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Study on enthalpy relaxation of glassy polystyrene using a structure-dependent Kohlrausch stretch exponent combined with coupling model

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Abstract

In this paper the enthalpy relaxation of polystyrene (PS) was restudied using a structure-dependent Kohlrausch stretch exponent β with incorporation of a coupling model (CM). The structure dependence of β is described in 3 semi-phenomenological equations. The temperature and structure dependence of the relaxation time of the Johari-Goldstein (JG) relaxation (τ JG) is presented using the traditional Tools-Narayanaswamy-Moynihan (TNM) and Adam-Gibbs-Vogel (AGV) equations. The fitting results of heat capacity data are much better than the conventional TNM and Adam-Gibbs (AG) models when the structure dependence of β is described using an exponential equation and τ JG is calculated using the AGV equation, although there are one fewer fitting parameters in the new model. The results indicate that both the structure dependence of β and the CM model may play considerable roles in the investigation on the structure relaxation process in polymers around the glass transition.

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References

  1. D. Cangialosi, V.M. Boucher, A. Alegría, J. Colmenero, Soft Matter 9, 8619 (2013).

    Article  ADS  Google Scholar 

  2. P.J. Pan, B. Zhu, Y. Inoue, Macromolecules 40, 9664 (2007).

    Article  ADS  Google Scholar 

  3. L. Andreozzi, M. Faetti, F. Zulli, M. Giordano, Macromolecules 37, 8010 (2004).

    Article  ADS  Google Scholar 

  4. A.D. Drozdov, Eur. Polym. J. 37, 1379 (2001).

    Article  Google Scholar 

  5. T.G. Fox, P.J. Flory, J. Phys. Chem. 55, 221 (1951).

    Article  Google Scholar 

  6. J.H. Gibbs, E.A. DiMarzio, J. Chem. Phys. 28, 373 (1958).

    Article  ADS  Google Scholar 

  7. J.L. Gómez Ribelles, M. Monleón Pradas, Macromolecules 28, 5867 (1995).

    Article  ADS  Google Scholar 

  8. A. Brunacci, J.M.G. Cowie, R. Ferguson, J.L. Gómez Ribelles, A. Vidaurre Garayo, Macromolecules 29, 7976 (1996).

    Article  ADS  Google Scholar 

  9. J.M.G. Cowie, S. Harris, I.J. McEwen, J. Polym. Sci. Part B, Polym. Phys. 35, 1107 (1997).

    Article  ADS  Google Scholar 

  10. L. Andreozzi, M. Faetti, M. Giordano, F. Zulli, Macromolecules 38, 6056 (2005).

    Article  ADS  Google Scholar 

  11. V.M. Boucher, D. Cangialosi, A. Alegría, J. Colmenero, Macromolecules 44, 8333 (2011).

    Article  ADS  Google Scholar 

  12. J.M. Hutchinson, P. Kumar, Thermochim. Acta 391, 197 (2002).

    Article  Google Scholar 

  13. Q.X. Li, S.L. Simon, Polymer 47, 4781 (2006).

    Article  Google Scholar 

  14. Y.P. Koh, S.L. Simon, Macromolecules 46, 5815 (2013).

    Article  ADS  Google Scholar 

  15. D. Cangialosi, V.M. Boucher, A. Alegría, J. Colmenero, Phys. Rev. Lett. 111, 095701 (2013).

    Article  ADS  Google Scholar 

  16. R. Kohlrausch, Ann. Phys. Chem. 91, 179 (1854).

    Article  ADS  Google Scholar 

  17. G. Williams, D.C. Watts, Trans. Faraday Soc. 66, 80 (1970).

    Article  Google Scholar 

  18. D.W. Davidson, R.H. Cole, J. Chem. Phys. 18, 1417 (1950).

    Article  ADS  Google Scholar 

  19. H. Vogel, Z. Phys. 22, 645 (1921).

    Google Scholar 

  20. M.L. Williams, R.F. Landel, J.D. Ferry, J. Am. Chem. Soc. 77, 3701 (1955).

    Article  Google Scholar 

  21. G. Adam, J.H. Gibbs, J. Chem. Phys. 43, 139 (1965).

    Article  ADS  Google Scholar 

  22. A.Q. Tool, J. Am. Ceram. Soc. 29, 240 (1946).

    Article  Google Scholar 

  23. O.S. Narayanaswamy, J. Am. Ceram. Soc. 54, 491 (1971).

    Article  Google Scholar 

  24. C.T. Moynihan, A.J. Easteal, M.A. DeBolt, J. Tucker, J. Am. Ceram. Soc. 59, 12 (1976).

    Article  Google Scholar 

  25. A.J. Kovacs, J.J. Aklonis, J.M. Hutchinson, A.R. Ramos, J. Polym. Sci. Polym. Phys. Ed. 17, 1097 (1979).

    Article  ADS  Google Scholar 

  26. C.A. Angell, J. Res. Natl. Inst. Stand. Technol. 102, 171 (1997).

    Article  Google Scholar 

  27. P. Badrinarayanan, S.L. Simon, R.J. Lyng, J.M. O’Reilly, Polymer 49, 3554 (2008).

    Article  Google Scholar 

  28. I.M. Hodge, Macromolecules 19, 936 (1986).

    Article  ADS  Google Scholar 

  29. I.M. Hodge, A.R. Berens, Macromolecules 15, 762 (1982).

    Article  ADS  Google Scholar 

  30. I.M. Hodge, Macromolecules 20, 2897 (1987).

    Article  ADS  Google Scholar 

  31. A. Agrawal, J. Polym. Sci. Part B, Polym. Phys. 27, 1449 (1989).

    Article  ADS  Google Scholar 

  32. J.M.G. Cowie, R. Ferguson, Macromolecules 22, 2307 (1989).

    Article  ADS  Google Scholar 

  33. J.M.G. Cowie, R. Ferguson, Macromolecules 22, 2312 (1989).

    Article  ADS  Google Scholar 

  34. P. Lunkenheimer, A. Pimenov, M. Dressel, Y.G. Goncharov, R. Böhmer, A. Loidl. Phys. Rev. Lett. 77, 318 (1996).

    Article  ADS  Google Scholar 

  35. K.L. Ngai, J. Chem. Phys. 111, 3639 (1999).

    Article  ADS  Google Scholar 

  36. C. León, K.L. Ngai, J. Phys. Chem. B 103, 4045 (1999).

    Article  Google Scholar 

  37. U. Schneider, P. Lunkenheimer, R. Brand, A. Loidl, Phys. Rev. E 59, 6924 (1999).

    Article  ADS  Google Scholar 

  38. S. Sastry, P.G. Debenedetti, F.H. Stillinger, Nature 393, 554 (1998).

    Article  ADS  Google Scholar 

  39. J.J. Tribone, J.M. O’Reilly, J. Greener, Macromolecules 19, 1732 (1986).

    Article  ADS  Google Scholar 

  40. A.A.C.M. Oudhuis, G.T. Brinke, Macromolecules 25, 698 (1992).

    Article  ADS  Google Scholar 

  41. A. Alegría, L. Goitiandía, I. Tellería, J. Colmenero, Macromolecules 30, 3881 (1997).

    Article  ADS  Google Scholar 

  42. E.V. Russell, N.E. Israeloff., Nature 408, 695 (2000).

    Article  ADS  Google Scholar 

  43. J.M. O’Reilly, I.M. Hodge, J. Non-Cryst. Solids 131-133, 451 (1991).

    Article  Google Scholar 

  44. S.A. Luthra, I.M. Hodge, M.J. Pikal, J. Pharm. Sci. 97, 3084 (2008).

    Article  Google Scholar 

  45. G.P. Johari, M. Goldstein, J. Chem. Phys. 53, 2372 (1970).

    Article  ADS  Google Scholar 

  46. G.P. Johari, J. Chem. Phys. 58, 1766 (1973).

    Article  ADS  Google Scholar 

  47. G.P. Johari, Ann. N.Y. Acad. Sci. 279, 117 (1976).

    Article  ADS  Google Scholar 

  48. G.P. Johari, J. Non-Cryst. Solids 307-310, 317 (2002).

    Article  ADS  Google Scholar 

  49. K.L. Ngai, J. Phys.: Condens. Matter 15, S1107 (2003).

    ADS  Google Scholar 

  50. K.L. Ngai, M. Paluch, J. Chem. Phys. 120, 857 (2004).

    Article  ADS  Google Scholar 

  51. D. Prevosto, S. Capaccioli, M. Lucchesi, P.A. Rolla, K.L. Ngai, J. Chem. Phys. 120, 4808 (2004).

    Article  ADS  Google Scholar 

  52. J.Y. Cavaille, J. Perez, G.P. Johari, Phys. Rev. B 39, 2411 (1989).

    Article  ADS  Google Scholar 

  53. K.L. Ngai, J. Non-Cryst. Solids 351, 2635 (2005).

    Article  ADS  Google Scholar 

  54. H.N. Ritland, J. Am. Ceram. Soc. 37, 370-78 (1954).

    Article  Google Scholar 

  55. P.K. Dixon, L. Wu, S.R. Nagel, B.D. Williams, J.P. Carini, Phys. Rev. Lett. 65, 1108 (1990).

    Article  ADS  Google Scholar 

  56. N.B. Olsen, T. Christensen, J.C. Dyre, Phys. Rev. E 62, 4435 (2000).

    Article  ADS  Google Scholar 

  57. N.B. Olsen, T. Christensen, J.C. Dyre, Phys. Rev. Lett. 86, 1271 (2001).

    Article  ADS  Google Scholar 

  58. H. Wagner, R Richert, J. Phys. Chem. B 103, 4071 (1999).

    Article  Google Scholar 

  59. T. Fujima, H. Frusawa, K. Ito, Phys. Rev. E 66, 031503 (2002).

    Article  ADS  Google Scholar 

  60. R. Nozaki, H. Zenitani, A. Minoguchi, K. Kitai, J. Non-Cryst. Solids 307-310, 349 (2002).

    Article  ADS  Google Scholar 

  61. M. Paluch, C.M. Roland, S. Pawlus, J. Zioło, K.L. Ngai, Phys. Rev. Lett. 91, 115701 (2003).

    Article  ADS  Google Scholar 

  62. I.M. Hodge, Macromolecules 16, 898 (1983).

    Article  ADS  Google Scholar 

  63. S.L. Simon, Macromolecules 30, 4056 (1997).

    Article  ADS  Google Scholar 

  64. G.D. Liu, L.X. Li, Y. Zheng, Y. Zuo, J. Non-Cryst. Solids 365, 13 (2013).

    Article  ADS  Google Scholar 

  65. Y. Zuo, M. Feng, G.D. Liu, J. Non-Cryst. Solids 387, 86 (2014).

    Article  ADS  Google Scholar 

  66. I.M. Hodge, R. Heslin, J. Non-Cryst. Solids 356, 1479 (2010).

    Article  ADS  Google Scholar 

Download references

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Liu, G., Zuo, Y., Lin, J. et al. Study on enthalpy relaxation of glassy polystyrene using a structure-dependent Kohlrausch stretch exponent combined with coupling model. Eur. Phys. J. E 37, 63 (2014). https://doi.org/10.1140/epje/i2014-14063-8

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  • DOI: https://doi.org/10.1140/epje/i2014-14063-8

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