Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Electro-thermal actuation in percolative ferroelectric polymer nanocomposites


The interconversion between electrical and mechanical energies is pivotal to ferroelectrics to enable their applications in transducers, actuators and sensors. Ferroelectric polymers exhibit a giant electric-field-induced strain (>4.0%), markedly exceeding the actuation strain (≤1.7%) of piezoelectric ceramics and crystals. However, their normalized elastic energy densities remain orders of magnitude smaller than those of piezoelectric ceramics and crystals, severely limiting their practical applications in soft actuators. Here we report the use of electro-thermally induced ferroelectric phase transition in percolative ferroelectric polymer nanocomposites to achieve high strain performance in electric-field-driven actuation materials. We demonstrate a strain of over 8% and an output mechanical energy density of 11.3 J cm−3 at an electric field of 40 MV m−1 in the composite, outperforming the benchmark relaxor single-crystal ferroelectrics. This approach overcomes the trade-off between mechanical modulus and electro-strains in conventional piezoelectric polymer composites and opens up an avenue for high-performance ferroelectric actuators.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Electro-thermal actuation performance of the PVDF/TiO2 nanocomposite.
Fig. 2: Thermally induced phase transition in the PVDF/TiO2 nanocomposite.
Fig. 3: Electro-thermal phase transition in the PVDF/TiO2 nanocomposite.
Fig. 4: Structural analysis of the induced polar phase and phase-field simulations in the PVDF/TiO2 nanocomposite.

Data availability

The main data supporting the findings of this study are available within this Article and its Supplementary Information. The Source Data that support the findings of this study are publicly available via figshare at Source data are provided with this paper.

Code availability

Quantum ESPRESSO for DFT calculations is available at The atomic coordinates of the optimized computational models are publicly available via figshare at


  1. Park, S. E. & Shrout, T. R. Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals. J. Appl. Phys. 82, 1804–1811 (1997).

    Article  CAS  Google Scholar 

  2. Li, F. et al. Giant piezoelectricity of Sm-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals. Science 364, 264–268 (2019).

    Article  CAS  Google Scholar 

  3. Liao, W. Q. et al. A molecular perovskite solid solution with piezoelectricity stronger than lead zirconate titanate. Science 363, 1206–1210 (2019).

    Article  CAS  Google Scholar 

  4. Liu, H. et al. Giant piezoelectricity in oxide thin films with nanopillar structure. Science 369, 292–297 (2020).

    Article  CAS  Google Scholar 

  5. Zhang, Q. M., Bharti, V. & Zhao, X. Giant electrostriction and relaxor ferroelectric behavior in electron-irradiated poly(vinylidene fluoride-trifluoroethylene) copolymer. Science 280, 2101–2104 (1998).

    Article  CAS  Google Scholar 

  6. Liu, Y. et al. Ferroelectric polymers exhibiting behaviour reminiscent of a morphotropic phase boundary. Nature 562, 96–100 (2018).

    Article  CAS  Google Scholar 

  7. Chen, X. et al. Relaxor ferroelectric polymer exhibits ultrahigh electromechanical coupling at low electric field. Science 375, 1418–1422 (2022).

    Article  CAS  Google Scholar 

  8. Jaffe, B., Roth, R. S. & Marzullo, S. Piezoelectric properties of lead zirconate-lead titanate solid-solution ceramics. J. Appl. Phys. 25, 809–810 (1954).

    Article  CAS  Google Scholar 

  9. Guo, R. et al. Origin of the high piezoelectric response in PbZr1–xTixO3. Phys. Rev. Lett. 84, 5423–5426 (2000).

    Article  CAS  Google Scholar 

  10. Cross, L. E. Ferroelectric ceramics: materials and application issues. Ceram. Trans. 68, 15–55 (1996).

    CAS  Google Scholar 

  11. Xu, H. et al. Ferroelectric and electromechanical properties of poly(vinylidene-fluoride-trifluoroethylene-chlorotrifluoroethylene) terpolymer. Appl. Phys. Lett. 78, 2360–2362 (2001).

    Article  CAS  Google Scholar 

  12. Li, F. et al. Ultrahigh piezoelectricity in ferroelectric ceramics by design. Nat. Mater. 17, 349–354 (2018).

    Article  CAS  Google Scholar 

  13. Fook, T. H. T., Jeon, J. H. & Lee, P. S. Transparent flexible polymer actuator with enhanced output force enabled by conductive nanowires interlayer. Adv. Mater. Technol. 5, 1900762 (2020).

    Article  CAS  Google Scholar 

  14. Choi, S. T., Kwon, J. O. & Bauer, F. Multilayered relaxor ferroelectric polymer actuators for low-voltage operation fabricated with an adhesion-mediated film transfer technique. Sens. Actuator A Phys. 203, 282–290 (2013).

    Article  Google Scholar 

  15. Kim, J. S. et al. Sensing and memorising liquids with polarity-interactive ferroelectric sound. Nat. Commun. 10, 3575 (2019).

    Article  Google Scholar 

  16. Liu, Y. et al. Chirality-induced relaxor properties in ferroelectric polymers. Nat. Mater. 19, 1169–1174 (2020).

    Article  CAS  Google Scholar 

  17. Gao, X. et al. Piezoelectric actuators and motors: materials, designs, and applications. Adv. Mater. Technol. 5, 1900716 (2020).

    Article  CAS  Google Scholar 

  18. Zhang, Q. M. et al. An all-organic composite actuator material with a high dielectric constant. Nature 419, 284–287 (2002).

    Article  CAS  Google Scholar 

  19. Davis, G. T., McKinney, J. E., Broadhurst, M. G. & Roth, S. C. Electric‐field‐induced phase changes in poly(vinylidene fluoride). J. Appl. Phys. 49, 4998–5002 (1978).

    Article  CAS  Google Scholar 

  20. Ranjan, V., Nardelli, M. B. & Bernholc, J. Electric field induced phase transitions in polymers: a novel mechanism for high speed energy storage. Phys. Rev. Lett. 108, 087802 (2012).

    Article  CAS  Google Scholar 

  21. Bellet-Amalricand, E. & Legrand, J. F. Crystalline structures and phase transition of the ferroelectric P(VDF-TrFE) copolymers, a neutron diffraction study. Eur. Phys. J. B 3, 225–236 (1998).

    Article  Google Scholar 

  22. Jani, J. M., Leary, M., Subic, A. & Gibson, M. A. A review of shape memory alloy research, applications and opportunities. Mater. Des. 56, 1078–1113 (2014).

    Article  Google Scholar 

  23. Huber, J. E., Fleck, N. A. & Ashby, M. F. The selection of mechanical actuators based on performance indices. Proc. R. Soc. Lond. A 453, 2185–2205 (1997).

    Article  Google Scholar 

  24. Liu, Y. et al. Structural insight in the interfacial effect in ferroelectric polymer nanocomposites. Adv. Mater. 32, 2005431 (2020).

    Article  CAS  Google Scholar 

  25. Huang, X., Jiang, P. & Xie, L. Ferroelectric polymer/silver nanocomposites with high dielectric constant and high thermal conductivity. Appl. Phys. Lett. 95, 242901 (2009).

    Article  Google Scholar 

  26. Zhang, G., Li, Y., Tang, S., Thompson, R. D. & Zhu, L. The role of field electron emission in polypropylene/aluminum nanodielectrics under high electric fields. ACS Appl. Mater. Interfaces 9, 10106–10119 (2017).

    Article  CAS  Google Scholar 

  27. Yang, X., Hu, J., Chen, S. & He, J. L. Understanding the percolation characteristics of nonlinear composite dielectrics. Sci. Rep. 6, 30597 (2016).

    Article  CAS  Google Scholar 

  28. Almond, D. P. & Bowen, C. R. Anomalous power law dispersions in a.c. conductivity and permittivity shown to be characteristics of microstructural electrical networks. Phys. Rev. Lett. 92, 157601 (2004).

    Article  CAS  Google Scholar 

  29. Geng, H. et al. Giant electric field-induced strain in lead-free piezoceramics. Science 378, 1125–1130 (2022).

    Article  CAS  Google Scholar 

  30. Trolier-McKinstry, S., Zhang, S., Bell, A. J. & Tan, X. High-performance piezoelectric crystals, ceramics, and films. Annu. Rev. Mater. Res. 48, 191–217 (2018).

    Article  CAS  Google Scholar 

  31. Martins, P., Lopes, A. C. & Lanceros-Mendez, S. Electroactive phases of poly(vinylidene fluoride): determination, processing and applications. Prog. Polym. Sci. 39, 683–706 (2014).

    Article  CAS  Google Scholar 

  32. Su, J., Moses, P. & Zhang, Q. M. A bimorph based dilatometer for field induced strain measurement in soft and thin free standing polymer films. Rev. Sci. Instrum. 69, 2480–2483 (1998).

    Article  CAS  Google Scholar 

  33. Wang, J., Ma, X., Li, Q., Britson, J. & Chen, L. Q. Phase transitions and domain structures of ferroelectric nanoparticles: phase field model incorporating strong mechanical and dielectric inhomogeneity. Acta Mater. 61, 7591–7603 (2013).

    Article  CAS  Google Scholar 

  34. Bakri, A. et al. Effect of annealing temperature of titanium dioxide thin films on structural and electrical properties. AIP Conf. Proc. 1788, 030030 (2017).

    Article  Google Scholar 

  35. Li, Y. L., Hu, S. Y., Liu, Z. K. & Chen, L. Q. Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films. Acta Mater. 50, 395–411 (2002).

    Article  CAS  Google Scholar 

  36. Chen, L. Q. Phase‐field method of phase transitions/domain structures in ferroelectric thin films: a review. J. Am. Ceram. Soc. 91, 1835–1844 (2008).

    Article  CAS  Google Scholar 

  37. Gomes, J., Nunes, J. S., Sencadas, V. & Lanceros-Méndez, S. Influence of the β-phase content and degree of crystallinity on the piezo- and ferroelectric properties of poly(vinylidene fluoride). Smart Mater. Struct. 19, 065010 (2010).

    Article  Google Scholar 

  38. Wang, B. & Huang, H. X. Incorporation of halloysite nanotubes into PVDF matrix: nucleation of electroactive phase accompany with significant reinforcement and dimensional stability improvement. Compos. A: Appl. Sci. Manuf. 66, 16–24 (2014).

    Article  CAS  Google Scholar 

  39. Hummer, D., Heaney, P. J. & Post, J. Thermal expansion of anatase and rutile between 300 and 575 K using synchrotron powder X-ray diffraction. Powder Diffr. 22, 352–357 (2007).

    Article  CAS  Google Scholar 

  40. Chen, L. Q. & Shen, J. Applications of semi-implicit Fourier-spectral method to phase field equations. Comput. Phys. Commun. 108, 147–158 (1998).

    Article  CAS  Google Scholar 

  41. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

  42. Prandini, G., Marrazzo, A., Castelli, I. E., Mounet, N. & Marzari, N. Precision and efficiency in solid-state pseudopotential calculations. npj Comput. Mater. 4, 72 (2018).

    Article  Google Scholar 

  43. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  CAS  Google Scholar 

  44. Thonhauser, T. et al. Van der Waals density functional: self-consistent potential and the nature of the van der Waals bond. Phys. Rev. B 76, 125112 (2007).

    Article  Google Scholar 

  45. Li, F., Xu, Z. & Zhang, S. J. The effect of polar nanoregions on electromechanical properties of relaxor-PbTiO3 crystals: extracting from electric-field-induced polarization and strain behaviors. Appl. Phys. Lett. 105, 122904 (2014).

    Article  Google Scholar 

Download references


This research was funded by the US AFOSR (FA9550-19-1-0008 to Q.W.), the US ONR (N00014-19-1-2033 to J.B.), the National Natural Science Foundation of China (12274152 to Y.L.) and initial financial support from HUST (3004110155 to Y.L.). The phase-field simulation effort was supported as part of the Computational Materials Sciences Program funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (award no. DE-SC0020145 to T.Y. and L.-Q.C.), and the Mu-PRO Ferroelectric software package was used. The atomistic calculations were performed at Oak Ridge Leadership Computing Facility, supported by DOE contract DE-AC05-00OR22725.

Author information

Authors and Affiliations



Y.L. and Q.W. conceived and designed the research. Y.L. and Y.Z. prepared the samples. Y.L., Y.Z. and X.C. conducted the electrical and electromechanical measurements. Y.L. and X.C. collected the XRD and FTIR data under an electric field. Y.L. performed the temperature-dependent XRD and dielectric measurements. Y.L. and Y.Z. performed the AFM-IR measurements. Y.L. and X.C. measured the Joule heating, temperature change and fatigue tests. Y.Z. performed the DSC and piezoelectric measurements. Y.Z., X.C. and Z.H. performed the blocking force and strain–frequency measurements. L.L. and K.W. carried out the transmission electron microscopy measurements. H.Q., B.Z., W.L. and J.B. performed and analysed the DFT calculations. T.Y. and L.-Q.C. performed and analysed the phase-field simulations. Y.L., Y.Z. and Q.W. wrote the manuscript with input from all authors. Q.W. supervised the research.

Corresponding authors

Correspondence to Yang Liu or Qing Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Chris Bowen, Senentxu Lanceros-Méndez and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Strain-electric field loops of the PVDF/TiO2 nanocomposites with different TiO2 contents under various bipolar electric fields at 1 Hz.

a, 0 vol%. b, 2.1 vol%. c, 4.3 vol%. d, 9.3 vol%. e, 12.0 vol%. f, 14.9 vol%. g, 21.4 vol%.

Source data

Extended Data Fig. 2 Electrical conduction of the PVDF/TiO2 nanocomposites.

a, Conduction current density of the PVDF/TiO2 nanocomposites under 10 MV m−1 electric field. b, TiO2 content-dependent conductivity of the PVDF/TiO2 nanocomposites. The red line is the fitting of the conductivity by the percolation model, which gives a percolation threshold (fc) of about 15 vol% as indicated by the blue line.

Source data

Extended Data Fig. 3 Temperature-dependent dielectric spectra of the PVDF/TiO2 nanocomposites with different TiO2 contents at 1 kHz.

a, Dielectric constant. b, Dissipation factor. The red arrows indicate the electro-thermal phase transition temperature of about 29 °C.

Source data

Extended Data Fig. 4 Comparison of different types of phase transitions in ferroelectric polymers.

Top panel: a typical ferroelectric-to-paraelectric phase transition is characterized by a structure change from orthorhombic phase to hexagonal phase, which can be triggered by heating above the Curie temperature. The application of an electric field always favors the orthorhombic ferroelectric phase. In the low field regime (≤50 MV m−1), only piezoelectricity or electrostriction contributes to the strain response. Bottom panel: electro-thermal phase transition corresponds to phase switching from orthorhombic phase to monoclinic phase induced by directly heating or the Joule heat from the applied electric field. Here, an electric field may stabilize the monoclinic nonpolar phase rather than the orthorhombic polar phase. The electric field can be as low as around 40 MV m−1 in percolative polymer nanocomposites.

Extended Data Fig. 5 Unipolar and frequency-dependent strain of the percolative PVDF/TiO2 nanocomposites (=14.9 vol%).

a, Comparison of the strain-electric field loops of the percolative PVDF/TiO2 nanocomposite under 40 MV m−1 bipolar and unipolar electric field. b, Frequency-dependent strain of the percolative PVDF/TiO2 nanocomposite. Error bars represent the standard deviation of the mean obtained from at least three measurements using different samples.

Source data

Extended Data Fig. 6 Temperature changes in PVDF and percolative PVDF/TiO2 nanocomposite (\(\bf {c}_{{{\rm{TiO}}}_{2}}\) = 14.9 vol%).

The temperature change is generated due to Joule heating upon the application of an electric field of 40 MV m−1.

Source data

Extended Data Fig. 7 Electro-thermal actuation of the PVDF/ZnO nanocomposites.

a, Strain of the PVDF/ZnO nanocomposites under various bipolar electric fields at 1 Hz. Error bars represent the standard deviation of the mean obtained from at least three measurements using different samples. b-h, Strain-electric field loops of the PVDF/ZnO nanocomposites with the ZnO content of 0 vol% (b), 2.1 vol% (c), 4.3 vol% (d), 9.3 vol% (e), 12.0 vol% (f), 14.9 vol% (g) and 21.4 vol% (h) under various bipolar electric fields at 1 Hz.

Source data

Extended Data Fig. 8 Electro-thermal actuation of the P(VDF-HFP)/TiO2 nanocomposites.

a, Strain of the P(VDF-HFP)/TiO2 nanocomposites under various bipolar electric fields at 1 Hz. Error bars represent the standard deviation of the mean obtained from at least three measurements using different samples. b, Strain-electric field loops of the P(VDF-HFP)/TiO2-14.9 vol% nanocomposite under various bipolar electric fields at 1 Hz.

Source data

Extended Data Fig. 9 Temperature-dependent strain upon heating.

a, PVDF/ZnO. b, PVDF/TiO2-nanowires. c, P(VDF-HFP)/TiO2. The thermally-induced strain in PVDF/ZnO, PVDF/TiO2-nanowires and P(VDF-HFP)/TiO2 is 5.4%, 0.28% and 3.9%, which are consistent well with the electric field-induced strain triggered by Joule heating of 5.3%, 0.21% and 3.7%, respectively.

Source data

Extended Data Table 1 Comparison of the electromechanical responses in typical actuation materials

Supplementary information

Supplementary Information

Supplementary Figs. 1–16, Notes 1–3, Tables 1 and 2 and references 1–13.

Source data

Source Data Fig. 1

Bipolar electric field–strain data (Fig. 1b), strain–electric field loops (Fig. 1c), normalized strain data (Fig. 1d) and comparison of the electromechanical performance data (Fig. 1e).

Source Data Fig. 2

Temperature-dependent dielectric constant data (Fig. 2a), temperature-dependent strain data (Fig. 2b) and XRD data (Fig. 2c,d).

Source Data Fig. 3

XRD data (Fig. 3a), FTIR data (Fig. 3b) and strain and temperature data (Fig. 3d).

Source Data Fig. 4

Local IR data (Fig. 4c,d).

Source Data Extended Data Fig. 1

Strain–electric field data (Extended Data Fig. 1a–g).

Source Data Extended Data Fig. 2

Conduction current density data (Extended Data Fig. 2a) and conductivity data (Extended Data Fig. 2b).

Source Data Extended Data Fig. 3

Dielectric constant data (Extended Data Fig. 3a) and dissipation data (Extended Data Fig. 3b).

Source Data Extended Data Fig. 5

Strain–electric field data (Extended Data Fig. 5a) and frequency-dependent strain data (Extended Data Fig. 5b).

Source Data Extended Data Fig. 6

Temperature change data (Extended Data Fig. 6).

Source Data Extended Data Fig. 7

Strain data (Extended Data Fig. 7a) and strain–electric field data (Extended Data Fig. 7b–h).

Source Data Extended Data Fig. 8

Strain data (Extended Data Fig. 8a) and strain–electric field data (Extended Data Fig. 8b).

Source Data Extended Data Fig. 9

Temperature-dependent strain data (Extended Data Fig. 9a–c).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Zhou, Y., Qin, H. et al. Electro-thermal actuation in percolative ferroelectric polymer nanocomposites. Nat. Mater. (2023).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing