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Glass: Kohlrausch exponent, fragility, anharmonicity

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Abstract

The thermodynamical and mechanical properties of (fragile and strong) glass are modeled based on a generalised activation energy relationship log τ = ΔG β /RTn(T′) process of glass-forming liquids. This cooperative process involves 1/n(T′) elementary β motions of activation Gibbs energy ΔG β dependent on the equivalent temperature T′, the temperature of the liquid in equilibrium having the volume of the glass, function of temperature and aging conditions. From this modified VFT law the relaxation of any properties (V , H , stress, creep) can be calculated and approximated by the Kohlrausch function. This model predicts consistency relationships for: a) the temperature (and aging time) variation of the Kohlrausch exponent; b) the temperature dependence of the stabilisation time domain of strong and fragile glass; c) the linear relation between the activation parameters (E * energy, S * entropy, V * volume) of the α and β transition. The Lawson and Keyes (LK) relations are recalled and it is shown that these relations (somewhat equivalant to the compensation law or Meyer-Neldel rule) are observed generally in glass. Morever the (macroscopic) ratios ΔH/ΔV observed during aging or after a temperature jump and the (microscopic) ratio E */V * are found equal to κγ (κ compressibily, γ Grüneisen parameter), in agreement with the LK predictions. From various experiments and in agreement with predictions of this model we conclude that the Grüneisen parameter γ B (pressure derivative of the bulk modulus) and the Mean Square Displacement (MSD) characterising the anharmonicity of solids (and liquids) are the main parameters which govern the relaxation properties of the glass state. Linear relations between the parameters γ B , the fragility m, and the Kohlrausch exponent n g at T g are explained. These correlations underscore a strong relationship between the fragilty of glass formers and the extent of the anharmonicity in the interatomic interactions.

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References

  1. E. Donth, The Glass Transition (Springer, Berlin, 2001).

  2. F. Kremer, A. Schönhals, Broadband Dielectric Spectroscopy, (Spinger, Berlin, 2003).

  3. J.C. Dyre, Rev. Mod. Phys. 78, 953 (2006).

    ADS  Google Scholar 

  4. K.L. Ngai, J. Non-Cryst. Solids 275, 7 (2000).

    ADS  Google Scholar 

  5. C.A. Angell, K.L. Ngai, G.B. McKenna, P.F. McMillan, S.W. Martin, J. Appl. Phys. 88, 3113 (2000).

    ADS  Google Scholar 

  6. C.M. Roland, S. Hensel-Bielowska, M. Paluch, R. Casalini, Rep. Prog. Phys. 68, 1405 (2005).

    ADS  Google Scholar 

  7. H. Bässler, Phys. Rev. Lett. 58, 767 (1987).

    ADS  Google Scholar 

  8. J. Rault, J. Non-Cryst. Solids 260, 164 (1999).

    ADS  Google Scholar 

  9. J. Rault, J. Non-Cryst. Solids 271, 177 (2000).

    ADS  Google Scholar 

  10. F. Stickel, E.W. Fischer, R. Richert, J. Chem. Phys. 102, 6251 (1995).

    ADS  Google Scholar 

  11. J. Dudowicz, K.F. Freed, J.F. Douglas, Adv. Chem. Phys. 137, 125 (2008).

    Google Scholar 

  12. J.C Dyre, N.B. Olsen, T. Christensen, Phys. Rev. B 53, 2171 (1996).

    ADS  Google Scholar 

  13. C.A. Angell, J. Non-Cryst. Solids 131-133, 13 (1991).

    ADS  Google Scholar 

  14. R. Böhmer, C.A. Angell, Phys. Rev. B 45, 45 (1992).

    Google Scholar 

  15. R. Böhmer, K.L. Ngai, C.A. Angell, D.J. Plazek, J. Chem. Phys. 99, 4201 (1993).

    ADS  Google Scholar 

  16. J. Wu, G. Huang, L. Qu, J. Zheng, J. Non-Cryst. Solids 355, 1755 (2009).

    ADS  Google Scholar 

  17. V.N. Novikov, A.P. Sokolov, Phys. Rev. B 74, 064203 (2006).

    ADS  Google Scholar 

  18. P. Lukenheimer, A. Loidl, Chem. Phys. 284, 205 (2002).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  20. V.N. Novikov, A.P. Sokolov, Phys. Rev. E 67, 031507 (2003).

    ADS  Google Scholar 

  21. D.J. Plazek, K.L. Ngai, Macromolecules 24, 1222 (1991).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  23. J. Rault, Physical Aging of Glass: the VFT approach (Nova Science Publishers, New York, 2009).

  24. J. Rault, J. Non-Cryst. Solids 357, 339 (2011).

    ADS  Google Scholar 

  25. A. Kovacs, J. Polym. Sci. 30, 131 (1958).

    Google Scholar 

  26. A. Kovacs, Forthschr. Hochpolym. Forsch. 3, 394 (1964).

    Google Scholar 

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

    ADS  Google Scholar 

  28. G. Williams, Trans. Faraday Soc. 62, 2091 (1966).

    Google Scholar 

  29. G. Williams, Adv. Polym. Sci. 33, 60 (1979).

    Google Scholar 

  30. P.K. Dixon, Phys. Rev. B 42, 8179 (1990).

    ADS  Google Scholar 

  31. C. Leon, K.L. Ngai, J. Phys. Chem. B 103, 4045 (1999).

    Google Scholar 

  32. M.I. Ojovan, JETP Lett. 79, 632 (2004).

    ADS  Google Scholar 

  33. J.A. Bucaro, H.D. Dardy, J. Non-Cryst. Solids 24, 121 (1977).

    ADS  Google Scholar 

  34. K.M. Bernatz, I. Echeverria, S.L. Simon, D.J. Plazek, J. Non-Cryst. Solids 307-310, 790 (2002).

    ADS  Google Scholar 

  35. U. Pschorn, E. Rössler, H. Sillescu, S. Kaufmann, D. Scheaffer, H.W. Spiess, Macromolecules 24, 398 (1991).

    ADS  Google Scholar 

  36. A. Soldera, Y. Grohens, Polymer 45, 1307 (2004).

    Google Scholar 

  37. S. Palato, N. Metala, A. Soldera, Eur. Phys. J. E 34, 90 (2012).

    Google Scholar 

  38. R. Bergman, F. Alvarez, A. Alegria, J. Colmenero, J. Non-Cryst. Solids 235-237, 580 (1998).

    ADS  Google Scholar 

  39. H. Wagner, R. Richtert, J. Phys. Chem. B 103, 4071 (1999).

    Google Scholar 

  40. K.L. Ngai, J. Chem. Phys. 109, 6982 (1998).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  42. J. Perez, Physique et Mécanique des Polymères Amorphes (Edit. Tech. Doc., Paris, 1992).

  43. R. Richter, M. Monkenbucsch, A. Arbe, J. Colmenero, Adv. Polym. Sci. 174, 1 (2005).

    ADS  Google Scholar 

  44. M. Paluch, J. Gapinski, A. Patkovski, E.W. Fisher, J. Chem. Phys. 114, 8040 (2001).

    ADS  Google Scholar 

  45. C.M. Roland, S. Hensel-Bielowska, M. Paluch, R. Casalini, Rep. Prog. Phys. 68, 1405 (2005).

    ADS  Google Scholar 

  46. J.F. Douglas, J.B. Hubbard, Macromolecules 24, 3163 (1991).

    ADS  Google Scholar 

  47. L.C.E. Struik, Physical Aging in Amorphous Polymers and other Materials (Elsevier, Amsterdam, 1978).

  48. J. Rault, J. Non-Cryst. Solids 352, 4946 (2006).

    ADS  Google Scholar 

  49. W. Meyer, H. Neldel, Z. Tech. Phys. 12, 588 (1937).

    Google Scholar 

  50. A. Yelon, B. Movagha, Phys. Rev. Lett. 65, 618 (1960).

    ADS  Google Scholar 

  51. A. Yelon, B. Movagha, H.M. Branz, Phys. Rev. B 46, 12244 (1992).

    ADS  Google Scholar 

  52. E. Peacock-Lopez, H. Suhl, Phys. Rev. B 26, 3774 (1982).

    ADS  Google Scholar 

  53. K.F. Freed, J. Phys. Chem. B 115, 1689 (2011).

    Google Scholar 

  54. L. Liu, Q-X. Guo, Chem. Rev. 101, 673 (2001).

    Google Scholar 

  55. T. Psurek, C.L. Soles, K.A. Page, M.T. Marcus, T. Cicerone, J.F. Douglas, J. Phys. Chem. B 112, 15980 (2008).

    Google Scholar 

  56. A. Anopchenko, T. Psurek, V. VanderHart, J.F. Douglas, J. Obbrzut, Phys. Rev. E 74, 031501 (2006).

    ADS  Google Scholar 

  57. Y. Hiki, H. Takahashi, H. Kobayashi, Solid State Ionics 53-56, 1157 (1992).

    Google Scholar 

  58. Y. Hiki, J. Non-Cryst. Solids 357, 357 (2011).

    ADS  Google Scholar 

  59. A.W. Lawson, J. Phys. Solids 3, 250 (1957).

    ADS  Google Scholar 

  60. A.W. Lawson, J. Chem. Phys. 32, 131 (1960).

    ADS  Google Scholar 

  61. R.W. Keyes, J. Chem. Phys. 29, 467 (1958).

    ADS  Google Scholar 

  62. A.L. Kovarskii, High-Pressure Chemistry and Physics of Polymers (CRC Press, Boca Raton, 1993).

  63. G. Allen, G. Gee, H.A. Lanceley, D. Mangaraj, J. Polym. Sci. 34, 349 (1959).

    ADS  Google Scholar 

  64. V.A. Bershtein, V.M. Egorov, Differential Scanning Calorimetry of Polymers (Ellis Horwoood, Chichester, 1994).

  65. M. Noaki, M. Motomura, T. Nose, J. Polym. Sci. (Phys. Ed.) 13, 1737 (1975).

    Google Scholar 

  66. M. Noaki, M. Motomura, T. Nose, J. Polym. Sci. (Phys. Ed.) 13, 1893 (1975).

    Google Scholar 

  67. J.P. Crine, J. Macrol. Sci. B 23, 201 (1984).

    Google Scholar 

  68. A. Dufresne, C. Lavergne, C. Lacabane, Solid State Commun. 88, 753 (1993).

    ADS  Google Scholar 

  69. G. Teyssedre, C. Lacabanne, J. Phys. D: Appl. Phys. 28, 1478 (1995).

    ADS  Google Scholar 

  70. J.J. del Val, J. Colmenero, Polym. Bull. 17, 489 (1987).

    Google Scholar 

  71. R.N. Haward, The Physics of Glassy Polymer (Wiley, New York, 1973).

  72. C. Bauwens-Crozet, J.C. Bauwens, Polymer 23, 1599 (1982).

    Google Scholar 

  73. J.C. Bauwens, J. Polym. Sci. 33, 123 (1971).

    Google Scholar 

  74. J.C. Bauwens, J. Mater. Sci. 7, 577 (1972).

    ADS  Google Scholar 

  75. C. Bauwens-Crowet, J. Mater. Sci. 8, 968 (1973).

    ADS  Google Scholar 

  76. Y. Nanzai, Prog. Polym. Sci. 18, 437 (1993).

    Google Scholar 

  77. Y. Nanzai, N. Nakayama, J. Non-Cryst. Solids 172-174, 771 (1994).

    ADS  Google Scholar 

  78. J.M. Lefebre, B. Escaig, J. Mater. Sci. 20, 438 (1985).

    ADS  Google Scholar 

  79. R.N. Haward, Colloid Polym. Sci. 258, 42 (1980).

    Google Scholar 

  80. S.K. Sharma, D. Virgo, I. Kushiro, J. Non-Cryst. Solids 33, 235 (1979).

    ADS  Google Scholar 

  81. J. Malek, Thermochim. Acta 311, 183 (1998).

    Google Scholar 

  82. J.M. Hutchinson, J. Polym. Sci. B Polym. Phys. 28, 2127 (1990).

    ADS  Google Scholar 

  83. A.J. Kovacs, Thesis, Paris, 1954.

  84. A.J. Kovacs, J. Polym. Sci. 30, 131 (1958).

    Google Scholar 

  85. R. Greiner, F.R. Schwarzl, Rheol. Acta 23, 378 (1984).

    Google Scholar 

  86. J. Malek, J. Non-Cryst. Solids 235-237, 527 (1998).

    ADS  Google Scholar 

  87. J. Malek, J. Shanelova, J. Non-Cryst. Solids 307-310, 463 (2002).

    ADS  Google Scholar 

  88. J. Rault, J. Phys.: Condens. Matter 15, S1193 (2003).

    ADS  Google Scholar 

  89. JK.M. Bernatz, I. Echeverria, S.L. Simon, D.J. Plazek, J. Non-Cryst. Solids 307-310, 790 (2002).

    ADS  Google Scholar 

  90. P. Badrinarayanan, S.L. Simon, Polymer 48, 1464 (2007).

    Google Scholar 

  91. Y.K. Jeong, I.K. Moon, Phys. Rev. B 52, 6381 (1995).

    ADS  Google Scholar 

  92. C.A. Angell, J. Non-Cryst. Solids 131-133, 13 (1991).

    ADS  Google Scholar 

  93. K. Takegawa, K. Fukao, Y. Saruyama, Thermochim. Acta 461, 67 (2007).

    Google Scholar 

  94. T.H.K. Barron, G.K. White, Heat Capacity and Thermal Expansion at Low Temperatures (Kluwer Academic Plenum Publishers, New York, 1999).

  95. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 2004).

  96. R. Simha, P.S. Wilson, O. Olabisi, Kolloid-Z. Z. Polym. 251, 402 (1973).

    Google Scholar 

  97. A. Quach, R. Simha, J. Appl. Phys. 42, 4592 (1971).

    ADS  Google Scholar 

  98. Slobodian, P. Riha, P. Lengalova, A. Hadac, J. Saha, P. Kubat J., J. Non-Cryst. Solids 148-157, 344 (2004).

    Google Scholar 

  99. G. Allen, G. Gee, H.A. Lanceley, D. Mangaraj, J. Polym. Sci. 34, 349 (1959).

    ADS  Google Scholar 

  100. R. Zallen, Phys. Rev. B 9, 4485 (1974).

    ADS  Google Scholar 

  101. C.K. Wu, G. Jura, M. Shen, J. Appl. Phys. 43, 4348 (1972).

    ADS  Google Scholar 

  102. R.V. Gopala Rao, R. Venkatesh, J. Non-Cryst. Solids 175, 278 (1994).

    Google Scholar 

  103. J.C. Slater, Introduction to Chemical Physics (McGraw-Hill, New York, 1939).

  104. L.S. Dubrovinsky, S.K. Saxena, N.A. Dubrovinskaia, S. Rekhi, T. le Bihan, Amer. Mineral. 85, 386 (2000).

    Google Scholar 

  105. D.H. Huang, X.R. Liu, L. Su, C.G. Shao, R. Jia, S.M. Hong, J. Phys. D: Appl. Phys. 40, 5327 (2007).

    ADS  Google Scholar 

  106. W.W. Anderson, T.J. Ahrens, J. Geophys. Res 39, 4273 (1994).

    ADS  Google Scholar 

  107. R. Grosse, P. Krause, M. Meissner, A. Tausend, J. Phys. C, Solid State Phys. 11, 45 (1978).

    ADS  Google Scholar 

  108. R.W. Warfield, Makromol. Chem. 175, 3285 (1974).

    Google Scholar 

  109. Y. Wada, A. Itani, T. Nishi, J. Polym. Sci. 7, 201 (1969).

    Google Scholar 

  110. R.E. Barker, J. Appl. Phys. 38, 4234 (1967).

    ADS  Google Scholar 

  111. R. Grosse, P. Krause, M. Meissner, A. Tausend, J. Phys. C, Solid State Phys. 11, 45 (1978).

    ADS  Google Scholar 

  112. J.K. Krüger, K.P. Bohn, M. Pietralla, J. Schreiber, J. Phys.: Condens. Matter 8, 10863 (1996).

    ADS  Google Scholar 

  113. J.E. Mark (Editor), Physical Properties of Polymers Handbook (AIP Press, New York, 1995).

  114. T.D. Melʼnichenko, V.M. Rizak, V.I.T. Fedelesh, T.N. Melʼnichenko, D.S. Sanditov, S.S. Badmaev, Glass Physics and Chemistry, Vol. 32 (4) (Pleiades Publishing, 2006) p. 399.

  115. U. Buchenau, R. Zorn, Europhys. Lett. 18, 523 (1992).

    ADS  Google Scholar 

  116. A. Mermet, E. Duval, N.V. Surovtsev, J.F. Jal, A.J. Dianoux, A.F. Yee, Europhys. Lett. 38, 515 (1997).

    ADS  Google Scholar 

  117. J. Bartos, J. Kristiak, T. Kanaya, Physica, B 234-236, 435 (1997).

    ADS  Google Scholar 

  118. T. Psurek, C.L. Soles, K.A. Page, M.T. Marcus, T. Cicerone, J.F. Douglas, J. Phys. Chem. B 112, 15980 (2008).

    Google Scholar 

  119. K. Niss, C. Dalle-Ferrier, B. Frick, D. Russo, J. Dyre, C. Alba-Simionesco, Phys. Rev. E 82, 021508 (2010).

    ADS  Google Scholar 

  120. W. Petry, E. Bartsch, F. Fujaro, M. Kiebel, Z. Phys. B, Condens. Matter 83, 175 (1991).

    ADS  Google Scholar 

  121. S. Koizumi, K. Saijo, T. Hashimoto, Prog. Theor. Phys. Supl. 126, 223 (1997).

    ADS  Google Scholar 

  122. L. Comez, S. Corezzi, D. Fioretto, Philos. Mag. 84, 1521 (2004).

    ADS  Google Scholar 

  123. Frick, D. Richter, Phys. Rev. B 47, 14795 (1993).

    ADS  Google Scholar 

  124. T. Scopigno, G. Ruocco, F. Sette, G. Monako, Science 302, 849 (2003).

    ADS  Google Scholar 

  125. V.N. Novikov, A.P. Sokolov, Nature 431, 7011 (2004).

    Google Scholar 

  126. A. Arbe, D. Richter, J. Colmenero, B. Farago, Phys. Rev. E 54, 3853 (1996).

    ADS  Google Scholar 

  127. F.W. Wette, L.H. Fowler, B.R.A. Nijboer, Physica 54, 292 (1971).

    ADS  Google Scholar 

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    J. Rault

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Rault, J. Glass: Kohlrausch exponent, fragility, anharmonicity. Eur. Phys. J. E 35, 26 (2012). https://doi.org/10.1140/epje/i2012-12026-9

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