Pressed-and-folded PVDF for electric energy storage

Our approach uses a unique processing route called “pressing-and-folding” (P&F), which draws inspiration from the process used by bakers to prepare puff pastry and croissants32. 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 works36,37,38, 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 α- and β- phase only or containing a mixture of α-, β- and 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 α- and pure β-PVDF of 1.68, 1.92 and 1.97 g cm−3, respectively39,40. The calculated values of the degree of crystallinity are typical of PVDF41. 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 work35, 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 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 films31 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).

Fig. 1 Pressed and folded poly(vinylidene fluoride) compared with stretched samples. a Schematic demonstration of P&F technique. b Cross-sectional SEM images of P&F samples folded at 165 °C and 300 kN after different numbers of folding cycles. A fine and discrete layered structure is generated during P&F. 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 Full size image

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 \(P_i\left( n \right) = P_1\left( {\frac{2}{a}} \right)^{n - 1}\), 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.

Fig. 2 Morphological changes of poly(vinylidene fluoride) samples. a Variation of overall sample area, thickness and volume with the number of P&F cycles. 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 Full size image

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 \(\Omega \left( n \right) = P_1\left( {1 - h} \right)\frac{{1 - \left( {2h} \right)^n}}{{1 - 2h}}\) (Supplementary Note 2), where h = 0.61 (±0.09) 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 Å3) compared to the α-phase (118.6 Å3) for the same number of atoms11. Moreover, judging by the calculated values of intra- and inter-molecular potential energy, −6.03 and −5.73 kcal mol−1 for α- and β-phase, respectively, the β-phase is slightly energetically less stable42. 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 drawn43,44, solid-state compression45 and rolling processed46 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 tension47. 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 1 – f β , as when all 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:

$$f_{\upbeta} \left( \Omega \right) = 1 - \left( {1 - f_{\upbeta 0}} \right)e^{ - b\Omega }$$ (1)

or, in terms of P&F cycles,

$$f_{{\upbeta}} \left( n \right) = 1 - \left( {1 - f_{{{\upbeta}}0}} \right)e^{ - c\left[ {1 - \left( {2h} \right)^n} \right]},$$ (2)

where b and \(c = bP_1\frac{{1 - h}}{{1 - 2h}}\) 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-dependent48. 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 (left-hand dataset) having different A 0 (25, 4.5 and 1 cm3) 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 energy48 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.

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 T anneal (denoted by the γ-characteristic band at 1234 cm−1) and high M w favours the transformation of β-phase (inset). For PVDF with M w of 180, 534 and 670 kg mol−1, T m was 169, 172 and 172 °C, respectively. e Demonstration of phase evolution with T anneal and M w during P&F and schematic diagram of chain conformation, crystal structure and polarization of PVDF. The HP (no folding) films are mainly α-phase, with two trans-gauche-trans-gauche′ (TGTG′) chains anti-parallel packed in a pseudo-orthorhombic unit cell. The symbols and arrows represent the in-plane and out-of-plane contributions to the dipole moments. After P&F at different temperatures (room temperature to T m ), films formed into β-phase (>90 wt %) with all-trans (TTT) chain conformation. Low T anneal and high M w favour the formation of β-phase Full size image

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 α- to 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 °C49. 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 behaviour50 (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.

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 Full size image

Previous to P&F, PVDF was reported to show double hysteresis loops, but only at an extreme condition51, −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 ferroelectric53 and paraelectric to ferroelectric54 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 quadrants55,56 (<150 kV mm−1), which is ascribed to the reversible field-induced structural change between the disordered trans phase (weak polar) and well-ordered all-trans 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.