Large piezoelectricity in crosslinked ferroelectric polymers

Domain: chemistry
Published: 2026-02-25
Editorial outcome: major_revision

Abstract
Ferroelectric polymers exhibit numerous advantages for flexible and wearable electromechanical applications. However, their piezoelectric coefficient d33 remains relatively low while most previous approaches to improved mainly focus on intramolecular engineering. Other than using intramolecular approaches, here we describe an intermolecular crosslinking strategy to achieve markedly enhanced d33 of −95.0 picocoulombs per newton in crosslinked ferroelectric poly(vinylidene fluoride-co-trifluoroethylene) copolymers. First-principles calculations reveal that intermolecular crosslinking creates strong local conformational heterogeneity facilitating ease of bond rotation near the crosslinking sites, which leads to a flattened energy landscape, resulting in substantially improved d33 response. We show that crosslinking enabled by solution casting process enhances piezoelectric properties across a variety of crosslinking agents. Our work offers a facile platform for rational modulation of piezoelectricity of ferroelectric polymers, representing a crucial step towards large-scale manufacturing of lightweight, flexible, and scalable ferroelectric polymers for developing high-performance electromechanical devices.

Introduction
Piezoelectric materials exhibiting the interconversion between electrical and mechanical energies are essential to modernelectronics and technology including medical, industrial, military, and other electromechanical applications1–4. Piezoelectricity was discovered in quartz in 1880. The breakthrough occurring in 1940s was achieved in barium titanate (BaTiO3) ceramics (ref. 5), which has paved the exploration of perovskite oxides for piezoelectric applications4. Moreover, through the morphotropic phase boundary (MPB) concept, tremendous advances have been seen in lead-contained compounds such as lead zirconate titanate (PZT or Pb(Zr1-xTix)O3)6 and relaxor-PT crystals Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT)7 with exceptional piezoelectric properties. MPB refers to the transition region separated by two competing symmetries with distinct polar axes near which energetically nearly degenerate polar states are facile to be varied by applying a small stimulus, leading to largely enhanced d33 response8–10. More recently, there is an exponentially growing need for practical use of piezoelectrics which expands from traditional electromechanical devices mainly based on rigid ceramics to emerging technology including soft robotics, wearable electronics, bio-implanted devices, and flexible energy harvesters11–16. Consequently, lightweight, flexible, and scalable organic piezoelectrics are highly desirable especially with high piezoelectric properties.

In this context, ferroelectric polymers such as poly(vinylidene fluoride) (PVDF) and its copolymers poly(vinylidene fluoride-co-trifluoroethylene) (P(VDF-TrFE)) are ideal organic candidates as they are lead-free, lightweight, flexible, and easy to process into large area films and other desired shapes17–19. Meanwhile, they show the highest piezoelectric coefficient d33 among piezoelectric polymers17–19. However, despite the growing interest for over 50 years, their intrinsic d33 remains much lower than that of oxide perovskites20–27. Various approaches including high crystallinity22, MPB25, ultrahigh-field poling26 and electrostriction27 were developed. For instance, an appreciably improved d33 of −63.5 pC N-1 was achieved at the stereochemical-induced MPB locating at 50/50 mol% composition of P(VDF-TrFE) copolymers25 which is over twice as large as that (d33 ≈ −26.0 pC N-1) of PVDF homopolymers21.

In this work, we describe a molecular mechanism by using crosslinking to enable the rational design of ferroelectric polymers with greatly improved piezoelectric properties. Previous works engineered d33 mainly using intramolecular design of chain conformation25,28. For instance, incorporation of chiral units causes local conformational disorder28 driving the phase transition from ordered all-trans to disordered helix conformation mediated by the phase coexisting or MPB region25, within which markedly increased d33 is achieved. However, only weak local angular distortions (about 5o) in helical conformation can be induced by intramolecular strategy28 (Fig. 1a), limiting the strength of conformational heterogeneity and thus the ability to modify the flatness of the energetic landscape. Here we report a scheme based on intermolecular crosslinking which can locally create remarkably stronger conformational inhomogeneities (about 25o) near the crosslinking sites. This may induce the formation of markedly flattened energetic landscape which largely benefits piezoelectricity. Our results also overturn the previous belief that crosslinking was undesired for enhancing piezoelectric response as crosslinking is detrimental to crystallization of ferroelectric polymers29. Moreover, our work addresses that markedly enhanced piezoelectric response induced by crosslinking is achieved in ferroelectric polymers with nearly vanishing barriers between different crystalline chain conformations, which have not been revealed in previous studies on crosslinked PVDF30,31 with the energetically more favorable paraelectric phase yielding a weak d33 of -9.4 pC N-1 (ref. 31).

Given that crosslinking acting as a powerful tool has been widely used to improve mechanical, thermal, and chemical functionalities of fluorinated polymers32,33, our study demonstrates crosslinking as a versatile platform for developing high-performance piezoelectric polymers for flexible and wearable applications.

Results
Improved piezoelectricity by increasing local conformational heterogeneity
We synthesized crosslinked P(VDF-TrFE) copolymers with different crosslinking densities ρ whereas the representative crosslinking agents of ethylenediamine and 1,2-diaminopropane was used (Method). We choose a modest crosslinking density acting as a leverage to tune the energetic landscape of P(VDF-TrFE) copolymers near MPB mainly because the compositionally-induced MPB is sensitive to the small change in the VDF content according to the previous work25. Specially, we use a moderate crosslinking density from 0% to 3% according to the narrow MPB region (49 mol% ≤ cVDF ≤ 55 mol%) whereas crosslinking-induced dehydrofluorination may offer a tool to tune relative VDF ratio and thus the relative stability between competing crystalline phases. The underlying scheme of crosslinking with diamines typically involves the dehydrofluorination of a fluorinated polymer followed by the Michael addition reaction and the subsequent formation of C=N double bonds enabling a bridge between two fluorinated chains (Fig. 1b)32–34. For crosslinking we selected three typical polymer compositions which show distinct ground-state conformations: all-trans (cVDF = 65 mol%), coexisting all-trans and 3/1-helix (cVDF = 55 mol%), and 3/1-helix (cVDF = 47 mol%). Our Fourier-transform infrared spectroscopy (FTIR) shows the presence of crosslinked structure in terms of the appearance of IR band located at around 1652 cm-1 (Fig. 1c), which was regarded as the characteristic of C=N bonds15,34. X-ray photoelectron spectroscopy (XPS) manifests the existence of C=N double bonds introduced by crosslinking (Fig. 1d, Supplementary Figs. S1a and S1b). Moreover, our combined XPS (Supplementary Figs. S1c and S1d) and 1H nuclear magnetic resonance (NMR) data (Supplementary Fig. S2) rule out the presence of conjugated double bonds in crosslinked P(VDF-TrFE), which is consistent with the crosslinking reaction schemes occurring in fluorinated polymers32. The swelling experiments (Table S1) and thermogravimetric results (Supplementary Fig. S3) also support the presence of crosslinking.

We now leverage crosslinking to modulate the energetic competition between all-trans and 3/1-helix conformations for the MPB composition (cVDF = 55 mol%). Our X-ray diffraction (XRD) data show the stabilization of 3/1-helix induced by slight crosslinking (Fig. 1e and Supplementary Fig. S4a). For instance, we observe the development of the peak at 18.9o characteristic of 3/1-helix28 at the expense of smearing of the peak intensity locating at 19.3o indicative of all-trans as ρ increases. There exists a critical concentration ρc of 0.2% above which the density of peak identified by 3/1-helix exceeds that of all-trans, indicating the stabilization of helical conformation25. Given that ρc corresponds to only a modest VDF loss (ΔcVDF = 0.2 mol%) during the crosslinking reaction31–34 (Fig. 1b), a much narrower MPB region is anticipated driven by crosslinking (Fig. 2a) compared to previous compositionally-induced MPB25 with a ΔcVDF of 6 mol%. Our results therefore imply that crosslinking may be more effective to produce strong local conformational heterogeneity making helical conformation energetically more favorable above an ultra low ρc. Our results also indicate that crosslinking reaction cured by small molecule crosslinkers may occur in crystalline regions of thermoplastic polymers with relatively high crystallinity leading to a dramatic change in crystalline conformation (Fig. 1e and Supplementary Fig. S5), which has not been revealed in amorphous fluoroelastomers32,33 and/or the bulky crosslinkers15. The enhanced local heterogeneity degree caused by crosslinking is implied collaboratively by the growth of the IR band at 506 cm-1 assigned to 3/1-helix in the FTIR spectra25,28, accompanied by the smearing of the IR band at 1287 cm-1 assigned to all-trans (Supplementary Figs. S6 and S7). Consequently, our structural results indicate that intermolecular crosslinking enabled by solution casting process may give rise to stronger local heterogeneity than previous intramolecular approach obtained by suspension polymerization25,28, leading to rapid depression of ordered conformation and the formation of a narrow MPB region (0 ≤ ρ ≤ 0.2%).

The existence of crosslinking-driven phase transition is supported by disappearance of ferroelectric instability (Fig. 2b and Supplementary Fig. S8a) and growth of relaxor characteristics (Fig. 2c and Supplementary Fig. S9). For instance, polarization-electric field (P-E) hysteresis loops evolve from typical ferroelectric type (ρ = 0) into pinched type loops (ρ > ρc) indicative of relaxor phase25, in agreement with structural results (Fig. 1e). Near ρc, abrupt drop in the maximum polarization, remanent polarization Pr, and coercive field Ec (Supplementary Fig. S8b–d) is observed. Such crosslinking-driven polarization evolution behavior is also observed under other frequencies (Supplementary Figs. S10 and S11). Meanwhile, as ρ increases, the relaxor characteristics reflecting the strength of local conformational heterogeneity in helical conformation become stronger in terms of the rapidly increasing ΔTm (defined as the frequency-dependent shift in Tm between 1 MHz and 100 Hz) at around ρc which saturates at ρ = 1.8% (Fig. 2c). In addition, the phase transition near the dielectric peak temperature Tm becomes more diffused in terms of the increased diffuseness factor γ derived from modified Curie-Weiss law (Fig. 2c and Supplementary Fig. S12) and the smearing of the endothermic peak near 60°C in differential scanning calorimetry (DSC) heating scans (Supplementary Figs. S13), substantiating the order-to-disorder phase transition induced by slight crosslinking.

We show that markedly augmented d33 is observed at ρ = 1.2% (Fig. 2d), which locates at the right side of the MPB region (0 ≤ ρ ≤ 0.2%) characterized by disordered helical conformation with strong local conformational heterogeneity (Fig. 2a). Interestingly, our finding differs from compositionally-induced MPB in non-crosslinked P(VDF-TrFE) which displays the largest d33 at cVDF = 50 mol% occurring within the MPB region25. Instead, our results imply that enhancing the local conformational heterogeneity may be essential to improve d33 in crosslinked ferroelectric polymers. The highest d33 measured by the Berlincourt method (d33 meter) is -95.0 pC N-1 of ethylenediamine and -93.4 pC N-1 of 1,2-diaminopropane which is over twice as large as that of -40.0 pC N-1 without crosslinking (Supplementary Fig. S14), corresponding to approximately a 3.6-fold improvement in d33 compared to PVDF. The existence of enhanced d33 is also confirmed by using the electric field induced strain at small electric fields (below the coercive field) via the converse piezoelectric effect (Fig. 2e and Supplementary Fig. S15). At low fields below the coercive field, the polarization response is entirely dominated by the elastic stretching and reorientation of dipoles, P-E loops are paraelectric-like (Supplementary Fig. S15). Our results also exceed that obtained by conventional MPB approach25 by nearly 50% (Table S2), demonstrating a promising approach for design of high-performance ferroelectric polymers. We also evaluate the mechanical stability and observe that d33 of free-standing crosslinked piezoelectric polymers shows nearly no degradation after undergoing 105 mechanical cycles (Supplementary Fig. S16), indicating long-term mechanical durability. We also observe that the elongation at break is improved considerably caused by crosslinking (Supplementary Fig. S17), suggesting improved mechanical properties. As crosslinking density increases above 1%, the interchain spacing remains nearly unchanged (Supplementary Figs. S4 and S18) which may reduce the piezoelectric sensitivity. For instance, it is found that piezoelectric voltage coefficient |g33| is maximized at ρ = 1.8% which is followed by a decline for ρ > 1.8% (Supplementary Fig. S19). This is accompanied by paraelectric behavior due to the stabilization of relaxor phase for ρ > 1.8% (Fig. 2a). In this regard, the crosslinked P(VDF-TrFE) with optimized piezoelectric properties is most suitable for piezoelectric applications with high piezoelectric sensitivity. Consequently, crosslinked ferroelectric polymers may offer promising candidates to meet the ever-increasing demand for high-performance flexible piezoelectric applications near room temperature.

Generality of large piezoelectricity from local conformational heterogeneity
We show that improved d33 induced by crosslinking is general to other crosslinkers (Supplementary Figs. S20–S24). Interestingly, we find that improvement in d33 depends sensitively on crosslinkers and crosslinking density while the polymer crystallinity obtained by different crosslinkers at the same crosslinking density remains nearly the same (Supplementary Figs. S25 and S26). For instance, the |d33| exhibits a considerable decrease from 95.0 pC N-1 for ethylenediamine to 68.5 pC N-1 for 1,12-dodecanediamine with increasing the length of zigzag-type crosslinkers at ρ = 1.2% (Fig. 2f and Supplementary Figs. S20–S24). As revealed later by our theoretical computations, crosslinkers with short length may create stronger local heterogeneity near the crosslinking sites leading to more flattened energy landscape which yields a larger d33. This insight also rationalizes a weak d33 of 11.3 pm V-1 reported in P(VDF-TrFE) 55/45 mol% cured by bulky polyethyleneglycol15. Moreover, replacement of H in crosslinkers by other groups such as CH3 may further bring intramolecular interactions resulting in the rotation of NH2 (Supplementary Fig. S27). For instance, our computations reveal that this may result in a considerably reduced length (2.82 Å) in 1,2-diaminopropane compared to that (3.75 Å) of ethylenediamine, which tends to favor enhanced d33. Meanwhile, the concomitant steric hindrance introduced by CH3 may impose constraint for bond rotation, which in turn limits the piezoelectric response. As a result of these two competing effects, we observe that the largest |d33| (93.4 pC N-1) by 1,2-diaminopropane is slightly smaller than that (95.0 pC N-1) by ethylenediamine (Fig. 2d and Supplementary Fig. S20), which suggests the importance of steric effect caused by incorporating bulky chemical groups. Consequently, our results elucidate the crucial role of crosslinkers in tuning d33 which may inspire future studies to further optimize piezoelectricity through a rich spectrum of crosslinking strategies29,30 including diamines, bisphenols, peroxides, and high-energy irradiation.

We also evaluated d33 responses of other polymer compositions. We find the absence of substantially improved d33 in crosslinked ferroelectric polymers with either ferroelectric (i.e., P(VDF-TrFE) 65/35 mol% in Fig. 2d) or relaxor phase as the ground state (i.e., P(VDF-TrFE) 47/53 mol% in Fig. 2d). To further demonstrate the generality of crosslinking strategy, we show that markedly enhanced d33 is achieved in other crosslinked polymers such as P(VDF-TFE) copolymer where TFE denotes the tetrafluoroethylene. The incorporation of TFE introduces head-head-tail-tail defects which stabilizes ferroelectric all-trans conformation against paraelectric phase in P(VDF-TFE) copolymer35,36. At low defect concentration such as 5 mol%, the energetic barrier between polar and non-polar phases is relatively small35,36 whereas crosslinking with inherently local conformational heterogeneity may help to modify the relative energetic stability between different crystalline chain conformations. Our structural evidence explicitly confirms this picture by showing a newly formed peak at the lower 2θ = 18.5o (Supplementary Fig. S28) differing from the singlet at around 2θ = 19.2o in pristine P(VDF-TFE) 95/5 mol% characteristic of all-trans conformation32. We show that long-range ferroelectric instability is considerably suppressed by crosslinking, like the results obtained in crosslinked P(VDF-TrFE) 55/45 mol% (Supplementary Fig. S29). Such energetically nearly degenerate phases may benefit the d33. For instance, d33 of crosslinked P(VDF-TFE) 95/5 mol% is -44.2 pC N-1 at ρ = 1.8% corresponding to over 145% improvement over pristine counterpart (Supplementary Fig. S30). Moreover, as the phase transition temperature usually determines the upper limit on the operating temperature of ferroelectrics, the presence of a much higher phase transition temperature (above 140°C, Supplementary Fig. S31) in crosslinked P(VDF-TFE) 95/5 mol% than that (about 61°C) of crosslinked P(VDF-TrFE) 55/45 mol% is conducive to practical piezoelectric applications with a wide operating temperature range. In addition, our approach is also generally applicable to ferroelectric polymer blends where crosslinking enables markedly enhanced d33 response (Supplementary Figs. S32-S42). As PVDF adopts the well-defined ground state corresponding to ferroelectric all-trans conformation like P(VDF-TrFE) 80/20 mol%, greatly enhanced d33 is not achieved upon crosslinking (Supplementary Figs. S43 and S44). We therefore identify that greatly augmented d33 driven by crosslinking requires the presence of energetically nearly degenerate phases25,37–39, which is generic to ferroelectric polymers crosslinked by a wider range of crosslinking agents.

Origin of local conformational heterogeneity induced by crosslinking
To provide structural insights into enhanced d33, we performed electric field-dependent XRD (Figs. 3–c). We observe that the doublet identified by phase coexistence of all-trans and 3/1-helix tends to merge into a singlet at around 19.6o characteristic of all-trans as the electric field increases. This finding is an indication of polarization rotation stemming from electric-field-induced phase transition from helical phase to trans-planar phase (Fig. 1a), which occurs regardless of crosslinking. Moreover, crosslinking inhibits such phase transition requiring a much high electric field (> 200 MV m-1, Fig. 3c) than non-crosslinked counterpart (about 100 MV m-1). For instance, the presence of a shoulder at around 19.2o remains in crosslinked case even under 200 MV m-1 (Figs. 3b and 3c) owing to the existence of strong local conformational heterogeneity in contrast with the non-crosslinked XRD results (Fig. 3a). Consequently, electric field-dependent XRD results provide strong structural implications that enhanced degree of local conformational heterogeneity created by crosslinking may be vital to characterize greatly improved d33.

To shed light on the origin of local conformational heterogeneity, we performed density functional theory (DFT) simulations. In the light of the conformational disorder model28, we used Δτ defined as local deviations of the gauche torsional angles from τ = 60o in the regular 3/1-helix (Fig. 1a, Supplementary Figs. S45 and S46) to account for local conformational heterogeneity. We show that the values of Δτ away from the crosslinking sites are about 5o-7o, which are well consistent with that (≈ 5o) obtained by intramolecular method28. Figures 4b, e show that the largest angular distortion Δτmax (> 15o) is always observed close to the gauche angle 5 corresponding to the crosslinking sites (Figs. 4a, d) independent of crosslinkers. We find that short ethylenediamine (3.75 Å) generates a much larger Δτ of 24.6o when compared with that (15.4o) of 1,3-diaminopropane (4.98 Å) indicating stronger local inhomogeneities. Meanwhile, 1,2-diaminopropane induces strongly spatially varying Δτ for two crosslinked chains, compared with ethylenediamine and 1,3-diaminopropane with the absence of CH3. These theoretical results explicitly reveal the presence of strong local conformational heterogeneity induced by intermolecular crosslinking, which has not been attainable by previously intramolecular strategy28.

Engineering local structural heterogeneity is crucial to piezoelectric coefficients of classic perovskite relaxors40,41. Our combined experimental and theoretical results elucidate that higher d33 can be achieved by increasing the local conformational heterogeneity. To correlate the local conformational heterogeneity with piezoelectric response from a molecular perspective, here we calculated the energy gain ΔU by allowing local rotation of τ by a small angle Δφ (|Δφ| ≤ 10o). We find that ΔU near the crosslinking sites (i.e., gauche angle 5) is much lower than that at the locations (i.e., gauche angle 7 and 9) away from the crosslinking sites (Figs. 4c, f), which explains why Δτmax occurs near the crosslinking sites (Figs. 4b, e). Moreover, ethylenediamine enables a smaller rotational energy barrier near the crosslinking sites than 1,3-diaminopropane (Figs. 4c, f), rationalizing a larger Δτmax (Figs. 4b, e), which is essential to improved d33 (Fig. 2f). In addition, the existence of CH3 in 1,2-diaminopropane lowers the rotational energy barrier (ΔU < 0) for the angle 5 within a small angle range 0 < Δφ < 4o while it brings a considerably bigger energetic penalty than ethylenediamine and 1,3-diaminopropane at relatively larger distortive angle Δφ > 4o (Supplementary Figs. S47a and S47c), reconciling the steric effect by CH3. This may lead to a smaller Δτ than ethylenediamine (Fig. 4b and Supplementary Fig. S47b) and thus lowered d33 response despite shorter interchain distance. We therefore address that the smearing of rotational energies near the crosslinking sites gives rise to enhanced local heterogeneity, which completely differs from increasing interfacial energies related to local polarization and strain discontinuity in classic perovskite relaxors40,41. The nearly vanishing energy barriers for local bond rotations near the crosslinking sites may further flatten the energetic landscape, which brings huge responses to a small stimulus and thus generates a remarkably improved d33, compared to conventional MPB approach25. The mechanistic insights at the molecular scale are unambiguously supported by experimental data, validating the computational approach, which also provide further support that crosslinking here occurs mainly in crystalline domains rather than amorphous regions in previous works15,32,33. Consequently, we reveal that enhancing local conformational heterogeneity introduced by interchain crosslinking may benefit piezoelectricity, bringing a viable strategy for designing ferroelectric polymers with large piezoelectricity.

Methods
Materials
P(VDF-TrFE) (80/20 mol%, 65/35 mol%, 55/45 mol%, and 43/57 mol%), were purchased from Piezotech at Arkema. P(VDF-TFE) 95/5 mol% was purchased from PolyK Technologies. PVDF was purchased from Sigma-Aldrich. The crosslinking agents including ethylenediamine (Mw = 60.1 g mol-1), 1,2-diaminopropane (Mw = 74.1 g mol-1), 1,3-diaminopropane (Mw = 74.1 g mol-1), 1,5-diaminopentane (Mw = 102.2 g mol-1), 1,10-diaminodecane (Mw = 172.3 g mol-1), and 1,12-dodecanediamine (Mw = 200.4 g mol-1) were purchased from Sigma-Aldrich. All solvents including N,N-dimethylformamide, cyclohexanone, tetrahydrofuran, and dimethylsulfoxide were purchased from Sigma-Aldrich. All chemicals were used as received.

Synthesis of crosslinked polymers
The ferroelectric polymer (i.e., P(VDF-TrFE) and polymer blends) powder of 300 mg was dissolved in cyclohexanone (5 ml). The P(VDF-TFE) powder of 300 mg was dissolved in N,N-dimethylformamide (5 ml). The PVDF powder of 800 mg was dissolved in N,N-dimethylformamide (5 ml). The solution was stirred with a rate of 400 r.p.m. overnight. After that, crosslinking agent (i.e., ethylenediamine) was added into the solution and stirred overnight. The solution was cast onto glass plates, followed by annealing at 220°C for 1 h for thermal crosslinking. This optimized thermal condition was obtained through the orthogonal experiments on d33 obtained by different thermal conditions, as summarized in Table S3. It was observed that high d33 values were generally achieved across a high-temperature range (190°C−250°C) where the specific condition under 220°C for 1 h yielded the maximum |d33| of 93.4 pC N-1. Extending the reaction time (e.g., to 4 h) or further increasing the temperature (e.g., to 250°C) did not result in further improvements in d33, indicating that the property enhancement enabled by thermal processing had reached saturation. The crosslinked polymer films were peeled off from the glass plates. The crosslinked PVDF were stretched 5 times to obtain a β-phase dominated samples. The typical thickness of synthesized polymer films is about 30 µm.

Following the reaction mechanism (Fig. 1b), the crosslinking density ρ was calculated by the relationship ρ = 2 × (n/60.10)/(m/72.1) × 100 where n and m are the masses of ethylenediamine and P(VDF-TrFE). For other crosslinkers and polymer compositions, ρ can be obtained by changing the molecular weights of polymer and crosslinking agent. The polymer blends with different ratios consisted of 70 wt% P(VDF-TrFE) 43/57 mol% and 30 wt% P(VDF-TrFE) 65/35 mol%, 85 wt% P(VDF-TrFE) 47/53 mol% and 15 wt% P(VDF-TrFE) 65/35 mol%, respectively.

NMR
1H NMR spectroscopy was conducted by using an AscendTM 600 MHz spectrometer (Bruker). The samples were dissolved in acetonitrile-d3.

XPS
XPS spectra were recorded with a SCIENTIFIC ESCALAB 250Xi (Thermo, USA). A monochromatized Al target was employed as the excitation source with a voltage of 12.0 kV and a current of 6 mA. The vacuum level was maintained at 5 × 10-9 mbar. Two passes of energy were utilized, with 150 eV for the survey mode and 30 eV for the high-resolution mode. The work function was set to 4.20 eV. Charge correction was performed by referencing the high-resolution peak of C1s, which exhibited a binding energy of 284.5 eV.

Swelling measurement
Crosslinked polymer films were dipped into different solvents including N,N-dimethylformamide, dimethylsulfoxide and tetrahydrofuran, respectively. The degree of swelling was obtained by ΔW = ((Wf-Wi)/Wi) × 100 where Wi and Wf correspond to the weights of crosslinked P(VDF-TrFE) before and after swelling in a solvent, respectively.

XRD
XRD measurement was performed by the diffractometer (PANalytical Empyrean) under Bragg-Brentano geometry (CuKα1 source with the wavelength λ = 1.54 Å). For electric field-dependent XRD, polymer films with gold electrodes were prepared. Silver wires were used to connect the samples with Trek 610E amplifier. To ensure electrical insulation, a Teflon layer was introduced to separate the sample from XRD sample holder. After electric field was applied by a specifical voltage generated by the amplifier, XRD scans were performed.

FTIR
FTIR spectra were obtained by using a spectrometer (Nicolet iS50R) in the attenuated total reflectance mode. The fraction of different chain conformations was estimated by calculating the relative ratio between the integration of absorption bands of different chain conformations in FTIR spectra32.

DSC
DSC measurement was carried out by using a Diamond DSC (PerkinElmer Instruments) with a heating rate of 10°C min-1. The crystallinity can be obtained through the calculations of melting enthalpy following the relation Xc = ΔHm / [xVDF ΔH0], where ΔHm corresponds to the melting enthalpy of the polymer, calculated by integrating the melting peak, xVDF is the mass ratio of VDF in P(VDF-TrFE)15,25, and ΔH0 is the melting enthalpy of a 100% crystalline PVDF (ΔH0 = 103.4 J g-1) (ref. 23). The VDF loss due to crosslinking was considered in the calculations of the crystallinity.

DMA
The stress-strain curves of the samples were tested using the Diamond DMA (PerkinElmer Instruments).

Dielectric measurement
For electrical measurements, gold electrodes of a typical thickness of 50 nm were sputtered (Quorum Q150RS plus) on both sides of the polymer films. The temperature dependence of the dielectric response was measured using an LCR meter (E4980A, Keysight) connected to an oven with a heating rate of 1°C min-1 and a frequency range from 100 Hz to 1 MHz.

The dielectric constant above Tm at the frequency of 1 MHz was analyzed by using modified Curie-Weiss law which is expressed as (T-Tm)γ/C = 1/ε - 1/εmax (T=Tm) (γ is the relaxor diffuseness factor and C is a constant). To deduce γ, the data points in terms of ln(1/ε - 1/εmax) versus ln(T-Tm) were plotted whereas the slope of the curve corresponded to the value of the diffuseness factor γ.

The dielectric spectra of crosslinked P(VDF-TrFE) was analyzed by fitting the dielectric parameters with the Vogel-Fulcher law ln f = ln f0 - Ea / kB(T - Tf) (where Ea is the activation energy and f0 is the characteristic frequency). The typical fitting results were summarized in Supplementary Fig. S49, supporting the existence of relaxor behavior in crosslinked P(VDF-TrFE) copolymers.

Piezoelectric measurement
The piezoelectric coefficient d33 was measured by a quasi-static d33-meter (PKD3−2000, PolyK Technologies) through the quasi-static Berlincourt method (with a dynamic force of 0.25 N at a frequency of 110 Hz under an applied static force of 0.5 N).

Electric-field-induced strain measurement was used to determine d33 through a laser interferometer (SIOS SP-S120E), which is similar to previous experimental setup21,27. The ac electric field well below Ec was applied during the strain measurement.

Before piezoelectric measurements, the samples underwent d.c. poling (i.e., electric field of 150 MV m-1, 10 min) at room temperature18.

P-E loop measurement
A modified Sawyer-Tower circuit was employed in P-E loops measurement whereas an electric field with the triangular waveform was applied.

DFT calculations
DFT calculations were performed using the Gaussian program package42. The structures include crosslinker molecules (i.e., ethylenediamine, 1,2-diaminopropane, 1,3-diaminopropane, 1,5-diaminopentane, 1,10-diaminodecane, and 1,12-dodecanediamine) and two PVDF chains crosslinked with ethylenediamine, 1,2-diaminopropane and 1,3-diaminopropane were studied in our computations. The structural optimization was carried out at B3LYP/6-311+G(d,p) level of theory43, and the DFT-D3 method with Becke-Johnson damping function was adopted for the dispersion energy correction44,45. We considered simplified systems relevant to our work, which are computationally tractable. Specifically, we used PVDF chains by ignoring the contribution of chiral TrFE to address the role of crosslinking in tailoring the energetics and local inhomogeneities. In this regard, the periodic boundary condition was not necessarily imposed, and the symmetry was not constrained on our structures. Initially, two identical PVDF chains with two different chain conformations, namely 3/1-helix and all-trans, were crosslinked by different crosslinkers including ethylenediamine, 1,2-diaminopropane and 1,3-diaminopropane, respectively. The PVDF chain was composed of 24 C atoms, 24 F atoms and 26 H atoms whereas the terminal groups were saturated with H atoms. For the 3/1-helix chain, the gauche angle τ was defined as the dihedral angle of sequential backbone of C-C-C-C. The gauche angle τ in the initial regular 3/1-helix structure was 60°. As shown in Supplementary Fig. S45, there were totally 11 C-C-C-C dihedral angles in each chain. Considering the two different PVDF conformations, the crosslinkers (with varied crosslinking degree) and total twelve molecules were optimized.

Rigid potential energy surface (PES) scans, depicting the contribution of the local rotation of the different dihedral angles to energy gain, were performed42. The energy gain ΔU induced by local bond rotation was calculated by allowing a specific gauche angle τ to rotate by a small angle Δφ (|Δφ| ≤ 10o) while the frozen constraint was imposed on the other angles. The initial gauche angles τ (Δφ = 0) corresponded to the equilibrium values obtained by the above DFT calculations. Accordingly, the energy for Δφ = 0 was fixed to be zero as the reference. Δφ was set from -10o to 10o in a step of 1o. By relaxing the structure, ΔE with respect to that under Δφ = 0 was obtained.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript validates the effect of intermolecular crosslinking on the ferroelectric copolymer with various cross-linking agents to attain a strong conformational heterogeneity, thereby inducing a large piezoelectric response. In this process, various cross-linking agents were used to analyze its piezoelectric response and it was found that PVDF-TrFE cross-linked with 1, 2 diamino propane exhibited a maximum piezoelectric coefficient of -95 pC N-1, indicating its suitability for various electromechanical devices. My specific comments are as follows:\n1. On what aspect, the cross-linking density values were chosen?\n2. The increase in lattice spacing values with increasing cross-linking densities for all three polymeric concentrations should be provided.\n3. Authors should project a reliable comparison of the FTIR and XRD data in Figures 1c and 1e, as they display different density values. Also, the number of points taken for analysis differs for the optimized cross-linker (Figure S16) and polymer concentration (Figure 2d) with the concurrent ones.\n4. P-E loop measurements for different frequencies should be given.\n5. Have the authors validated the strain % with the induced polarization?\n6. Did the authors check the mechanical stability of the freestanding crosslinked piezoelectric polymer?", "reviewer_2": "This paper presents a type of ferroelectric polymers by intermolecular crosslinking for enhancing d33 response. The crosslinked P(VDF-TrFE) exhibits large d33 of -95.0 pC N-1 engineered via enhancing the local conformational heterogeneity, which is over twice as large as that of -40.1 pC N-1 without crosslinking. However, there still lack of enough deep understanding about such piezoelectric performance enhancement. Here are the detail comments:\n1.Related studies (Chemical Engineering Journal 433 (2022): 134475.; Science 375.6587 (2022): 1418-1422.; ACS Applied Materials & Interfaces 14.35 (2022): 40331-40343.; Journal of Materials Science: Materials in Electronics 32 (2021): 28708-28717.; ACS Applied Materials & Interfaces 12.19 (2020): 21871-21882.) have shown that the crosslinking strategies can improve the piezoelectricity of fluoropolymers. What is the innovation of the method proposed in this study to improve the piezoelectricity of ferroelectric polymers by crosslinking? The authors should elaborate on the previous related studies on crosslinking strategies to improve piezoelectricity in the introduction, and explain the differences between this study and previous studies. The highlights of this study are further emphasized.\n2.In Fig. 1, the authors provide a crosslinking mechanism through FTIR and XPS analysis, which is insufficient. P(VDF-TrFE) and 1,2-propylenediamine may also undergo an elimination reaction to form conjugated double bonds, whose infrared vibration peaks are also near the C=N vibration peak. In addition, Fig. S22 shows that the freestanding crosslinked P(VDF-TrFE) 55/45 mol% copolymer is light yellow, which further indicates that double bonds may exist. Therefore, the authors should provide detailed NMR and other data analysis to analyze whether double bonds are formed. If double bonds exist, the effect of conjugated double bonds on piezoelectricity should be analyzed in depth.\n3.The authors claim that, \"the cross-linking reaction of small molecule cross-linking agents may occur in the crystalline region of thermoplastic polymers with higher crystallinity.\" The evidence from XRD analysis solely is obviously insufficient. Please provide more reliable and intuitive evidence.\n4.The calculation of the diffuseness factor γ via the modified Curie-Weiss law should be clearly presented.\n5.The crosslinked P(VDF-TrFE) with a copolymerization ratio of 55/45% in Fig. 2d has significantly improved piezoelectricity, while the piezoelectricity enhancement effect of crosslinked ferroelectrics with other copolymerization ratios is not obvious, or even reduced. Previous literature (Nature 562.7725 (2018): 96-100.) has demonstrated the role of MPB in enhancing piezoelectricity, and its copolymerization ratio range of MPB is 49 mol% ≤ C ≤ 55 mol%. In this study, the VDF markedly augmented d33 is observed at ρ=1.8%, which locates at the right side of the MPB region (0≤ρ≤0.2%). First, how do we determine the crosslinking density range in which the MPB phenomenon occurs? Does the MPB phenomenon exist outside the narrow MPB region (0≤ρ≤0.2%)? Then, is the improvement of piezoelectricity determined by crosslinking, or is it a synergistic effect of crosslinking and MPB in this study?\n6.In Fig. S16, as the crosslinking density increases, the polymer crystallinity decreases significantly rather than remaining almost unchanged. The conclusions claimed by the authors are not valid.\n7.The largest |d33| (93.4 pC N-1) of by 1,2-diaminopropane is slightly smaller than that (95.0 pC N-1) by ethylenediamine. Why was the ethylenediamine not chosen in the previous research?\n8.The significance of this paper would be further emphasized if the authors demonstrate that their concept can be applied to other ferroelectric polymers combinations as well. For instance, can the piezoelectric properties of crosslinked ferroelectric polymers be improved using a similar method when P(VDF-TrFE) is replaced with another ferroelectric polymers? This would help clarify the versatility of the study.\n9.As a ferroelectric polymer, P(VDF-TrFE) has a clear Curie temperature Tc, which determines the upper limit of this ferroelectric's operating temperature. The authors claim that crosslinked P(VDF-TrFE) has high piezoelectricity, but this study lacks the effect of cross-linking on Tc, which is not conducive to practical applications.", "reviewer_3": "This work provided a unique strategy for designing ferroelectric polymer with ultra-high piezoelectric performance by using crosslnking. The intermolecular crosslinking can locally create remarkably stronger conformational inhomogeneities (about 25°) near the crosslinking sites, which is much larger than local angular distortions (about 5°) in helical conformation induced by intramolecular strategy. The large conformational inhomogeneities induce the formation of markedly flattened energetic landscape, thus leading to high piezoelectricity. The corsslinking strategy used in this work is fascinating and pioneering since previous work about corsslinking PVDF or PVDF-TrFE suggest that crosslinking should inhibit chain rotation and reduce piezoelectricity. This work can be a very valuable reference for developing high-performance piezoelectric polymers. However, several minor questions should be addressed before this paper can be published.\n1. The MPB region of the crosslinked PVDF-TrFE located at 0≤ρ≤0.2%, while the highest d33 is observed at ρ=1.8%.\nHowever, for piezoelectric ceramics and previously reported PVDF-TrFE exhibiting MPB, the highest d33 located within the MPB. Why the highest d33 of the crosslinking PVDF-TrFE located outside the MPB region？\n2. From the field-dependent XRD results, it can be seen that the crosslinked PVDF-TrFE required a higher electric field to trigger phase transition (i.e. 100 MV/m for non-crosslinked sample and 200 MV/m for crosslinked sample). Was this result contradictory to the high d33 of crosslinked PVDF-TrFE? Since a easier phase transition may lead to strong converse piezoelectricity.\n3. Only d33 cannot reflect the overall piezoelectric performance of material. What about the piezoelectric voltage coefficient g33 and electromechanical coupling factor k33 of the state-of-art crosslinked PVDF-TrFE?\n3. Is this crosslinking strategy also suitable for improving the piezoelectricity or electric strain ability of pristine PVDF and terpolymer PVDF-TrFE-CFE? The author can anticipate the influence of introducing corsslinking into these polymers."}, "author_response": "Comment #1: This manuscript validates the effect of intermolecular crosslinking on the ferroelectric copolymer with various crosslinking agents to attain a strong conformational heterogeneity, thereby inducing a large piezoelectric response. In this process, various crosslinking agents were used to analyze its piezoelectric response and it was found that PVDF-TrFE cross-linked with 1,2 diamino propane exhibited a maximum piezoelectric coefficient of -95 pC N-1, indicating its suitability for various electromechanical devices. My specific comments are as follows:\nOn what aspect, the crosslinking density values were chosen?\nResponse: To address this comment, we add the following sentence into our revised manuscript as “We choose a modest crosslinking density acting as a leverage to tune the energetic landscape of P(VDF-TrFE) copolymers near MPB mainly because the compositionally-induced MPB is sensitive to the small change in the VDF content according to the previous work25.”\nComment #2: The increase in lattice spacing values with increasing crosslinking densities for all three polymeric concentrations should be provided.\nResponse: To address this comment, we provide the lattice spacing data as Supplementary Figs. S4 and S5. Meanwhile, we also add the following discussions into our revised manuscript “We also observe the increased lattice spacing with increasing ρ which applies to various copolymer compositions (Supplementary Figs. S4 and S5).”\nComment #3: Authors should project a reliable comparison of the FTIR and XRD data in Figures 1c and 1e, as they display different density values. Also, the number of points taken for analysis differs for the optimized cross-linker (Figure S16) and polymer concentration (Figure 2d) with the concurrent ones.\nResponse: To address this comment, we have updated Fig. 1c (FTIR) and Fig. 1e (XRD), Fig 2d and Fig. S16 to ensure the data presented using the same crosslinking densities.\nComment #4: P-E loop measurements for different frequencies should be given.\nResponse: To address this comment, we add the P-E loop data under different frequencies together with the following discussions into our revised manuscript “Such crosslinking-driven polarization evolution behavior is also observed under other frequencies (Supplementary Figs. S11 and S12).”\nComment #5: Have the authors validated the strain % with the induced polarization?\nResponse: To address this comment, we add polarization-electric field loops measured at low fields which are not open and paraelectric-like because the field used is below the coercive field. We therefore add a new figure into our revised Supplementary Information and one sentence to address this comment “At low fields, P-E loops are paraelectric-like as the driving field is below the coercive field (Supplementary Fig. S16).”\nComment #6: Did the authors check the mechanical stability of the freestanding crosslinked piezoelectric polymer?\nResponse: To address this comment, we add more discussions on the mechanical stability into revised manuscript as “We also evaluate the mechanical stability and observe that d of freestanding crosslinked piezoelectric polymers shows nearly no 33 degradation after undergoing 105 mechanical cycles (Supplementary Fig. S17), indicating long-term mechanical durability. We also observe that the elongation at break is improved considerably caused by crosslinking (Supplementary Fig. S18), suggesting improved mechanical properties.”\nReviewer #2:\nThis paper presents a type of ferroelectric polymers by intermolecular crosslinking for enhancing d33 response. The crosslinked P(VDF-TrFE) exhibits large d33 of -95.0 pC N-1 engineered via enhancing the local conformational heterogeneity, which is over twice as large as that of -40.1 pC N-1 without crosslinking. However, there still lack of enough deep understanding about such piezoelectric performance enhancement. Here are the detail comments:\nResponse: We thank Reviewer #2 for carefully reading our manuscript. He/she evoked main concerns on conceptual advance with respect to previous ones in Comment #1, the presence of conjugated double bonds in Comment #2, applicability to other polymers in Comment #8 and practical applications at higher temperature in #9. He/she also raises several other technical comments. We fully address all the comments/suggestions by Reviewer #2 in our revised version of manuscript. We sincerely thank Reviewer #2 for the valuable suggestions and comments, which have significantly improved the quality of our manuscript. We hope that the novelty, originality, and relevance of our work are now more evident. With the opportunity to review our responses and the improved manuscript, we sincerely hope that Reviewer #2 might reconsider his/her conclusions and recommend publication of this manuscript.\nComment 1: Related studies (Chemical Engineering Journal 433 (2022): 134475.; Science 375.6587 (2022): 1418-1422.; ACS Applied Materials & Interfaces 14.35 (2022): 40331-40343.; Journal of Materials Science: Materials in Electronics 32 (2021): 28708-28717.; ACS Applied Materials & Interfaces 12.19 (2020): 21871-21882.) have shown that the crosslinking strategies can improve the piezoelectricity of fluoropolymers. What is the innovation of the method proposed in this study to improve the piezoelectricity of ferroelectric polymers by crosslinking? The authors should elaborate on the previous related studies on crosslinking strategies to improve piezoelectricity in the introduction, and explain the differences between this study and previous studies. The highlights of this study are further emphasized.\nResponse: We thank Reviewer #2’s comment on conceptual advance with respect to previous studies. To clarify the novelty of our work, we summarize the main differences between our results and previous studies mentioned by Reviewer #2. Among the five references provided by Reviewer #2, Table R1 summarizes that two are relevant to crosslinking (Chemical Engineering Journal 433 (2022); ACS Applied Materials & Interfaces 14.35 (2022): 40331-40343) while the other three are related to the C=C double bonds (Science 375.6587 (2022); Journal of Materials Science: Materials in Electronics 32 (2021): 28708-28717; ACS Applied Materials & Interfaces 12.19 (2020): 21871-21882). Following the suggestion by Reviewer #2 on the comparison of the novelty between this work and previous studies, we mainly focus on crosslinking studies. Different from our work, these previous crosslinking studies used PVDF as the base polymer while the observed d is as low as -9.4 pC N-1 (ACS Applied Materials 33 & Interfaces 14.35 (2022)).\nThis weak response is consistent with our molecular framework as our study reveals that greatly augmented d driven by crosslinking requires the presence of energetically 33 nearly degenerate phases. As PVDF adopts the energetically more favorable TGTḠ conformation, a modest d is achieved in crosslinked PVDF (ACS Applied Materials 33 & Interfaces 14.35 (2022)). In addition, we find that crosslinking is carefully avoided in one reference mentioned by Reviewer #2 (ACS Applied Materials & Interfaces 12.19 (2020): 21871-21882), as it was believed that undesired crosslinking is detrimental to crystallization of PVDF and thus piezoelectric response. Our work also overturns this belief by observing markedly improved d despite reduced crystallinity induced by 33 crosslinking.\nComment #2: In Fig. 1, the authors provide a crosslinking mechanism through FTIR and XPS analysis, which is insufficient. P(VDF-TrFE) and 1,2-propylenediamine may also undergo an elimination reaction to form conjugated double bonds, whose infrared vibration peaks are also near the C=N vibration peak. In addition, Fig. S22 shows that the freestanding crosslinked P(VDF-TrFE) 55/45 mol% copolymer is light yellow, which further indicates that double bonds may exist. Therefore, the authors should provide detailed NMR and other data analysis to analyze whether double bonds are formed. If double bonds exist, the effect of conjugated double bonds on piezoelectricity should be analyzed in depth.\nResponse: We provide direct XPS combined with NMR data to rule out the presence of conjugated double bonds in crosslinked P(VDF-TrFE). For instance, C 1s XPS spectra (Fig. R1) of crosslinked P(VDF-TrFE) show the absence of characteristic absorption peak at around 283 eV corresponding to C=C double bonds (ACS Appl. Mater. Interfaces 12, 21871-21882, (2020); J. Mater. Sci.: Mater. Electron. 17, 1005-1009, (2006)). This result can be understood as follows. The crosslinking process in our study occurs under high-temperature conditions. In this melting state, the C=C double bonds formed via dehydrofluorination reactions would immediately generate the Michael addition reactions with the diamine which prevents the accumulation of stable C=C conjugated structures. Specifically, the nitrogen atom of the diamine acts as a nucleophilic center, utilizing its lone pair electrons to attack an electrophilic carbon of the activated C=C double bond. This nucleophilic attack results in the opening of the double bond and the subsequent formation of a new C-N single bond, thereby incorporating the diamine into the polymer chain and eliminating the unsaturation. After that, further dehydrofluorination reactions are triggered, leading to the formation of C=N bonds. The above analysis has been documented in previous review (Adv. Polym. Sci. 184 (2005) 127-211).\nComment #3: The authors claim that, \"the crosslinking reaction of small molecule crosslinking agents may occur in the crystalline region of thermoplastic polymers with higher crystallinity.\" The evidence from XRD analysis solely is obviously insufficient. Please provide more reliable and intuitive evidence.\nResponse: In addition to XRD, P-E loop results provide direct evidence to support our claim. For instance, if the crosslinking occurs in amorphous regions, the decrease in crystallinity by about 18% should have resulted in a decrease in the long-range ferroelectricity by around 18% as ferroelectric instability originates from the crystalline regions of ferroelectric polymers. By contrast, the remanent polarization deduced from P-E loops shows a more dramatic reduction of 38%. This in turn indicates that crosslinking agents with small molecule sizes may enter crystalline regions.\nComment #4: The calculation of the diffuseness factor γ via the modified Curie-Weiss law should be clearly presented.\nResponse: To address this comment, we add more detailed information in the method part “To deduce γ, the data points in terms of ln(1/ε -1/ε ) versus ln(T-T ) were plotted r max m whereas the slope of the curve corresponded to the value of the diffuseness factor γ.”\nComment #5: The crosslinked P(VDF-TrFE) with a copolymerization ratio of 55/45% in Fig. 2d has significantly improved piezoelectricity, while the piezoelectricity enhancement effect of crosslinked ferroelectrics with other copolymerization ratios is not obvious, or even reduced. Previous literature (Nature 562.7725 (2018): 96-100.) has demonstrated the role of MPB in enhancing piezoelectricity, and its copolymerization ratio range of MPB is 49 mol% ≤ C ≤ 55 mol%. In this study, the VDF markedly augmented d33 is observed at ρ=1.8%, which locates at the right side of the MPB region (0≤ρ≤0.2%). First, how do we determine the crosslinking density range in which the MPB phenomenon occurs? Does the MPB phenomenon exist outside the narrow MPB region (0≤ρ≤0.2%)? Then, is the improvement of piezoelectricity determined by crosslinking, or is it a synergistic effect of crosslinking and MPB in this study?\nResponse: To address this comment, we add the following discussions into our revised manuscript to further clarify the main difference between our results and previous one in compositionally-induced MPB in P(VDF-TrFE) as follows “The highest d is 33 observed in the relaxor region rather than the phase coexisting region observed in compositionally-induced MPB in P(VDF-TrFE) recalling MPB here is mainly defined as phase transition region where both competing relaxor order and ferroelectric order exist with each other25. This is mainly attributed to strong local conformational heterogeneity introduced by crosslinking. For instance, crosslinking may yield the stabilization of relaxor phase even at an ultralow ρ of 0.2% according to our structural and electrical results (Figs. 1e, 2b and 2c). In this regard, VDF varies by only a slight 10 decrease of 0.2 mol% due to dehydrofluorination during the crosslinking reactions. As a result, this leads to a very narrow MPB region (0≤ρ≤0.2%). By contrast, breaking of delicate balance between normal ferroelectric phase and relaxor phase requires reduced VDF content of about 6 mol%25. This contrasting behavior illustrates the unique feature of crosslinking in generating local conformational heterogeneity which critically correlates with enhanced piezoelectric response occurring in relaxor regime.\nComment #6: In Fig. S16, as the crosslinking density increases, the polymer crystallinity decreases significantly rather than remaining almost unchanged. The conclusions claimed by the authors are not valid.\nResponse: We agree with Reviewer #2’s comment. Indeed, we clarify that “we find that improvement in d depends sensitively on crosslinkers while the polymer 33 crystallinity remains nearly the same” mentioned in our manuscript describes that the crystallinity induced by different crosslinkers at the same crosslinking density is nearly the same. To address this comment, we modify this sentence as follows “the polymer crystallinity obtained by different crosslinkers at the same crosslinking density is nearly the same. For instance, using ethylenediamine, 1,2-diaminopropane, 1,3-diaminopropane, and 1,5-diaminopentane, at ρ=1.8%, the crystallinity values are 45.2%, 46.2%, 46.3%, and 47.1%, respectively (Supplementary Fig. S25).”\nComment #7: The largest |d33| (93.4 pC N-1) of by 1,2-diaminopropane is slightly smaller than that (95.0 pC N-1) by ethylenediamine. Why was the ethylenediamine not chosen in the previous research?\nResponse: Indeed, we have mentioned why we used the small molecule as the crosslinkers by saying that “Crosslinking using the same P(VDF-TrFE) 55/45 mol% copolymer has been also conducted in previous work15 using a bulky crosslinker. By contrast, our work uses much smaller crosslinkers which yield a completely different outcome. For instance, the presence of crosslinking reactions in the amorphous region generally excludes the structural change in crystalline region as reported in previous work15, which is completely different from the order-to-disorder phase transition in crystalline regions observed in this work.” Previous studies in this field usually use long-chain crosslinkers whereas the crosslinking mainly occurs in the amorphous regions as the bulky crosslinkers are difficult to enter the crystalline regions.\nComment #8: The significance of this paper would be further emphasized if the authors demonstrate that their concept can be applied to other ferroelectric polymers combinations as well. For instance, can the piezoelectric properties of crosslinked ferroelectric polymers be improved using a similar method when P(VDF-TrFE) is replaced with another ferroelectric polymers? This would help clarify the versatility of the study.\nResponse: The generality of crosslinking strategy is further demonstrated in other crosslinked polymers. Here we choose P(VDF-TFE) 95/5 mol% due to much higher Curie temperature (Macromolecules 19, 1491-1494 (1986)). The Curie temperature of P(VDF-TFE) 95/5 mol% is above its melting temperature of around 150 oC (Macromolecules 19, 1491-1494 (1986)). The incorporation of TFE at a small content of 5 mol% may stabilize the ferroelectric all-trans conformation (Macromolecules 19, 1491-1494 (1986); J. Appl. Phys. 43, 4293-4303 (1972)) which is characterized by the singlet at 2θ=19.2o in XRD pattern. After crosslinking, paraelectric-like phase is stabilized by splitting of the singlet. The peak at lower 2θ=18.5o assigned to the paraelectric-like phase develops at the expense of the peak intensity at higher 2θ=19.2o. Moreover, piezoelectric coefficient |d | is markedly enhanced from 17.8 pC N-1 at ρ=0% 33 to 44.2 pC N-1 at ρ=1.8%. These results explicitly demonstrate that crosslinking strategy developed in this work is generic to enhance piezoelectric properties of ferroelectric polymers with small energetic barriers between different crystalline chain conformations which may inspire future studies on uncovering novel high-performance piezoelectric polymers for flexible and wearable electromechanical applications.\nComment #9: As a ferroelectric polymer, P(VDF-TrFE) has a clear Curie temperature Tc, which determines the upper limit of this ferroelectric's operating temperature. The authors claim that crosslinked P(VDF-TrFE) has high piezoelectricity, but this study lacks the effect of cross-linking on Tc, which is not conducive to practical applications.\nResponse: This comment has been addressed in our response to Comment #8.\nReviewer #3\nComment: This work provided a unique strategy for designing ferroelectric polymer with ultra-high piezoelectric performance by using crosslinking. The intermolecular crosslinking can locally create remarkably stronger conformational inhomogeneities (about 25°) near the crosslinking sites, which is much larger than local angular distortions (about 5°) in helical conformation induced by intramolecular strategy. The large conformational inhomogeneities induce the formation of markedly flattened energetic landscape, thus leading to high piezoelectricity. The crosslinking strategy used in this work is fascinating and pioneering since previous work about crosslinking PVDF or PVDF-TrFE suggest that crosslinking should inhibit chain rotation and reduce piezoelectricity. This work can be a very valuable reference for developing high-performance piezoelectric polymers. However, several minor questions should be addressed before this paper can be published.\nResponse: We thank Reviewer #3 for recognition that “This work provided a unique strategy for designing ferroelectric polymer with ultra-high piezoelectric performance by using crosslinking.” and “The crosslinking strategy used in this work is fascinating and pioneering since previous work about crosslinking PVDF or PVDF-TrFE suggest that crosslinking should inhibit chain rotation and reduce piezoelectricity.” encouraging remark that our study may inspire follow-up studies “This work can be a very valuable reference for developing high-performance piezoelectric polymers.”\nComment #1: The MPB region of the crosslinked PVDF-TrFE located at 0≤ρ≤0.2%, while the highest d is observed at ρ=1.8%. However, for piezoelectric ceramics and 33 previously reported PVDF-TrFE exhibiting MPB, the highest d located within the 33 MPB. Why the highest d of the crosslinking PVDF-TrFE located outside the MPB 33 region?\nResponse: To address this comment, we add the following discussions into our revised manuscript to further clarify the main difference between our results and previous one in compositionally-induced MPB in P(VDF-TrFE) as follows “The highest d is 33 observed in the relaxor region rather than the phase coexisting region observed in compositionally-induced MPB in P(VDF-TrFE) recalling that MPB is defined as the phase transition region where both competing local relaxor order and long-range ferroelectric order coexist with each other25. This is mainly attributed to the presence of strong local conformational heterogeneity introduced by crosslinking. For instance, crosslinking may yield the stabilization of the short-range relaxor phase even at an ultralow ρ of 0.2% according to our structural and electrical results (Figs. 1e, 2b and 2c). In this regard, VDF concentration varies slightly by only a modest decrease of 0.2 mol% due to dehydrofluorination during the crosslinking reactions. As a result, this leads to the formation of a very narrow MPB region (0≤ρ≤0.2%). By contrast, breaking of delicate balance between normal ferroelectric phase and relaxor phase requires reducing the VDF content by 6 mol% according to the previous work25. This contrasting behavior clearly illustrates the unique feature of crosslinking in generating local conformational heterogeneity which critically correlates with enhanced piezoelectric response occurring in relaxor regime instead of the phase existence region.\nComment #2: From the field-dependent XRD results, it can be seen that the crosslinked PVDF-TrFE required a higher electric field to trigger phase transition (i.e. 100 MV/m for non-crosslinked sample and 200 MV/m for crosslinked sample). Was this result contradictory to the high d of crosslinked PVDF-TrFE? Since a easier phase 33 transition may lead to strong converse piezoelectricity.\nResponse: To address this comment, we have added the following discussions into our revised manuscript as “In addition, our field-dependent structural results indicate that the presence of strong local conformational heterogeneity delays the complete phase transition from disordered phase to ordered phase rather than facilitating such phase transition. Combined with our DFT calculations, our results therefore suggest that the ease of bond rotations caused by crosslinking occurs locally rather than collectively in response to applied field, which is mainly responsible for higher d than that obtained 33 by conventional MPB approach25.”\nComment #3: Only d cannot reflect the overall piezoelectric performance of material. 33 What about the piezoelectric voltage coefficient g and electromechanical coupling 33 factor k of the state-of-art crosslinked PVDF-TrFE?\nResponse: The generality of crosslinking strategy is further demonstrated in other crosslinked polymers. Here we choose P(VDF-TFE) 95/5 mol% rather than terpolymer due to much higher Curie temperature (Macromolecules 19, 1491-1494 (1986)). The Curie temperature of P(VDF-TFE) 95/5 mol% is above its melting temperature of around 150 oC (Macromolecules 19, 1491-1494 (1986)). The incorporation of TFE at a small content of 5 mol% may stabilize the ferroelectric all-trans conformation (Macromolecules 19, 1491-1494 (1986); J. Appl. Phys. 43, 4293-4303 (1972)) which is characterized by the singlet at 2θ=19.2o in XRD pattern. After crosslinking, paraelectric-like phase is stabilized by splitting of the singlet. The peak at lower 2θ=18.5o assigned to the paraelectric-like phase develops at the expense of the peak intensity at higher 2θ=19.2o. Moreover, piezoelectric coefficient |d | is markedly 33 enhanced from 17.8 pC N-1 at ρ=0% to 44.2 pC N-1 at ρ=1.8%. These results explicitly demonstrate that crosslinking strategy developed in this work is generic to enhance piezoelectric properties of ferroelectric polymers with small energetic barriers between different crystalline chain conformations which may inspire future studies on uncovering novel high-performance piezoelectric polymers for flexible and wearable electromechanical applications."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all the comments of the reviewer. If a constant crystallinity is maintained, how is a moderate cross-linking density determined? However, the concern relating to constant lattice spacing with increasing cross-linking density values, as in comments #2 and 4, may improve the stability of the device, but can considerably reduce the piezoelectric sensitivity of the device should be addressed. This is also evident from comment#5 as paraelectric behaviour at lower field restricts domain switching, lowering the piezo response.", "reviewer_2": "I commend the authors for conducting additional experiments to justify the work they presented here in this manuscript. This has greatly enhanced the quality of the work. However, my comments have only been partially addressed. There are still a few remaining concerns that need to be clarified before the manuscript can be recommended for acceptance:\n1. The author chose to perform thermal crosslinking at 220 °C for 1 h. Why was this condition chosen for heat treatment? Is there any relevant orthogonal experiment to support this?\n2. Compared with the materials in the same field, what is the performance level of the piezoelectricity of the ferroelectric polymers in this paper? Please provide supported literature.\n3. Is the proposed strategy here specific to ferroelectric polymers? The authors mentioned potential of other polymers (i.e., tetrapolymers, polymer blends) able to use similar molecular mechanism for highly piezoelectricity, why not show them? With the current data, this remains a speculation and unable to justify the potential of this intermolecular crosslinking strategy. Otherwise, PVDF-TrFE and PVDF-TFE, as copolymers of PVDF, also need to consider cost issues in practical applications. Can PVDF homopolymers, which are relatively low in cost, achieve high piezoelectricity through the crosslinking strategy described in this manuscript? Please provide detailed arguments and analysis.\n4. In response to my previous comment 7, the authors misunderstood me. Regarding the application of typical crosslinking agents in the manuscript, the authors mainly focused on the effects of small molecule crosslinkers (i.e., 1,2-diaminopropane) on the structure and properties of P(VDF-TrFE). However, the |d33| of the obtained crosslinked P(VDF-TrFE) by 1,2-diaminopropane is not as good as that of crosslinked P(VDF-TrFE) by ethylenediamine. Thus, why did the authors not choose small molecule crosslinkers (i.e., ethylenediamine) for in-depth research in the manuscript?", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_5": "Both the early career researcher in my group and I think the authors have addressed the technical concerns of reviewer #3, and now the manuscript is suitable for publication."}, "author_response": "Reviewer #1 (Remarks to the Author):\nComments: The authors have addressed all the comments of the reviewer. If a constant crystallinity is maintained, how is a moderate cross-linking density determined? However, the concern relating to constant lattice spacing with increasing cross-linking density values, as in comments #2 and 4, may improve the stability of the device, but can considerably reduce the piezoelectric sensitivity of the device should be addressed. This is also evident from comment#5 as paraelectric behaviour at lower field restricts domain switching, lowering the piezo response.\nResponse: We thank Reviewer #1 for his/her recognition that “The authors have addressed all the comments of the reviewer”. We have carefully considered the concerns regarding the determination of crosslinking density and the relationship between lattice spacing and the piezoelectric sensitivity which are addressed as follows.\nRegarding the determination of crosslinking density, we add “Specially, we use a moderate crosslinking density from 0% to 3% according to the narrow MPB region (49 mol%≤c ≤55 mol%) whereas crosslinking-induced dehydrofluorination may offer VDF a tool to tune relative VDF ratio and thus the relative stability between competing crystalline phases.”\nRegarding the relationship between lattice spacing and the piezoelectric sensitivity, we add “As crosslinking density increases above 1%, the interchain spacing remains nearly unchanged (Supplementary Figs. S4 and S18) which may reduce the piezoelectric sensitivity. For instance, it is found that piezoelectric voltage coefficient |g | is maximized at ρ=1.8% which is followed by a decline for ρ>1.8% 33 (Supplementary Fig. S19). In this regard, the crosslinked P(VDF-TrFE) with optimized piezoelectric properties is most suitable for piezoelectric applications with high piezoelectric sensitivity.”\nIn addition, regarding the paraelectric behavior, we add “This is accompanied by paraelectric behavior due to the stabilization of relaxor phase for ρ>1.8% (Fig. 2a).”\nReviewer #2 (Remarks to the Author):\nComments: I commend the authors for conducting additional experiments to justify the work they presented here in this manuscript. This has greatly enhanced the quality of the work. However, my comments have only been partially addressed. There are still a few remaining concerns that need to be clarified before the manuscript can be recommended for acceptance:\nResponse: We thank Reviewer #2 for recognition that “the authors for conducting additional experiments to justify the work they presented here in this manuscript”. We have provided a point-by-point response to the remaining concerns by Reviewer #2 which are listed as follows.\nComment #1: The author chose to perform thermal crosslinking at 220 °C for 1 h. Why was this condition chosen for heat treatment? Is there any relevant orthogonal experiment to support this?\nResponse: To address this comment, we have added more experimental details using orthogonal experiment (see Table S3). We also add the following discussions into our revised method part “The solution was cast onto glass plates, followed by annealing at 220 °C for 1 h for thermal crosslinking. This optimized thermal condition was obtained through the orthogonal experiments on d obtained by different thermal conditions, as 33 summarized in Table S3. It was observed that high d values were generally achieved 33 across a high-temperature range (190 °C-250 °C) where the specific condition under 220 °C for 1 h yielded the maximum |d |of 93.4 pC N-1. Extending the reaction time 33 (e.g., to 4 h) or further increasing the temperature (e.g., to 250 °C) did not result in further improvements in d , indicating that the property enhancement enabled by 33 thermal processing had reached saturation.”\nComment #2: Compared with the materials in the same field, what is the performance level of the piezoelectricity of the ferroelectric polymers in this paper? Please provide supported literature.\nResponse: To address this comment, we have added more results on piezoelectricity of ferroelectric polymers. We show that our results are comparable with the best regard reported in recent results on intrinsic piezoelectricity of ferroelectric polymers. We also add the giant extrinsic d value of 1050 pm V-1 (Science 375, 1418-1422, (2022)).\nIndeed, the main advance of our work is not limited to d values. Instead, our 33 characterization of d is made through comprehensive piezoelectric measurements by 33 combining both direct and converse d which remains rare in the literature. Moreover, 33 the scalability of various methods to enhance d remains rarely reported. 33\nWe add “We have synthesized crosslinked ferroelectric polymers delivering large d of 33 -95.0 pC N-1 engineered via enhancing the local conformational heterogeneity. The markedly enhanced d is demonstrated through comprehensive piezoelectric 33 measurements as well as scalability which remains rarely reported in the literature (Table S2).”\nComment #3: Is the proposed strategy here specific to ferroelectric polymers? The authors mentioned potential of other polymers (i.e., tetrapolymers, polymer blends) able to use similar molecular mechanism for highly piezoelectricity, why not show them? With the current data, this remains a speculation and unable to justify the potential of this intermolecular crosslinking strategy. Otherwise, PVDF-TrFE and PVDF-TFE, as copolymers of PVDF, also need to consider cost issues in practical applications. Can PVDF homopolymers, which are relatively low in cost, achieve high piezoelectricity through the crosslinking strategy described in this manuscript? Please provide detailed arguments and analysis.\nResponse: We have demonstrated the generality of our approach in different polymers including P(VDF-TrFE) and P(VDF-TFE) and various crosslinkers. These comprehensive datasets support our main claim of this work. To clarify the issue on “other polymers (i.e., tetrapolymers, polymer blends)” mentioned by the reviewer, we further show that our approach is applicable to ferroelectric polymer blends. Specifically, polymer blends with various compositions were fabricated such as polymer blend-70/30 consisting of 70 wt% P(VDF-TrFE) 43/57 mol% and 30 wt% P(VDF-TrFE) 65/35 mol%, polymer blend-85/15 consisting of 85 wt% P(VDF-TrFE) 47/53 mol% and 15 wt% P(VDF-TrFE) 65/35 mol% and polymer blend-75/25 consisting of 75 wt% P(VDF-TrFE) 47/53 mol% and 25 wt% P(VDF-TrFE) 65/35 mol%, respectively. Markedly enhanced d is achieved in various crosslinked polymer 33 blends. For instance, |d | of polymer blend-70/30 increases from 25.4 pC N-1 at ρ=0% 33 to 45.9 pC N-1 at ρ=1.2%; |d | of polymer blend-85/15 increases from 41.4 pC N-1 at 33 ρ=0% to 66.5 pC N-1 at ρ=1.2%; |d | of polymer blend-75/25 increases from 37.4 pC 33 N-1 at ρ=0% to 59.5 pC N-1 at ρ=1.8%.\nComment #4: In response to my previous comment 7, the authors misunderstood me. Regarding the application of typical crosslinking agents in the manuscript, the authors mainly focused on the effects of small molecule crosslinkers (i.e., 1,2-diaminopropane) on the structure and properties of P(VDF-TrFE). However, the |d33| of the obtained crosslinked P(VDF-TrFE) by 1,2-diaminopropane is not as good as that of crosslinked P(VDF-TrFE) by ethylenediamine. Thus, why did the authors not choose small molecule crosslinkers (i.e., ethylenediamine) for in-depth research in the manuscript?\nResponse: Following the suggestions by the reviewer, we use ethylenediamine to describe the main results. All figures in the main text are replaced, accordingly.\nWe also add the following discussions into our revised manuscript “Compared with ethylenediamine, 1,2-diaminopropane may be more suitable for promising large-scale applications recalling that d obtained by ethylenediamine is only slightly higher than 33 that obtained by 1,2-diaminopropane. This mainly arises from the safety and cost concerns by using ethylenediamine which was regarded as highly regulated chemical reagents in some regions and more costly than 1,2-diaminopropane.”\nReviewer #4:\nComments: I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.\nResponse: We are grateful for your contributions as a co-reviewer. Your insightful comments are greatly appreciated.\nReviewer #5:\nComments: Both the early career researcher in my group and I think the authors have addressed the technical concerns of reviewer #3, and now the manuscript is suitable for publication.\nResponse: We are grateful for your comments and support for publication."}, {"round": 3, "reviewer_comments": {"reviewer_2": "This manuscript has been modified perfectly, I recommend it to be published in NC."}, "author_response": "Response: Thank you for your constructive feedback. Your valuable insights have greatly contributed to improving the manuscript."}]

Decision letter