The equation of state of polymers. Part III: Relation with the compensation law

Regular Article

Abstract.

The properties of amorphous polymers and of organic compounds under pressure are interpreted in the framework of the modified Van der Walls Equation of State (mVW-EOS) the Vogel-Fulcher-Tamann (VFT) law and of the compensation law. We have shown recently that polymers and organic compounds in amorphous liquid and crystalline states verify the mVW-EOS which depends on three parameters, \(P^{\ast}\)\(V^{\ast}\) and \(T^{\ast}\). In this paper we compare the characteristic pressure \(P^{\ast}\) of the mVW-EOS to the various pressures \(P_{X}= \Delta H_{X}/\Delta V_{X}\) deduced from thermodynamic and kinetic properties of polymers in the liquid and solid states. \(\Delta H_{X}\) and \(\Delta V_{X}\) are: a) the enthalpy and volume change at the melting and glass transitions (the glass being isotropic or oriented and annealed below \(T_{g}\) at various aging conditions); b) the activation parameters of individual \(\beta\) and cooperative \(\alpha\) motions in crystalline liquid and amorphous polymers studied by dielectric or mechanical spectroscopy; and c) the activation parameters of amorphous (solid and liquid) polymers submitted to a deformation depending on the time frequency temperature and strain rate. For a same material, whatever its state and whatever the experimental properties analyzed (dielectric and mechanical relaxation, viscosity, auto-diffusion, yielding under hydrostatic pressure), we demonstrate that \(P_{X}=P^{\ast}=1/\gamma\kappa\), (\(\gamma\) Grüneisen parameter, \(\kappa\) compressibility). In all polymers and organic compounds (and water), these pressures, weakly dependent on T and P near \(T_{g}\) and \( T_{m}\) at low pressure are characteristic of the H-H inter-molecular interactions. It is shown that the two empirical Lawson and Keyes relations of the compensation law can be deduced from the mVW-EOS.

Graphical abstract

Keywords

Soft Matter: Polymers and Polyelectrolytes 

References

  1. 1.
    J. Rault, Eur. Phys. J. E 37, 113 (2014)CrossRefGoogle Scholar
  2. 2.
    J. Rault, Eur. Phys. J. E 38, 91 (2015)ADSCrossRefGoogle Scholar
  3. 3.
    E. Brosh, G. Makov, R.Z. Shneck, J. Phys.: Condens. Matter 15, 2991 (2003)ADSGoogle Scholar
  4. 4.
    J.H. Rose, J. Smith, F. Guinea, J. Ferrante, Phys. Rev. B 29, 2963 (1984)ADSCrossRefGoogle Scholar
  5. 5.
    V.G. Baonza, M. Céceres, J. Nünez, Phys. Rev. B 51, 28 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    M. Taravillo, M. Baonza, V.G. Nunez, M. Caceres, High Temp. High Pressure 30, 97 (1998)CrossRefGoogle Scholar
  7. 7.
    J. Rault, Eur. Phys. J. E 35, 26 (2012)CrossRefGoogle Scholar
  8. 8.
    J.C. Slater, Introduction to Chemical Physics (McGraw-Hill, New York, 1939)Google Scholar
  9. 9.
    T.H.K. Barron, G.K. White, Heat Capacity and Thermal Expansion at Low Pressure (Kluker Academic, New York, 1999)Google Scholar
  10. 10.
    W. Meyer, H. Neldel, Z. Tech. Phys. 12, 588 (1937)Google Scholar
  11. 11.
    R.W. Keyes, J. Chem. Phys. 29, 467 (1958)ADSCrossRefGoogle Scholar
  12. 12.
    A.W. Lawson, J. Phys. Solids 3, 250 (1957)ADSCrossRefGoogle Scholar
  13. 13.
    A.W. Lawson, J. Chem. Phys. 32, 131 (1960)ADSCrossRefGoogle Scholar
  14. 14.
    A. Yelon, B. Movagha, Phys. Rev. Lett. 65, 618 (1960)ADSCrossRefGoogle Scholar
  15. 15.
    A. Yelon, B. Movagha, H.M. Branz, Phys. Rev. B 46, 12244 (1992)ADSCrossRefGoogle Scholar
  16. 16.
    E. Peacock-Lopez, H. Suhl, Phys. Rev. B 26, 3774 (1982)ADSCrossRefGoogle Scholar
  17. 17.
    K.L. Ngai, Solid State Ionics 105, 23 (1998)Google Scholar
  18. 18.
    K.F. Freed, J. Phys. Chem. B 115, 1689 (2011)CrossRefGoogle Scholar
  19. 19.
    L. Liu, Q.-X. Guo, Chem. Rev. 101, 673 (2001)CrossRefGoogle Scholar
  20. 20.
    T. Psurek, C.L. Soles, K.A. Page, M.T. Marcus, T. Cicerone, J.F. Douglas, J. Phys. Chem. B 112, 15980 (2008)CrossRefGoogle Scholar
  21. 21.
    A. Anopchenko, T. Psurek, V. VanderHart, J.F. Douglas, J. Obbrzut, Phys. Rev. E 74, 031501 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Y. Hiki, H. Takahashi, H. Kobayashi, Solid State Ionics 53-56, 1157 (1992)CrossRefGoogle Scholar
  23. 23.
    Y. Hiki, J. Non-Cryst. Solids 357, 357 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    Y. Adda, J. Philibert, La diffusion dans les solides (Presses Universitaires, 1966)Google Scholar
  25. 25.
    J. Philibert, Trans. Tech. Publ. 249, 61 (2006)Google Scholar
  26. 26.
    J. Rault, J. Non-Cryst. Solids 235-237, 737 (1998)ADSCrossRefGoogle Scholar
  27. 27.
    A.L. Kovarskii, High-Pressure Chemistry and Physics of Polymers (CRC Press, Boca Raton, 1993)Google Scholar
  28. 28.
    J.E. Mark (Editor), Physical Properties of Polymers Handbook (AIP Press, NY, 1995)Google Scholar
  29. 29.
    P. Zoller, J. Polym. Sci.: Polym. Phys. 16, 1261 (1978)ADSGoogle Scholar
  30. 30.
    Kell Whalley, J. Chem. Phys. 62, 1063 (2008)Google Scholar
  31. 31.
    J. Shanker, M. Kumar, Phys. Status Solidi B 179, 351 (1993)ADSCrossRefGoogle Scholar
  32. 32.
    T. Uchida, Y. Wang, M.L. Rivers, S.R. Sutton, J. Geophys. Res. B 106, 21799 (2001)ADSCrossRefGoogle Scholar
  33. 33.
    F.H. Fisher, O.E. Dial, Equation of State of Pure and Sea Water, Rep. SIO reference 75-28Google Scholar
  34. 34.
    J. Rault, Physical Aging of Glasses: the VFT approach (Nova Science Publishers, New York, 2009)Google Scholar
  35. 35.
    D.W. Van Krevelen, Properties of Polymers (Elsevier, Amsterdam, 1990)Google Scholar
  36. 36.
    J.I. Berg, R. Simha, J. Non-Cryst. Solids 22, 1 (1976)ADSCrossRefGoogle Scholar
  37. 37.
    E. Donth, The Glass Transition (Springer, Berlin, 2001)Google Scholar
  38. 38.
    R. Keller, W.B. Holzapfel, H. Schulz, Phys. Rev. 16, 1403 (1977)CrossRefGoogle Scholar
  39. 39.
    H. Liu, L. Wang, X. Xiao, F. De Carlo, J. Feng, H. Mao, R. Hemley, Proc. Natl. Acad. Sci. U.S.A. 105, 13229 (2008)ADSCrossRefGoogle Scholar
  40. 40.
    A. Drozd-Rzoska, S.J. Rzoska, A.R. Imre, J. Non-Cryst. Solids 353, 3915 (2007)ADSCrossRefGoogle Scholar
  41. 41.
    D. Fragiadakis, M.C. Roland, J. Phys. Rev. E 83, 031504 (2011)ADSCrossRefGoogle Scholar
  42. 42.
    J.P. Poirier, Geophys. J. 92, 99 (1988)ADSCrossRefGoogle Scholar
  43. 43.
    J. Rault, J. Phys.: Condens. Matter 15, S 1193 (2003)ADSGoogle Scholar
  44. 44.
    J. Rault, J. Non-Cryst. Solids 357, 339 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    J. Rault, J. Non-Cryst. Solids 352, 4946 (2006)ADSCrossRefGoogle Scholar
  46. 46.
    N.H. Nachtrieb, Adv. Phys. 16, 309 (1967)ADSCrossRefGoogle Scholar
  47. 47.
    V.A. Bershtein, V.M. Egorov, Differential Scanning Calorimetry of Polymers (Ellis Horwoood, Chischester, UK, 1994)Google Scholar
  48. 48.
    E. Donth, The Glass Transition (Springer, Berlin, 2001)Google Scholar
  49. 49.
    C. Bauwens-Crozet, J.C. Bauwens, Polymer 23, 1599 (1982)CrossRefGoogle Scholar
  50. 50.
    G. Adam, A. Cross, R.N.J. Haward, J. Mat. Sci. 10, 1582 (1975)ADSCrossRefGoogle Scholar
  51. 51.
    W.D. Cook, M. Mehrabi, G.H. Edward, Polymer 40, 1209 (1990)CrossRefGoogle Scholar
  52. 52.
    C. Bauwens-Crozet, J.C. Bauwens, G. Homes, J. Polym. Sci. 7, A-2 (1969)Google Scholar
  53. 53.
    E. Pink, H. Bouda, B.H. Bäck, Mater. Sci. Eng. 38, 89 (1979)CrossRefGoogle Scholar
  54. 54.
    F. Povolo, G. Schwartz, E.B. Hermida, J. Appl. Polym. Sci. 61, 109 (1996)CrossRefGoogle Scholar
  55. 55.
    Y. Nanzai, Prog. Polym. Sci. 18, 437 (1993)CrossRefGoogle Scholar
  56. 56.
    Y. Nanzai, N. Nakayama, J. Non-Cryst. Solids 172-174, 771 (1994)ADSCrossRefGoogle Scholar
  57. 57.
    Y. Nanzai, ISME Int. J. A 37, 149 (1994)Google Scholar
  58. 58.
    Y. Nanzai, T. Yamasaki, S. Yoshioka, ISME Int. J. A 41, 31 (1998)CrossRefGoogle Scholar
  59. 59.
    J.M. Lefebre, B. Escaig, J. Mater. Sci. 20, 438 (1985)ADSCrossRefGoogle Scholar
  60. 60.
    H.W. Zhang, G. Subhash, X.N. Jing, L.J. Kecskes, R.J. Dowding, Philos. Mag. Lett. 86, 333 (2006)ADSCrossRefGoogle Scholar
  61. 61.
    R.N. Haward, The Physics of Glassy Polymers (Applied Science Publishers Ltd, London, 1973)Google Scholar
  62. 62.
    S. Rabinowitz, I.M. Ward, J.S.C. Parry, J. Mater. Sci. 5, 29 (1970)ADSCrossRefGoogle Scholar
  63. 63.
    J.A. Sauer, D.R. Mears, K.D. Pae, J. Mater. Sci. 24, 451 (1970)Google Scholar
  64. 64.
    K.I. Tsirule, E.L. Tyunina, in High Pressure and Physics of Polymers, edited by A.L. Kovarskii (CRC Press, Boca Raton, US, 1994). Google Scholar
  65. 65.
    C.P.R. Hoppel, T.A. Bogetti, W. Gillepie, J. Therm. Comput. Mater. 8, 375 (1995)CrossRefGoogle Scholar
  66. 66.
    W.A. Spitzig, O. Richmond, Polym. Eng. Sci. 19, 1129 (1979)CrossRefGoogle Scholar
  67. 67.
    J.O. Chua, A.L. Ruoff, J. Appl. Phys. 46, 4659 (1975)ADSCrossRefGoogle Scholar
  68. 68.
    H.B. Yu, K. Samwer, Y. Wu, W.H. Wang, Phys. Rev. Lett. 109, 095508 (2012)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Laboratoire de Physique des Solides, CNRSUniversité de Paris-SudOrsayFrance

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