Abstract
Relaxor ferroelectrics have been intensively studied during the past two decades for capacitive energy storage in modern electronics and electrical power systems. However, the energy density of relaxor ferroelectrics is fundamentally limited by early polarization saturation and largely reduced polarization despite high dielectric constants. To overcome this challenge, here we report the formation of a high-entropy superparaelectric phase in relaxor ferroelectric polymers induced by low-dose proton irradiation, which exhibits delayed polarization saturation, reduced ferroelectric loss and markedly improved polarizability. Our combined theoretical and experimental results reveal that new chemical bonds generated by the irradiation-induced chemical reactions are essential to the formation of the high-entropy state in ferroelectric polymers. The high-entropy superparaelectric phase endows the polymer with a substantially enhanced intrinsic energy density of 45.7 J cm–3 at room temperature, outperforming the current ferroelectric polymers and nanocomposites under the same electric field. Our work widens the high-entropy concept in ferroelectrics and lays the foundation for the future exploration of high-performance ferroelectric polymers.
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Data availability
The main data supporting the findings of this study are available within this Article and its Supplementary Information. Additional data are available from the corresponding authors upon request. Source data are provided with this paper.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (grant nos. 12274152 and 92366302, to Yang L.), the Guangdong Basic and Applied Basic Research Foundation (grant no. 2024A1515010483, to Yang L.) and the initial financial support from Huazhong University of Science and Technology (to Yang L.). This work is also supported by the Guangdong Provincial Key Laboratory of Manufacturing Equipment Digitization (2023B1212060012). We thank the Analytical and Testing Center of Huazhong University of Science and Technology for technical assistance.
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Yang L., H. Zhou and Q.W. conceived the idea and designed the research. C.L. prepared the polymer films. B.L. carried out the irradiation experiment. C.L., Yuquan L., Z.Y., H.G., M.Y., S.T. and X.Y. collected the XRD, FTIR, UV–vis and DSC data. X.Y. prepared the sandwich structure. Yang L., C.L. and Yuquan L. performed the electrical measurements and AFM-IR measurements. Z.Y. performed the PFM measurement. B.L. performed the phase-field simulations under the supervision of Yang L. T.Y. and L.-Q.C. commented on the results of the phase-field simulations. X.Y., H.G. and Q.L. performed the measurements on the sandwiched structure. Yang L. and C.L. analysed the conduction. L.X., Y.G. and Z.F. performed the electrocaloric measurements. C.L. performed the DFT calculations under the supervision of Yang L., Yang L., C.L., H. Zhang, H. Zhou and Q.W. analysed the data. Yang L., H. Zhou and Q.W. wrote the paper with feedback from all authors.
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Extended data
Extended Data Fig. 1 Schematic of dielectric energy storage.
a, P-E loops in response to the application and removal of an unipolar electric field. The recoverable energy density (the grey area) is written as \({U}_{\text{d}}={\int }_{{P}_{\text{r}}}^{{P}_{\text{m}}}{EdP}\), where Pm and Pr are indicated. The efficiency is defined as η = Ud/(Ud+Uloss). The dashed arrows indicate the application and removal of an applied electric field corresponding to charge and discharge processes, respectively. b, Sketch of P-E loops in normal ferroelectrics. c, Intrinsic versus extrinsic εeff with respect to electric field. Intrinsic εeff is always smaller than εr in ferroelectrics regardless of normal ferroelectric or relaxor ferroelectrics (solid lines). Extrinsic εeff can markedly exceed εr (dashed lines). d, Sketch of dielectric relaxation occurring in relaxor ferroelectrics under different temperatures and frequencies (upper panel). Energy storage at different temperatures (bottom panel). Schematic of the all-trans and 3/1-helix conformation. e, All-trans. f, 3/1-helix. The arrows indicate the projections of the directions of -CF2- dipole on planes defined by the carbon backbone. g, Sketch of track of -CF2- dipole rotation in the 3/1-helical conformation. MPB phase in the main text refers to the coexistence of the all-trans and 3/1-helix conformations with flat energy landscape.
Extended Data Fig. 2 Temperature dependence of dielectric spectra upon heating.
a, x = 0 Mrad. b, x = 5 Mrad. c, x = 10 Mrad. d, x = 20 Mrad. e, x = 40 Mrad. f, g, Dielectric constant and loss at 1 kHz. h, The temperature difference (Tm-Tf) at 100 Hz as a function of irradiation dose. i, The maximum dielectric constant εmax(T = Tm) at 100 Hz under different irradiation doses. Dielectric loss under different frequencies can be found in Supplementary Fig. S22.
Extended Data Fig. 3 P-E loops under different irradiation doses at 200 MV m-1 and comparison of energy storage at a low field of 100 MV m−1.
a, x = 0 Mrad. b, x = 5 Mrad. c, x = 10 Mrad. d, x = 20 Mrad. e, x = 40 Mrad. f, Pristine P(VDF-TrFE-CTFE) 65.4/26.2/8.4 mol%. a-e correspond to the data obtained in P(VDF-TrFE-CTFE) 65/31/4 mol%. g, Unipolar P-E loops. h, Comparison of efficiency between the high-entropy and pristine terpolymers. i, Comparison of discharged energy density Ud between the high-entropy and pristine terpolymers. The high-field results in BOPP are also added in h and i. The dashed boxes in h and i indicate the results in ferroelectric polymers-based materials. CTFE7 represents the terpolymer P(VDF-TrFE-CTFE) 65.6/26.7/7.7 mol% from ref. 28. The red arrows describe the marked increase in both η and Ud enabled by high-entropy design.
Extended Data Fig. 4 Local switching-spectra measured by PFM in P(VDF-TrFE-CTFE) terpolymers irradiated with varied doses.
a, x = 0 Mrad. b, x = 10 Mrad. c, x = 20 Mrad. d, x = 40 Mrad.
Extended Data Fig. 5 FTIR spectra and XRD patterns.
a, FTIR spectra of the terpolymers irradiated with different does. b, Characteristic IR bands of C = C and C = O indicated by the dashed lines at around 1632 cm−1, 1731 cm−1, and 1851 cm−1, respectively. c, Characteristic IR bands of -OH at around 3326 cm−1. Temperature dependent-XRD patterns of the terpolymers upon heating: d, x = 0 Mrad; e, x = 20 Mrad. The dashed arrows indicate the characteristic peaks for the all-trans and 3/1-helix chain conformations. f, Temperature-dependent lattice spacing upon heating (x = 0 and 20 Mrad). g, Lattice spacing as a function of irradiation dose at room temperature, deduced from θ-2θ scans in Fig. 3b.
Extended Data Fig. 6 Origin of high-entropy state in irradiated ferroelectric polymers.
a, Schemes of representative chemical reactions induced by ion irradiation. b, ΔSconf due to irradiation-driven chemical reactions in P(VDF-TrFE-CTFE) 65/31/4 mol%. c, ΔSconf induced by incorporated chemical defects in P(VDF-TrFE-CTFE) 65/31/4 mol%. The black dashed lines are indicative of 1.5 R. The concentration in b describes an equal molar percentage of different chemical bonds produced in different reactions upon radiation. The concentration in c indicates the defect content. d, Energy difference ΔU between the 3/1-helix and all-trans conformations induced by different reactions associated with ion irradiation.
Extended Data Fig. 7 TDSC, bandgap, leakage current and conductive loss in irradiated terpolymers.
a, TSDC results. The peak at around 25 °C shifts towards lower temperatures as indicated by gray dashed arrow. The newly formed peak at around 50 °C in the irradiated terpolymer is indicated by the orange dashed arrow. b, UV-vis data where the bandgap Eg is indicated. c, Leakage current density. The results of the sandwiched PEI/irradiated P(VDF-TrFE-CTFE)/PEI films are also added. The solid lines are indicative of the fitting results by the hopping model.
Extended Data Fig. 8 Phase-field simulation results.
Domain structures under the application of electric field (E = 200 MV m−1). a, σ = 0; Δ = 0; b, σ ≠ 0; Δ = 0 (σ = 88 MV m−1); c, σ ≠ 0; Δ ≠ 0 (σ = 88 MV m−1). d, Pm as a function of σ (Δ = 3.6 K). e, Pm as a function of total system size (σ = 88 MV m−1; Δ = 3.6 K).
Extended Data Fig. 9 Comparison of intrinsic and extrinsic energy storage properties, the results obtained by sandwiched films, and comparison between the high-entropy terpolymer and ferroelectric polymers.
a, εeff as a function of electric field in PVDF. b, Ud as a function of electric field in PVDF. c, Comparison of Ud. Under intrinsic condition, εeff is always smaller than relative dielectric constant εr measured at 1 V (red dashed line) in ferroelectrics independent of normal ferroelectric or relaxor ferroelectrics. Under extrinsic conditions, εeff can be much larger than the εr. For bulk PVDF, εr is around 10. Via pressing-and-folding technique and internal stress engineering, εeff exceeds 30 which is 3 times as large as εr of PVDF. As a result, markedly enhanced Ud is achieved by using extrinsic approaches, which can be much larger than intrinsic values of Ud in PVDF. d, P-E loops of the all-organic sandwiched films. e, Ud and η. f, A radar comparison of the high-entropy terpolymer and ferroelectric polymers in terms of their Ud, η, Eb, εr, and Pm. Terpolymer refers to the relaxor ferroelectric P(VDF-TrFE-CTFE) 65.6/26.7/7.7 mol% obtained in ref. 28. Data of PVDF were taken from ref. 8. g, Comparison of conductive loss between high-entropy terpolymers (x = 20 Mrad) and pristine terpolymers. The grey arrow is indictive of the suppression of conductive loss enabled by high-entropy approach.
Extended Data Fig. 10 Electrocaloric effect of irradiated high-entropy terpolymer.
a, Electrocaloric heat flux signal upon applying and removing an electric field of 40 MV m−1 in the high-entropy terpolymer (20 Mrad). b, Electrocaloric heat flux signal upon applying and removing an electric field of 40 MV m−1 in the pristine terpolymer (0 Mrad). c, Adiabatic temperature change ΔT as a function of applied electric field. The grey region depicts the low-field region. The dashed arrow indicates the enhancement due to high-entropy design. The state-of-the-art results in terpolymers modified by C = C double bonds (ref. 45) are also added for comparison. Error bars represent the standard deviation of the mean obtained from at least three measurements using different samples.
Supplementary information
Supplementary Information
Supplementary Notes 1 and 2, Figs. 1–26, Tables 1–12, refs. 1–75 and additional methods.
Supplementary Data 1
Atomic coordinates of the optimized computational models for the electronic structure and the DFT calculations used in the main text and Supplementary Information.
Source data
Source Data Fig. 2
Dielectric data plotted in Fig. 2a–d and polarization data plotted in Fig. 2e,f.
Source Data Fig. 3
XRD data plotted in Fig. 3b, FTIR data plotted in Fig. 3c,d, DFT results plotted in Fig. 3e,f, AFM-IR data plotted in Fig. 3g,h and phase-field simulation results plotted in Fig. 3l.
Source Data Fig. 4
Dielectric energy storage data plotted in Fig. 4a–d and loss data plotted in Fig. 4e,f.
Source Data Extended Data Fig./Table 2
Dielectric data plotted in Extended Data Fig. 2a–i.
Source Data Extended Data Fig./Table 3
P–E loop data plotted in Extended Data Fig. 3a–g and dielectric energy storage data plotted in Extended Data Fig. 3h,i.
Source Data Extended Data Fig./Table 4
PFM amplitude and phase data plotted in Extended Data Fig. 4a–d.
Source Data Extended Data Fig./Table 5
FTIR data plotted in Extended Data Fig. 5a–c and XRD data plotted in Extended Data Fig. 5d–g.
Source Data Extended Data Fig./Table 6
Configurational entropy data plotted in Extended Data Fig. 6b,c and DFT data plotted in Extended Data Fig. 6d.
Source Data Extended Data Fig./Table 7
Thermally stimulated depolarization current data plotted in Extended Data Fig. 7a, bandgap data plotted in Extended Data Fig. 7b and leakage current data plotted in Extended Data Fig. 7c.
Source Data Extended Data Fig./Table 8
Phase-field simulation results plotted in Extended Data Fig. 8d,e.
Source Data Extended Data Fig./Table 9
Dielectric energy storage data plotted in Extended Data Fig. 9a–f and loss data plotted in Extended Data Fig. 9g.
Source Data Extended Data Fig./Table 10
Electrocaloric effect data plotted in Extended Data Fig. 10a–c.
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Li, C., Liu, Y., Li, B. et al. Enhanced energy storage in high-entropy ferroelectric polymers. Nat. Mater. (2025). https://doi.org/10.1038/s41563-025-02211-z
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DOI: https://doi.org/10.1038/s41563-025-02211-z
