A van der Waals density functional theory study of poly(vinylidene difluoride) crystalline phases


Ferroelectric polymers, such as poly(vinylidene difluoride) (PVDF), have many potential applications in flexible electronic devices. PVDF has six experimentally observed polymorphs, three of which are ferroelectric. In this work we use density functional theory to investigate the structural properties, energetics and polarisation of the stable α-phase, its ferroelectric analogue, the δ-phase, and the β-phase, which has the best ferroelectric properties. The results from a variety of exchange and correlation functionals were compared and it was found that van der Waals (vdW) interactions have an important effect on the calculated crystal structures and energetics, with the vdW-DF functional giving the best agreement with experimental lattice parameters. The spontaneous polarisation was found to strongly correlate with the unit cell volumes, which depend on the functional used. While the relative phase energies were not strongly dependent on the functional, the cohesive energies were significantly underestimated using the PBE functional. The inclusion of vdW interactions is, therefore, important to obtain the correct lattice structures, polarisation and energetics of PVDF polymorphs.

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  1. 1.

    J.F. Scott, Science 315, 954 (2007)

    ADS  Article  Google Scholar 

  2. 2.

    T. Someya, Y. Kato, T. Sekitani, S. Iba, Y. Noguchi, Y. Murase, H. Kawaguchi, T. Sakurai, PNAS 102, 12321 (2005)

    ADS  Article  Google Scholar 

  3. 3.

    V. Cauda, G. Canavese, S. Stassi, J. Appl. Poly. Sci., 41667 (2015)

  4. 4.

    M. Poulsen, S. Ducharme, IEEE Trans. Dielectr. Electr. Insul. 17, 1028 (2010)

    Article  Google Scholar 

  5. 5.

    M. Bachmann, W.L. Gordon, S. Weinhold, J.B. Lando, J. Appl. Phys. 51, 5095 (1980)

    ADS  Article  Google Scholar 

  6. 6.

    M. Li, H.J. Wondergem, M.-J. Spijkman, K. Asadi, I. Katsouras, P.W.M. Blom, D.M. de Leeuw, Nat. Mater. 12, 433 (2013)

    ADS  Article  Google Scholar 

  7. 7.

    R. Gregorio Jr., E.M. Ueno, J. Mat. Sci. 34, 4489 (1999)

    ADS  Article  Google Scholar 

  8. 8.

    S.M. Nakhmanson, M.B. Nardelli, J. Bernholc. Phys. Rev. Lett. 92, 115504 (2004)

    ADS  Article  Google Scholar 

  9. 9.

    S.M. Nakhmanson, M.B. Nardelli, J. Bernholc. Phys. Rev. B 72, 115210 (2005)

    ADS  Article  Google Scholar 

  10. 10.

    H. Su, A. Strachan, W.A. Phys. Rev. B 70, 064101 (2004)

    ADS  Article  Google Scholar 

  11. 11.

    V. Ranjan, L. Yu, Phys. Rev. Lett. 99, 047801 (2007)

    ADS  Article  Google Scholar 

  12. 12.

    W. Wang, H. Fan, Y. Ye, Polymer 51, 3575 (2010)

    Article  Google Scholar 

  13. 13.

    Y. Pei, X.C. Zeng, J. Appl. Phys. 109, 093514 (2011)

    ADS  Article  Google Scholar 

  14. 14.

    J.C. Li, R.Q. Zhang, C.L. Wang, N.B. Wong, Phys. Rev. B 75, 155408 (2007)

    ADS  Article  Google Scholar 

  15. 15.

    N.J. Ramer, C.M. Raynor, K.A. Stiso, Polymer 47, 424 (2006)

    Article  Google Scholar 

  16. 16.

    N.J. Ramer, T. Marrone, K.A. Stiso, Polymer 47, 7160 (2006)

    Article  Google Scholar 

  17. 17.

    S.M. Nakhmanson, R. Korlacki, J.T. Johnston, S. Ducharme, Z. Ge, J.M. Takacs, Phys. Rev. B 81, 174120 (2010)

    ADS  Article  Google Scholar 

  18. 18.

    J. Kleis, B.I. Lundqvist, D.C. Langreth, E. Schröder, Phys. Rev. B 76, 100201(R) (2007)

    ADS  Article  Google Scholar 

  19. 19.

    S. Grimme J. Comput. Chem. 27, 1787 (2006)

    Article  Google Scholar 

  20. 20.

    M. Dion, H. Rydberg, E. Schröder, D.C. Langreth, B.I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)

    ADS  Article  Google Scholar 

  21. 21.

    K. Lee, E.D. Murray, L. Kong, B.I. Lundqvist, D.C. Langreth, Phys. Rev. B 82, 081101(R) (2010)

    ADS  Article  Google Scholar 

  22. 22.

    P. Giannozzi, S. Baroni, N. Bonini, et al., J. Phys. Condens. Matter 21, 395502 (2009)

    Article  Google Scholar 

  23. 23.

    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    ADS  Article  Google Scholar 

  24. 24.

    T. Thonhauser, V.R. Cooper, S. Li, A. Puzder, P. Hyldgaard, D.C. Langreth, Phys. Rev. B 76, 125112 (2007)

    ADS  Article  Google Scholar 

  25. 25.

    R. Sabatini, E. Kucukbenli, B. Kolb, T. Thonhauser, S. de Gironcoli, J. Phys.: Condens. Matter 24, 424209 (2012)

    ADS  Google Scholar 

  26. 26.

    R.D. King-Smith, D. Vanderbilt, Phys. Rev. B 47, 1651 (1993)

    ADS  Article  Google Scholar 

  27. 27.

    R. Resta, Rev. Mod. Phys. 66, 899 (1994)

    ADS  Article  Google Scholar 

  28. 28.

    M. Kobayashi, K. Tashiro, H. Tadokoro, Macromol. 8, 158 (1974)

    ADS  Article  Google Scholar 

  29. 29.

    R. Hasegawa, Y. Takahashi, Y. Chatani, H. Tadokoro, Polymer J. 3, 600 (1972)

    Article  Google Scholar 

  30. 30.

    Y. Takahashi, H. Tadokoro, Macromol. 16(12), 1880 (1983)

    ADS  Article  Google Scholar 

  31. 31.

    A. Itoh, Y. Takahashi, T. Furukawa, H. Yajima, Polymer J. 46, 207 (2014)

    Article  Google Scholar 

  32. 32.

    W.J. Kim, M.H. Han, Y.-H. Shin, H. Kim, E.K. Lee, J. Phys. Chem. B (2016)

  33. 33.

    F.W. Billmeyer Jr., J. Appl. Phys. 28, 1114 (1957)

    ADS  Article  Google Scholar 

  34. 34.

    N.A. Spaldin, J. Solid. State. Chem. 195, 2 (2012)

    ADS  Article  Google Scholar 

  35. 35.

    J.E. McKinney, G.T. Davis, M.G. Broadhurst, J. Appl. Phys. 51, 1676 (1980)

    ADS  Article  Google Scholar 

  36. 36.

    K. Nakamura, M. Nagai, T. Kanamoto, Y. Takahashi, T. Furukawa, J. Polymer Science Part B: Polymer Physics 39(12), 1371 (2001)

    ADS  Article  Google Scholar 

  37. 37.

    K. Noda, K. Ishida, A. Kubono, T. Horiuchi, H. Yamada, K. Matsushige, J. Appl. Phys. 93, 2866 (2003)

    ADS  Article  Google Scholar 

  38. 38.

    N.J. Ramer, K.A. Stiso, Polymer 46, 10431 (2005)

    Article  Google Scholar 

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Correspondence to F. Pelizza or K. Johnston.

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Pelizza, F., Smith, B. & Johnston, K. A van der Waals density functional theory study of poly(vinylidene difluoride) crystalline phases. Eur. Phys. J. Spec. Top. 225, 1733–1742 (2016). https://doi.org/10.1140/epjst/e2016-60133-8

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