On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses

Journal of Chemical Physics

Volumn 121, Issue 15, 2004, Pages 7347-7354

  Bouchaud, Jean Philippe ^a,b   Biroli, Giulio ^c  

^a SERVICE DE PHYSIQUE DE L ETAT CONDENSÉ   (France)

^b Science and Finance   (France)

^c CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACTIVATION ENERGY; COMPUTER SIMULATION; ENTROPY; EXTRAPOLATION; FREE ENERGY; GLASS TRANSITION; REACTION KINETICS; VISCOSITY;

ENERGY BARRIERS; GLASS FORMING LIQUIDS; VICINITY;

GLASS;

EID: 8444220523     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1796231     Document Type: Article

References (91)

1. See. e.g., P. G. Debenedetti and F. H. Stillinger, Nature (London) 410, 259 (2001).
2. H. Vogel, Z. Phys. 22, 645 (1921); G. S. Fulcher, J. Am. Ceram. Soc. 6, 339 (1925).
3. H. Vogel, Z. Phys. 22, 645 (1921); G. S. Fulcher, J. Am. Ceram. Soc. 6, 339 (1925).
4. See the lucid papers of H. Bassler, Phys. Rev. Lett. 58, 767 (1987); R. Richter and H. Bassler. J. Cond. Mat. Phys. 2. 2273 (1990), and references therein.
5. See the lucid papers of H. Bassler, Phys. Rev. Lett. 58, 767 (1987); R. Richter and H. Bassler. J. Cond. Mat. Phys. 2. 2273 (1990), and references therein.
6. G. Tarjus and D. Kivelson, J. Chem. Phys. 103, 3071 (1995); D. Kivelson and G. Tarjus, Philos. Mag. B 77, 245 (1998).
7. G. Tarjus and D. Kivelson, J. Chem. Phys. 103, 3071 (1995); D. Kivelson and G. Tarjus, Philos. Mag. B 77, 245 (1998).
8. L. Berthier and J. P. Garrahan, Phys. Rev. E 68, 041201 (2003).
9. C. A. Angell, J. Res. NIST 102, 171 (1997); R. Richert and C. A. Angell, J. Chem. Phys. 108, 9016 (1998).
10. C. A. Angell, J. Res. NIST 102, 171 (1997); R. Richert and C. A. Angell, J. Chem. Phys. 108, 9016 (1998).
11. J. P. Sethna, J. D. Shore, and M. Huang, Phys. Rev. B 44, 4943 (1991); 47, 14661 (1993).
12. J. P. Sethna, J. D. Shore, and M. Huang, Phys. Rev. B 44, 4943 (1991); 47, 14661 (1993).
13. J. H. Gibbs and E. A. di Marzio, J. Chem. Phys. 28, 373 (1958).
14. G. Adam and J. H. Gibbs. J. Chem. Phys. 43, 139 (1958).
15. G. P. Johari, J. Chem. Phys. 112. 8958 (2000).
16. I. Hodge. J. Res. NIST 102, 195 (1997).
17. C. M. Roland, S. Capaccioli, M. Lucchesi, and R. Casalini, cond-mat/0404181.
18. T. Kirkpatrick and P. Wolynes, Phys. Rev. B 36, 8552 (1987); T. R. Kirkpatrick, D. Thirumalai, and P. G. Wolynes, Phys. Rev. A 40, 1045 (1989).
19. T. Kirkpatrick and P. Wolynes, Phys. Rev. B 36, 8552 (1987); T. R. Kirkpatrick, D. Thirumalai, and P. G. Wolynes, Phys. Rev. A 40, 1045 (1989).
20. P. G. Wolynes, J. Res. Natl, Inst. Stand. Technol. 102, 187 (1997).
21. X. Xia and P. G. Wolynes, Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000): Phys. Rev. Lett. 86, 5526 (2001).
22. X. Xia and P. G. Wolynes, Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000): Phys. Rev. Lett. 86, 5526 (2001).
23. V. Lubchenko and P. Wolynes, J. Chem. Phys. 119, 9088 (2003).
24. J.-P. Bouchaud, L. Cugliandolo, J. Kurchan, and M. Mézard, in Spinglasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998), and references therein; L. Cugliandolo, in Slow Relaxations and Non-equilibrium Dynamics in Condensed Matter, Les Houches, Session LXXVII, edited by J. L. Barrat, M. Feigelman, J. Kurchan, and J. Dalibard (Springer, Berlina, 2003).
25. J.-P. Bouchaud, L. Cugliandolo, J. Kurchan, and M. Mézard, in Spinglasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998), and references therein; L. Cugliandolo, in Slow Relaxations and Non-equilibrium Dynamics in Condensed Matter, Les Houches, Session LXXVII, edited by J. L. Barrat, M. Feigelman, J. Kurchan, and J. Dalibard (Springer, Berlina, 2003).
26. W. Götze and L. Sjögren, Rep. Prog. Phys. 55, 241 (1992): W. Götze, Condens. Matter Phys. 1. 873 (1998); W. Kob, in Les Houches, Session LXXVII (Springer, Berlin, 2003).
27. W. Götze and L. Sjögren, Rep. Prog. Phys. 55, 241 (1992): W. Götze, Condens. Matter Phys. 1. 873 (1998); W. Kob, in Les Houches, Session LXXVII (Springer, Berlin, 2003).
28. W. Götze and L. Sjögren, Rep. Prog. Phys. 55, 241 (1992): W. Götze, Condens. Matter Phys. 1. 873 (1998); W. Kob, in Les Houches, Session LXXVII (Springer, Berlin, 2003).
29. A. Barrat, R. Burioni, and M. Mézard, J. Phys. A 29, L81 (1996).
30. Depending on the author, the meaning of configurational entropy appears to be different. Here and in the following we call configurational entropy the logarithm of the number of metastable states. See Refs. 13, 69 for discussions.
31. K.
32. V. Lubchenko and P. G. Wolynes, cond-mat/0404276.
33. P. Goldbart and N. Goldenfeld, Phys. Rev. A 39, 1402 (1989).
34. B. Derrida, Phys. Rev. B 24, 2613 (1981).
35. J. P. Bouchaud and M. Mézard, J. Phys. A 30, 7997 (1997).
36. J. P. Bouchaud, J. Phys. (Paris) 2, 1705 (1992): J. P. Bouchaud and D. Dean, ibid. 5, 265 (1995).
37. J. P. Bouchaud, J. Phys. (Paris) 2, 1705 (1992): J. P. Bouchaud and D. Dean, ibid. 5, 265 (1995).
38. C. Monthus and J. P. Bouchaud, J. Phys. A 29, 3847 (1996).
39. G. Ben Arous, A. Bovier, and V. Gayrard, Phys. Rev. Lett. 88, 087201 (2002).
40. Y. Singh, J. P. Stoessel. and P. G. Wolynes, Phys. Rev. Lett. 54, 1059 (1985).
41. M. Mézard and G. Parisi, J. Chem. Phys. 111, 1076 (1999); J. Phys.: Condens. Matter 12, 6655 (2000); M. Mézard. in First Steps in Glass Theory, More is different, edited by Ong and Bhatt (Princeton University Press, Princeton, 2002); B. Coluzzi, M. Mézard, G. Parisi, and P. Verrocchio, J. Chem. Phys. 111, 9039 (1999).
42. M. Mézard and G. Parisi, J. Chem. Phys. 111, 1076 (1999); J. Phys.: Condens. Matter 12, 6655 (2000); M. Mézard. in First Steps in Glass Theory, More is different, edited by Ong and Bhatt (Princeton University Press, Princeton, 2002); B. Coluzzi, M. Mézard, G. Parisi, and P. Verrocchio, J. Chem. Phys. 111, 9039 (1999).
43. M. Mézard and G. Parisi, J. Chem. Phys. 111, 1076 (1999); J. Phys.: Condens. Matter 12, 6655 (2000); M. Mézard. in First Steps in Glass Theory, More is different, edited by Ong and Bhatt (Princeton University Press, Princeton, 2002); B. Coluzzi, M. Mézard, G. Parisi, and P. Verrocchio, J. Chem. Phys. 111, 9039 (1999).
44. M. Mézard and G. Parisi, J. Chem. Phys. 111, 1076 (1999); J. Phys.: Condens. Matter 12, 6655 (2000); M. Mézard. in First Steps in Glass Theory, More is different, edited by Ong and Bhatt (Princeton University Press, Princeton, 2002); B. Coluzzi, M. Mézard, G. Parisi, and P. Verrocchio, J. Chem. Phys. 111, 9039 (1999).
45. S. Franz, M. Cardenas, and G. Parisi, J. Phys. A 31, L163 (1998).
46. See D. S. Fisher, in Slow Relaxations and Non-equilibrium Dynamics in Condensed Matter, Les Houches, Session LXXVII, edited by J. L. Barrat, M. Feigelman, J. Kurchan, and J. Dalibard (Springer, Berlin. 2003), p. 534, and C. M. Newman and D. S. Stein, J. Stat. Phys. 106, 213 (2002).
47. See D. S. Fisher, in Slow Relaxations and Non-equilibrium Dynamics in Condensed Matter, Les Houches, Session LXXVII, edited by J. L. Barrat, M. Feigelman, J. Kurchan, and J. Dalibard (Springer, Berlin. 2003), p. 534, and C. M. Newman and D. S. Stein, J. Stat. Phys. 106, 213 (2002).
48. C. Bennemann, C. Donati, J. Baschnagel, and S. C. Glotzer, Nature (London) 399, 246 (1999); S. C. Glotzer, V. V. Novikov, and T. B. Schroeder, J. Chem. Phys. 112, 509 (2000); N. Laccvic, F. W. Starr, T. B. Schroeder, and S. C. Glotzer, J. Chem. Phys. 119, 7372 (2003), and references therein.
49. C. Bennemann, C. Donati, J. Baschnagel, and S. C. Glotzer, Nature (London) 399, 246 (1999); S. C. Glotzer, V. V. Novikov, and T. B. Schroeder, J. Chem. Phys. 112, 509 (2000); N. Laccvic, F. W. Starr, T. B. Schroeder, and S. C. Glotzer, J. Chem. Phys. 119, 7372 (2003), and references therein.
50. C. Bennemann, C. Donati, J. Baschnagel, and S. C. Glotzer, Nature (London) 399, 246 (1999); S. C. Glotzer, V. V. Novikov, and T. B. Schroeder, J. Chem. Phys. 112, 509 (2000); N. Laccvic, F. W. Starr, T. B. Schroeder, and S. C. Glotzer, J. Chem. Phys. 119, 7372 (2003), and references therein.
51. D. S. Fisher and D. Huse, Phys. Rev. B 38, 373 (1988).
52. G. Tarjus and D. Kivelson, J. Chem. Phys. 103, 3071 (1995).
53. We assumed that the configurational entropy vanishes linearly in f and that ∂S/∂T≤0 at least close to the lowest free-energy states.
54. See S. F. Swallon, P. A. Bonvallet, R. J. McMalhon, and M. D. Ediger, Phys. Rev. Lett. 90, 015901 (2003).
55. J. P. Bouchaud, in Slow Relaxations and Non-equilibrium Dynamics in Condensed Matter, Les Houches, Session LXXVII, edited by J. L. Barrat, M. Feigelman. J. Kurchan, and J. Dalibard (Springer. Berlina, 2003).
56. R. A. Denny, D. R. Reichman, and J. P. Bouchaud, Phys. Rev. Lett. 90, 025503 (2003).
57. B. Doliwa and A. Heuer. Phys. Rev. E 67, 030501 (2003); J. Phys.; Condens, Matter 15, S849 (2003).
58. B. Doliwa and A. Heuer. Phys. Rev. E 67, 030501 (2003); J. Phys.; Condens, Matter 15, S849 (2003).
59. W. Kob and H. C. Andersen, Phys. Rev. E 51, 4626 (1995); 52, 4134 (1995).
60. W. Kob and H. C. Andersen, Phys. Rev. E 51, 4626 (1995); 52, 4134 (1995).
61. C. Toninelli, G. Biroli, and D. S. Fisher, Phys. Rev. Lett. 92, 185504 (2004).
62. F. Ritort and P. Sollich, Adv. Phys. 52, 219 (2003).
63. G. Turjus, D. Kivelson, S. Mossa, and C. Alba-Simionesco, cond-mat/0309579.
64. C. Toninelli, G. Biroli, and D. S. Fisher (unpublished).
65. E. M. Bertin, J. Phys. A 36, 10710 (2003).
66. G. Biroli and J. P. Bouchaud (unpublished).
67. M. Goldstein, J. Chem. Phys. 51, 3728 (1969).
68. E. A. di Marzio and A. J. M. Yang, J. Res. Natl. Inst. Stand. Technol. 102, 135 (1997), and references therein.
69. J. Kurchan and L. Luloux, J. Phys. A 29, 1929 (1996).
70. A. Cavagna, Europhys. Lett. 53, 490 (2001); A. Cavagna, I. Giardina, and T. S. Grigera, J. Phys. A 36, 10721 (2003).
71. A. Cavagna, Europhys. Lett. 53, 490 (2001); A. Cavagna, I. Giardina, and T. S. Grigera, J. Phys. A 36, 10721 (2003).
72. P. Scheidler, W. Kob, and K. Binder, J. Phys. IV 10, 733 (2000); condmat/0309025.
73. K. Kim and R. Yamamoto, Phys. Rev. E 61, R41 (2000).
74. G. Biroli and J. P. Bouchaud, Europhys. Lett. 67, 21 (2004).
75. S. H. Glarum, J. Chem. Phys. 33, 639 (1960).
76. G. H. Frederickson and H. C. Andersen, Phys. Rev. Lett. 53, 1244 (1984); J. Chem. Phys. 83, 958 (1984).
77. G. H. Frederickson and H. C. Andersen, Phys. Rev. Lett. 53, 1244 (1984); J. Chem. Phys. 83, 958 (1984).
78. J. P. Garrahan and D. Chandler, Phys. Rev. Lett. 89, 035704 (2002); J. P. Garrahan and D. Chandler, Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003).
79. J. P. Garrahan and D. Chandler, Phys. Rev. Lett. 89, 035704 (2002); J. P. Garrahan and D. Chandler, Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003).
80. S. Whitelam, L. Berthier, and J. P. Garrahan, Phys. Rev. Lett. 92, 185705 (2004).
81. L. Berthier (private communication).
82. L. M. Martinez and C. A. Angell, Nature (London) 410, 663 (2002).
83. There is some ambiguity in the exact partitioning of the entropy into configurational and vibrational part but this does not affect the quoted order of magnitude.
84. See, e.g., M. D. Ediger, Ann. Rev. Chem. 51, 99 (2000).
85. M. M. Hurley and P. Harrowell, Phys. Rev. E 52, 1694 (1995), and references therein.
86. R. Yamamoto and A. Onuki, Phys. Rev. Lett. 81, 4915 (1998), and references therein.
87. L. Berthier, Phys. Rev. E 69, 020201 (R) (2004).
88. G. Biroli, C. Toninelli, M. Wyart, and J. P. Bouchaud (unpublished).
89. K.-K. Loh, K. Kawasaki, A. R. Bishop, T. Lookman, A. Saxena, J. Schmalian, and Z. Nussinov, cond-mat/0206494.
90. S. Franz and F. Toninelli, cond-mat/0404132.
91. G. Biroli and R. Monasson, Europhys. Lett. 50, 155 (2000).