 1 -10 6 W kg −1 and dielectric capacitors:~10 8 W kg −1 ), are used for rapid release of energy (<0.01 s) 2 . Electrochemical capacitors have at least an order of magnitude higher energy density compared to dielectric capacitors, but suffer from lower power density and lower output voltage. Only dielectric capacitors can meet the requirement of ultrahigh power density (up to~10 8 W kg −1 ) 1 , with the added benefits of long service life and fast release of energy 3 , which makes them important for high power/pulse power technologies, such as motor drives, mobile power systems, space-vehicle power systems, electrochemical guns, and so on 4,5 .
However, the application of dielectric capacitors is currently limited by their low energy density, especially in applications requiring large capacitances and small packaging size. For example, the best-performing commercial dielectric capacitor, biaxially oriented polypropylene (BOPP), only has an energy density of~1-2 J cm −3 , which is an order of magnitude lower compared to commercial electrochemical capacitors (20-29 J cm −3 ) 6,7 . Therefore, achieving high energy density in dielectric capacitors is a major bottleneck in extending their practical applications. The recoverable energy storage (U rec ) for dielectric capacitors is generally described by the following equation: U rec = ∫EdD, where E and D are electric field and displacement, respectively. Specifically, for linear dielectrics, where ε 0 and ε r are the vacuum and relative dielectric constant, respectively, and E b is the breakdown field. U rec has a quadratic dependence on E b . While polymers possess much lower dielectric constants compared to inorganic materials, they have at least an order of magnitude higher energy storage capacity as a result of their much higher breakdown fields (several hundreds of kV mm −1 ). Apart from their high E b , polymers have additional advantages, such as low density, high processability, mechanical flexibility and high toughness.
The relatively low ε r of polymers is the limiting factor for their U rec . The above-mentioned BOPP, for instance, has a ε r of~2. Polar polymers, with dipole moments in their polymer chains, can exhibit much higher ε r . Poly(vinylidene fluoride) (PVDF) is a typical example 8-10 with a ε r of~10. PVDF has at least four welldefined phases, α-, β-, γand δ-phase. The α-phase is non-polar, while the other three are polar phases, of which the β-phase shows the highest polarization and the most favourable ferroelectric properties [11][12][13][14] . However, PVDF crystallizes predominantly into α-phase from the melt, with fairly low content of β-phase (<8%) 15 , which can be increased by solid-state drawing and/or high electric field poling (~50-85%) 16 . β-PVDF exhibits broad ferroelectric hysteresis loops and is not suitable for energy storage (Supplementary Fig. 1) 17 . Relaxor ferroelectric (RFE) or anti-ferroelectric (AFE) behaviour is instead desirable for energy storage ( Supplementary Fig. 1) 17 . However, RFE or AFE behaviour have only been reported in the case of electronor γ-irradiated poly(vinylidene fluoride-trifluoroethylene) P (VDF-TrFE) 18 , ternary polymers poly(vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) P(VDF-TrFE-CFE) 19 and poly(vinylidene fluoride-trifluoroethylene-chlorotrifluoroethylene P(VDF-TrFE-CTFE) 20 and PVDF-based graft polymers such as P (VDF-CTFE)-graft-polystyrene 21 . The complexity and cost of the above polymers and processes present a major barrier to their commercial use.
Our work focuses on virgin, commercially available and inexpensive PVDF homopolymers, and demonstrates a facile and scalable processing route to obtain an ultrahigh content of β-phase (~98% of crystalline phase) with RFE-like behaviour that has an exceptionally high energy storage density of 35 J cm −3 , which is achieved by reversible field-induced transitions related to thermally unstable local polar structures. This is the highest value reported for a polymer-based dielectric material (Supplementary Table 1) [22][23][24][25][26][27][28][29][30][31] , to the best of our knowledge. The produced homopolymer PVDF films show the lowest dielectric loss (0.02 at 1 kHz) and highest maximum working temperature (120°C) in PVDF-based ferroelectric materials (dielectric loss: 0.03-0.05 for previously reported PVDF and copolymer films; 0.08-0.10 for terpolymer films; maximum working temperatures: 100-120°C for previously reported PVDF and copolymer films; 50-60°C for terpolymer films), which challenges the performance of commercial electrochemical capacitors and ceramic capacitors, with the added benefits of mechanical flexibility, toughness and low density.

Results
Pressed-and-folded PVDF for electric energy storage. Our approach uses a unique processing route called "pressing-andfolding" (P&F), which draws inspiration from the process used by bakers to prepare puff pastry and croissants 32 . P&F is an iterative process in which the P&F cycle can be applied an arbitrary number of times (Fig. 1a). Each P&F cycle is composed of a folding step, in which an approximately rectangular PVDF film, produced by hot pressing (HP), is folded, followed by a pressing and annealing step around the melting point (T m ) of PVDF (160-170°C). For example (samples characterized in Fig. 1b), the initial films (~50 mm × 50 mm, thickness~200 μm) were first folded and cold pressed with a compression force of 300 kN. The temperature was then increased from ambient temperature to 165°C. The folded films were then held for 5 min under the conditions of 165°C and 300 kN, followed by cold water quenching while maintaining the same compressive force. The maintenance of pressure during cooling was observed to facilitate the formation of β-phase ( Supplementary Fig. 2). During P&F, a fine and discrete layered structure is generated, with the thickness of each layer decreasing with the number of P&F cycles (Fig. 1b). As expected, the initial HP films (no folding) contained predominantly α-phase, as confirmed by Fourier transform infrared (FTIR) spectroscopy (presence of characteristic peaks of α-phase at 764, 975 and 1212 cm −1 , absence of the β/γ characteristic peaks at 840 cm −1 ) ( Fig. 1c) 33,34 . Surprisingly, P&F produced films containing about 98% of β-phase after seven P&F cycles (Fig. 1c), higher than for any other reported method (max 85% by unidirectional/biaxial drawing, as highlighted by the horizontal green shaded area in Fig. 1c) 16,[35][36][37][38] . The analysis of PVDF phase content has been well studied in previous research works [36][37][38] , which includes the determination of existing phases according to the appearance of exclusively characteristic bands (e.g. α-phase: 764 cm −1 ; β-phase: 1275 cm −1 and γ-phase: 1234 cm −1 listed in Supplementary Table 2) and then calculation using specific equations based on the sample containing αand βphase only or containing a mixture of α-, βand γ-phase. More details are summarized in Supplementary Note 1. The folded samples show similar melting points compared to the initial HP materials (no folding) (Supplementary Fig. 3 and Supplementary Table 3). The densities of the films were measured based on the Archimedes principle, and are~1.770 and 1.780 g cm −3 for HP and P&F samples, respectively. Consequently, the degree of crystallinity of HP and P&F samples are 41% and 38%, respectively, which was calculated using the densities of amorphous PVDF, pure αand pure β-PVDF of 1.68, 1.92 and 1.97 g cm −3 , respectively 39,40 . The calculated values of the degree of crystallinity are typical of PVDF 41 . For comparison, HP films were solid-state drawn to failure at 100°C and 10 mm min −1 , which was reported to be the optimum conditions for obtaining the β-phase in a previous work 35 , achieving only~65% of β-phase content (indicated by the blue dashed line in Fig. 1c) and a degree of crystallinity of 36% (density: 1.772 g cm −3 ). The ferroelectric hysteresis loops of the stretched films (thickness~35 μm) could only be tested at relatively low electric fields (<350 kV mm −1 ) due to the max limit of c The evolution of crystalline phases revealed by the FTIR absorbance spectrum. The initial hot-pressed (HP) films mainly crystallized into α-phase with characteristic peaks at 764, 975 and 1212 cm −1 highlighted by asterisks and transformed to about 98% β-phase (strong peak at 840 cm −1 ) after seven folding cycles. The horizontal green shaded area indicates the reported values of fraction of β-phase in commonly stretched PVDF films, the blue dashed line represents the fraction of β-phase for the stretched film in this work and the continuous line is the best fit of the experimental P&F data with Eq. 2 using c as free parameter (f β0 and h were set at 8% and 0.6, respectively). d A comparison of electric energy storage properties of P&F and stretched films, which includes unipolar ferroelectric hysteresis loops, schematic calculations of stored energy of ferroelectric materials and the recoverable energy density U rec and energy efficiency η of P&F and stretched films 10 kV applied voltage of our equipment (Fig. 1d). From the schematic diagram of stored energy in ferroelectrics (Fig. 1d), a lower remnant displacement (D r ), a higher maximum displacement (D max ) and a higher breakdown field (E b ) than the values found for the stretched films 31 would be favourable to obtain higher recoverable energy density U rec . The P&F sample (one layer extracted from a film processed with seven P&F cycles, as described in the section Materials and film preparation in Methods) showed an extremely high E b , 880 kV mm −1 . The D r and D max are 0.017 and 0.144 C m −2 , respectively. All of these parameters contribute to a high U rec of 35 J cm −3 , which is the highest value ever reported for any polymer-based dielectric capacitor. Despite the ultrahigh U rec , the P&F samples also had higher energy efficiency η (~74%) compared to the stretched film (~54%) (Fig. 1d). Moreover, the P&F films showed high breakdown strength with an average value of 789.5 kV mm −1 , as evaluated according to the criterion of Weibull distribution statistics ( Supplementary Fig. 4).
The above results raise two fundamental questions: Why does P&F generate such a high content of β-phase (~98%)? and Why do P&F films show relaxor-like ferroelectric behaviour?
Phase transformation from α to β during the P&F process. To answer the first question, we have investigated the dimensional changes of a sample during the P&F process (Fig. 2a). The sample deformed plastically at each cycle, but its volume always remained constant according to the experimental results (Fig. 2a). The maximum nominal stress (or pressure, Fig. 2b) reached at the end of each cycle increases during the process as P i n where n is the number of cycles, P 1 is the pressure applied at the first cycle and a = 1.65 (±0.14) is a factor that describes how much the sample area increases during compression (Supplementary Note 2). Atomic force microscopy (AFM) images ( Fig. 2c) reveal the change of morphology during P&F, from spherulites (~2-3 μm in diameter) in the initial HP film to small granular structure (~150 nm in diameter) due to the increasing applied pressure with increasing number of P&F cycles. The energy (Ω) that plastically deforms a unit volume of polymer provides the "driving force" for the phase transformation, and it grows with the number of cycles as Ω n ð Þ ¼ ) is a factor that describes how much the sample thickness decreases during compression. Within this context, it is worth noting that the β-phase has a smaller unit cell volume (108.2 Å 3 ) compared to the α-phase (118.6 Å 3 ) for the same number of atoms 11 . Moreover, judging by the calculated values of intra-and inter-molecular potential energy, −6.03 and −5.73 kcal mol −1 for αand β-phase, respectively, the β-phase is slightly energetically less stable 42 . The imposition of the ever increasing pressure P i leads to a closer packing of the atoms and, as a result, a favoured β-phase with all-trans chain conformation. These considerations are supported by studies on phase transformation in solid-state drawn 43,44 , solid-state compression 45 and rolling processed 46 PVDF films. The amount of β-phase (f β ) is proportional to Ω. Therefore, an advantage of the P&F process over the drawing process is that PVDF can always adsorb more "plastic energy" in compression than in tension 47 . Compression can be carried out in a broader (lower) temperature range than tension. Overall, the P&F process can allow higher phase conversions. Summarizing, the increment of β-phase (Δf β ) depends on the increment of plastic energy (ΔΩ) adsorbed by the material, and must be limited by the amount of α-phase, that is, by the term 1f β , as when all b Calculated pressure (nominal stress) in purple data points for different P&F cycles. c AFM topography images (5 µm × 5 µm) of initial HP (left) and P&F (right) after seven cycles, which show the evolution of morphology, from large spherulites in HP films to small granules after P&F films. d Theoretical changes of the β-phase content according to Eq. 2 with different values of parameter c of the α-phase is converted there cannot be further increments of β-phase. From these considerations, and assuming that the fraction of β-phase before starting the P&F process is f β0 (8%), a differential calculation leads us to the following relationship between the amount of β-phase and plastic energy: or, in terms of P&F cycles, where b and c ¼ bP 1 1Àh 1À2h are some proportionality constants. Figure 1c shows that the experimental data of f β can be well fitted by Eq. 2 with c = −1.1, whereas the effects of different values of c on the β-phase amount during the P&F process is illustrated in Fig. 2d. A number of factors should influence the relationship between f β and Ω (i.e. the proportionality constant b or c), as well as the amount of Ω that can be generated in the P&F process. We have tried to identify some of these factors, as it is clearly desirable to transform as much α-phase into β-phase as is possible with the lowest amount of plastic energy, or number of cycles.
First of all, the compressive stress-strain curve of PVDF is strain-rate-dependent 48 . Therefore, for the same final nominal stress, the energy adsorbed depends on the final strain; hence, there may be quicker phase conversion rates when pressing at higher strain rates. The second factor is the initial area (A 0 ) of the sample, a smaller A 0 corresponds to higher P 1 , hence greater Ω. If A 0 is small enough, the pressure applied to the sample could be big enough to induce total phase transformation in fewer cycles. Figure 3a shows the β-phase content of single-layer films (lefthand dataset) having different A 0 (25, 4.5 and 1 cm 3 ) after the initial pressure P 1 ; the film with the smallest A 0 allowed almost a complete phase transformation (95 ± 5%) in just one cycle. Figure 3a also shows the importance of a third factor, the number of initial stacked layers constituting a film. At the same P 1 , films made with six layers of HP films (Fig. 3b) presented much higher β-phase amounts than single-layer films. An explanation for this could lie in the friction between the PVDF and the hot-press platens. The friction induces shear stresses that could dissipate energy 48 and reduce the pure elongation of the material in the plane perpendicular to the compression direction. Finite element method (FEM) simulations of film compression (Fig. 3c) confirm that the internal layers of a multilayer structure can elongate and plastically deform more than the external layers, especially when the friction between the layers is smaller than the friction with the platens.
The two last important factors are the temperature of the annealing step (T anneal ) that follows the full closure of the hot press and the molecular weight (M w ) of PVDF. They have a similar effect: lower T anneal and higher M w give lower chain mobility. Figure 3d presents the FTIR spectra of different M w films annealed above their T m ; the β-phase increased more remarkably during the P&F process for higher M w (>530 kg mol −1 ) PVDFs. Moreover, in the low M w (180 kg mol −1 ) films also some γ-phase (chain conformation T 3 GT 3 G′; Fig. 3e) was produced. This is consistent with a previous work reporting αto γ-phase transition in PVDF (M w 180 kg mol −1 ) under a minimal applied pressure of 200 kPa and a temperature range of 167-180°C 49 . Apart from the M w , the T anneal plays a critical role; regardless of their M w , all of the films presented only β-phase (>90%) when processed below their T m , but maintained the non-polar α-phase when T anneal >> T m (Fig. 3e and Supplementary Fig. 5). More details on the factors influencing the phase transformation can be found in the Supplementary Note 2.
Relaxor-like ferroelectric behaviour in P&F films. Having observed the formation of ultrahigh content of β-phase by P&F and proposed a possible mechanism, hereafter we focus on the ferroelectric behaviour of P&F PVDF films. The bipolar ferroelectric current-displacement-electric field (I-D-E) characteristics were measured under different electric fields at room temperature using a triangle waveform with a frequency of 10 Hz (Fig. 4). It is noted that the D-E loops alone are insufficient to demonstrate ferroelectric properties and clarify the type of ferroelectric behaviour. Instead, it is more informative to study the raw I-E curves, in which the presence of ferroelectric domain switching peaks and/or field-induced structure transition can easily be identified. Only some of the P&F samples with higher M w polymer samples (534 and 670 kg mol −1 ) showed relaxor-like ferroelectric behaviour 50 (Fig. 4a), that is, slim D-E loops with low D r and high D max . The M w 180 kg mol −1 polymer samples showed four current peaks located in the first and third quadrant at electric fields lower than 200 kV mm −1 , which merged into two current peaks at 300 kV mm −1 (Fig. 4a), indicating the field-induced polar structural changes in P&F samples with low M w (180 kg mol −1 ). This is further proved by measuring the second ferroelectric hysteresis loops ( Supplementary Fig. 6), which differ from those obtained on pristine films (Fig. 4a), and demonstrate that the above structural changes are not reversible. The higher M w P&F samples (534 and 670 kg mol −1 ) show four current peaks located in all of the four quadrants (denoted as P 1 , P 1 ′, P 2 and P 2 ′ in Fig. 4a), which is related to the reversible field-induced polar structural changes. P 1 and P 1 ′ correspond to the regulation of polar structures upon the application of electric field, and the appearance of P 2 and P 2 ′ demonstrates that the polar structures can reverse back to the original state upon the removal of electric field, which is also proved by almost the same shape of re-measured hysteresis I-D-E loops ( Supplementary Fig. 6). Note that P 2 and P 2 ′ shifted across the y-axis with further increase in the electric field up to 800 kV mm −1 , which makes the four current peaks locate in the first and third quadrant and highlights the existence of partial irreversible phase transition due to the influence of ultrahigh electric field.
Previous to P&F, PVDF was reported to show double hysteresis loops, but only at an extreme condition 51 , −100°C, 0.003 Hz and 240 kV mm −1 , and more importantly, detailed studies with regard to I-E loops were not presented. Zhu et al. 52 also studied the ferroelectric hysteresis loops of e-beam-irradiated PVDF-TrFE-and PVDF-TrFE-based terpolymers, and concluded that pinning polymer chains makes the e-beam-irradiated PVDF-TrFE show RFE narrow hysteresis loops and PVDF-TrFE-based terpolymers present double hysteresis loops; however, without the interpretation of I-E curves, the underlying physical mechanisms cannot be precisely decoded. The double hysteresis D-E loops can be produced by the phase transition between anti-ferroelectric to ferroelectric 53 and paraelectric to ferroelectric 54 with two completely different physics mechanisms. In the literature, PVDF-TrFE with high content of TrFE (47/53 and 37/63 mol%) and PTrFE materials were reported to show four current peaks located in all four quadrants 55,56 (<150 kV mm −1 ), which is ascribed to the reversible field-induced structural change between the disordered trans phase (weak polar) and well-ordered alltrans phase (strong polar), as supported by in situ X-ray diffraction (XRD) measurement with applied electric field, being consistent with our analysis for P&F PVDF.
XRD was conducted to gain further insight into the fieldinduced structural changes in the P&F samples ( Supplementary  Fig. 7). The XRD data show a reduction of the mean size of the crystallites, from~20 nm in the initial HP films to~5 nm after the P&F treatment (Supplementary Table 4). The average size of the crystallites in the P&F samples decreased from 6 to 3.5 nm with increasing M w from 180 to 670-700 kg mol −1 (Supplementary Table 4), which can be related to the reduced chain mobility with increasing M w . In P&F films with low M w , it is believed that relatively large-sized polar structures possess higher thermal stability 57 . The application of an external electric field will induce the re-orientation of CF 2 dipoles and cause the regularization of the polymer chains 58 , leading to a structural change of long-range ferroelectric order (schematic images in Fig. 4b). In the P&F films with high M w (534 and 670-700 kg mol −1 ), the small-sized polar structures are not stable due to the randomization of polarization induced by thermal activation 57 . In this case, the polar structures remain relatively small, despite the influence of the external field (schematic images in Fig. 4b). Consequently, a significant fraction of dipoles will reverse upon decreasing the electric field, as evidenced by the much lower D r , 0.020 C m −2 (Fig. 4b), compared to 0.076 C m −2 in P&F with low M w (Fig. 4b). Consistently, the    T  T T  T T  T  T  T  T   T  T   T  T   T   T   T  T   T  T   T  piezoelectric resonance peak could be detected in the frequency dependence of the dielectric spectra of the poled 670-700 kg mol −1 P&F films, while a small but clear peak (thickness extension mode) can be seen for the poled 180 kg mol −1 P&F films ( Supplementary   Fig. 3 Factors influencing the formation of β-phase during processing. a Comparison of the phase transition in samples (670-700 kg mol −1 ) with monolayer and six multi-stacked layers at three different pressures (force 300 kN), 120, 667 and 3000 MPa, followed by pressure annealing at 165°C for 5 min, which indicates that high pressure and layered structure favour the formation of β-phase. b Fraction of β-phase for samples (670-700 kg mol −1 ) with the same dimensions, but composed of different numbers of layers that were pressed once at 667 MPa (force 300 kN) followed by pressure annealing at 165°C for 5 min and cold water quenching. c FEM simulations of film compression in the cases of monolayer film, four-layer film with same friction coefficients µ between layer and platen and between layers, and four-layer film with µ between layer and platen higher than µ between the layers. The bar scale represents the overall strain deformations. d FTIR of samples with different M w , which indicates the formation of γ-phase in PVDF (low M w ) at higher   Fig. 4 Ferroelectric properties of pressed and folded poly(vinylidene fluoride) samples. a Bipolar current-electric field (I-E) and displacement-electric field (P-E) loops of P&F PVDF after seven cycles with different M w of 180, 534 and 670 kg mol −1 . P 1 and P 1 ′ denote the peaks appeared during the application of electric field. P 2 and P 2 ′ denote the peaks appeared during the reversal of electric field. b A comparison of bipolar remnant polarization P r and maximum polarization P max of P&F films with different M w , and schematic diagram of polar structure change during charging and discharging processes, where the green blocks represent the crystallites, red lines represent the polymer chains with arrows denoting the dipole moment and the dashed lines highlight the polar structure, which was enhanced and grew larger under electric field  Fig. 8). This confirms the existence of readily reversible polar structures in high M w P&F films. At high temperatures, the smallsized polar structures in P&F samples suffer severe thermal fluctuation and become even more unstable, as highlighted by the temperature dependence of the dielectric permittivity (Supplementary Fig. 9) and ferroelectric hysteresis loops measured at high temperatures ( Supplementary Fig. 10), where the dielectric constant showed a declining trend at temperatures above 50°C and the disappearance of current peaks (P 1 ′ and P 2 ′) upon the removal of electric fields (>140°C).

Discussion
In summary, we have demonstrated a facile, readily implementable and scalable process, P&F, to produce PVDF with good ferroelectric properties. Only seven P&F cycles are needed to transform the nonpolar α-phase PVDF into the predominantly ferroelectric β-phase PVDF (~98%). The formation of the β-phase is proposed to be a result of a pressure-induced phase transformation, and importantly, more effective stress transfer during P&F. Moreover, studies of the ferroelectric behaviour revealed relaxor-like ferroelectricity in P&F PVDF films with high M w (534 and 670-700 kg mol −1 ), which is attributed to reversible field-induced structural change induced by the thermally unstable small-sized polar structures, as suggested by the decreasing crystallite size (down to~4 nm) after P&F. An ultrahigh energy density of 35 J cm −3 was achieved at 880 kV mm −1 in a P&F PVDF film with M w of 670-700 kg mol −1 , which is the highest value reported for a polymeric dielectric capacitor, to the best of our knowledge, and well beyond the value for commercial electrochemical capacitors (20-29 J cm −3 ). This finding promises to have a significant impact on the field of pulse power applications and could produce a step change in the field of dielectric capacitors, so far limited by their low energy storage density.

Methods
Materials and film preparation. PVDF pellets or powders with different M w of 180 and 534 kg mol −1 were purchased from Sigma-Aldrich Chemical Co. PVDF with M w of 670-700 kg mol −1 (Solef ® 6020) was purchased from Solvay S.A. The initial HP films with an average area of 5 cm × 5 cm were prepared using a Collin hot-press P300E (Germany) at 180°C and 113 kN for 2 min followed by cold water quenching to room temperature. The initial films were first folded and cold pressed at 300 kN. The temperature was then increased from ambient temperature to 165°C. The folded films were then held for 5 min under the conditions of 165°C and 300 kN, followed by cold water quenching with the pressure maintained. The overall thickness of the P&F films increases with the number of P&F cycles. For instance, the films thickness increases from 250 to 350 μm for HP film to 1.0-1.2 mm for films after seven cycles.
Microstructure characterization. FTIR spectroscopy (Tensor 27, Bruker Optik GmbH, Ettlingen, Germany) and wide-angle XRD with Cu/Kα radiation (wavelength 0.15418 nm) (X'Pert Pro, PANalytical, Almelo, The Netherlands) were used to characterize the crystalline structure of the samples. Thermal analysis was performed using differential scanning calorimeter (DSC) (DSC 25, TA Instruments, Asse, Belgium) with a heating/cooling rate of 10°C min −1 . The degrees of crystallinity of films were determined via measuring the densities of samples based on the Archimedes principle. The densities of amorphous PVDF, pure αand pure β-PVDF are 1.68, 1.92 and 1.97 g cm −3 , respectively 39,40 . The morphology of samples was characterized using a scanning electron microscopy (FEI Inspect-F, Hillsboro, OR, USA) and AFM (NT-MDT, Ntegra systems, Russia). The AFM images were obtained using tapping mode and recorded horizontally from left up to right bottom at a scanning rate of 1 Hz with pixel scan of 256×256. Nanoprobe cantilevers (PPP-NCHR, Nanosensors, Neuchatel, Switzerland) designed for noncontact AFM mode were used to acquire images.
Functional properties characterization. The temperature and frequency dependence of dielectric properties were characterized using a LCR meter (4284A, Agilent, Santa Clara, CA) and Precision Impedance Analyser (4294A, Agilent, Santa Clara, CA), respectively. Unipolar and bipolar ferroelectric hysteresis loops were obtained on a ferroelectric tester (NPL, Teddington, UK) at room temperature using a triangle waveform with a frequency of 10 Hz. The tester can only generate a maximum voltage of 10 kV, which significantly limits the field that can be applied to relatively thick specimens. This is particularly problematic as the thickness of P&F films increases with P&F cycles (1.0-1.2 mm). In order to obtain films of relatively low thickness (~10 μm) comparable to stretched films (~35 μm), a thin layer of PTFE release agent was sprayed on the film surface before each P&F cycle. This allowed the separation of an individual thin layer from the multilayer P&F films. The presence of PTFE did not significantly modify the overall crystalline content, crystalline phase and discharged energy density ( Supplementary Fig. 11). The two-parameter Weibull analysis was performed to study the characteristic breakdown strength E b of the one single layer of P&F film after seven cycles, The E is the breakdown field of ten samples measured during the ferroelectric hysteresis test, E b is characteristic breakdown strength at which the probability of dielectric breakdown is 63.2%, P(E) is the statistic cumulative probability of dielectric breakdown and β is the parameter related to the reliability of films.
FEM modelling. The commercial package Abaqus Standard 6.14 (Dassault Systemes) was used to conduct simulations for this study. In all simulations, the models were discretized with eight-node brick element with reduced integration (C3D8R). A static analysis with large deformation formulation was performed; the material behavior was captured using a NeoHookean material perfectly plastic after the yield point. Contact between surfaces employed the Coulomb model of friction. Symmetry planes were used for the model geometry.