Two-order-parameter description of liquids. I. a general model of glass transition covering its strong to fragile limit

Journal of Chemical Physics

Volumn 111, Issue 7, 1999, Pages 3163-3174

  Tanaka, Hajime ^a,b  

^a INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142072152     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.479596     Document Type: Article

References (75)

1. J. Jäckle, Rep. Prog. Phys. 49, 171 (1986).
2. Disorder Effects on Relaxational Processes, edited by R. Richert and A. Blumen (Springer-Verlag, Berlin, 1994).
3. "Proceedings of the second international discussion meeting on relaxations in complex systems," J. Non-Cryst. Solids. 172-174 (1994);
4. "Proceedings of the third international discussion meeting on relaxations in complex systems," J. Non-Cryst. Solids ibid. 235-237 (1998).
5. C. A. Angell, Science 267, 1924 (1995).
6. F. S. Stillinger, Science 267, 1935 (1995).
7. M. Ediger, C. A. Angell, and S. R. Nagel, J. Phys. Chem. 100, 13200 (1996).
8. P. G. Debenedetti, Metastable Liquids (Princeton University Press, Princeton, NJ, 1997).
9. J. C. Phillips, Rep. Prog. Phys. 59, 1133 (1996).
10. C. A. Angell, J. Phys. Chem. Solids 49, 863 (1988);
11. J. Non-Cryst. Solids 131-133, 13 (1991).
12. M. H. Cohen and D. Turnbull, J. Chem. Phys. 31, 1164 (1959).
13. G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965).
14. W. Götze and L. Sjögren, Rep. Prog. Phys. 55, 241 (1992).
15. E. Leutheusser, Phys. Rev. A 29, 2765 (1984).
16. U. Bengtzelius, W. Götze, and L. Sjögren, J. Phys. C 17, 5915 (1984).
17. J. P. Bouchaud, L. Cugliandolo, J. Kurchan, and M. Mezard, cond-mat 970270 and references therein.
18. J. P. Sethna, Europhys. Lett. 6, 529 (1988).
19. T. R. Kirkpatrick and D. Thirumalai, J. Phys. A 22, L149 (1989).
20. T. R. Kirkpatrick, D. Thirumalai, and P. G. Wolynes, Phys. Rev. A 40, 1045 (1989).
21. D. R. Nelson, Phys. Rev. B 28, 5515 (1983);
22. P. J. Steinhardt, D. R. Nelson, and M. Rochetti, Phys. Rev. B ibid. 28, 784 (1983).
23. S. A. Kivelson, X. Zhao, D. Kivelson, T. M. Fisher, and C. Knobler, J. Chem. Phys. 101, 2391 (1994).
24. D. Kivelson, S. A. Kivelson, X. Zhao, Z. Nussinov, and G. Tarjus, Physica A 219, 27 (1995).
25. E. W. Fischer, Physica A 201, 183 (1993).
26. D. Turnbull and M. H. Cohen, J. Chem. Phys. 29, 1049 (1958);
27. D. Turnbull and M. H. Cohen, J. Chem. Phys. 34, 120 (1961).
28. D. Turnbull, Contemp. Phys. 10, 473 (1969).
29. D. R. Uhlmann, J. Non-Cryst. Solids 7, 337 (1972).
30. T. A. Vilgis, in Ref. 2.
31. T. A. Vilgis, Phys. Rev. B 47, 2882 (1993).
32. U. Mohanty, I. Oppenheim, and C. H. Taubes, Science 266, 425 (1994).
33. M. Goldstein, J. Chem. Phys. 51, 3728 (1969).
34. H. Tanaka, J. Chem. Phys. 105, 9375 (1996).
35. H. Tanaka, J. Phys.: Condens. Matter 10, 207 (1998).
36. H. Tanaka, J. Phys.: Condens. Matter 11, L159 (1999).
37. H. Tanaka, Phys. Rev. Lett. 80, 5750 (1998).
38. It should be noted that there are exceptions for this inconsistency of locally favored structures with crystallographic symmetry. For example, bond ordering (the long-range ordering of locally favored structures) leads to crystallization of water into ice Ih (Ref. 18).
39. V. S. Dotzenko, Phys. Usp. 38, 475 (1995).
40. F. C. Frank, Proc. R. Soc. London, Ser. A 215, 43 (1952).
41. M. Kelman and J. F. Sadoc, J. Phys. (Paris) Lett. 40, L569 (1979);
42. M. Kiemen, J. Phys. (Paris) 43, 1389 (1892).
43. F. H. Stillinger, J. Chem. Phys. 89, 6461 (1988).
44. S. Dattagupta and L. A. Turski, Phys. Rev. E 47, 1222 (1993).
45. J. P. Sethna, Phys. Rev. Lett. 51, 2198 (1983);
46. Phys. Rev. B 31, 6278 (1985).
47. S. Duttagupta, J. Non-Cryst. Solids 172-174, 197 (1994).
48. H. Jonsson and H. C. Andersen, Phys. Rev. Lett. 60, 2295 (1988).
49. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995).
50. Strictly speaking, we have to divide ΔV(Ω) into a part that is consistent with the crystallographic symmetry and one that is not consistent with it, in order to define the two order parameters in a more unambiguous way: For example, this can be done by decomposing ΔV into a spherical harmonic functions. For simplicity, however, we assume in this paper that all the parts of ΔV are not consistent with the crystallographic symmetry.
51. K. K. Kobayashi, J. Phys. Soc. Jpn. 27, 1116 (1969).
52. T. Schneider, R. Brout, H. Thomas, and J. Feder, Phys. Rev. Lett. 25, 1423 (1970).
53. T. R. Kirkpatrick, Phys. Rev. A 32, 3130 (1985).
54. T. Munakata, J. Phys. Soc. Jpn. 43, 1723 (1977).
55. K. Kawasaki, Physica A 217, 124 (1995).
56. V. Novikov, E. Rössler, and V. Malnikovsky, Prog. Theor. Phys. Suppl. 126, 387 (1997);
57. E. Rössler, K.-U. Hess, and V. N. Novikov, J. Non-Cryst. Solids 223, 207 (1998).
58. m*, probably due to the complexity of molecules themselves (e.g., the distribution of hydrogen-bonding states).
59. R. B. Griffiths, Phys. Rev. Lett. 23, 17 (1969).
60. A. J. Bray, Phys. Rev. Lett. 59, 586 (1987).
61. R. G. Palmer, D. L. Stein, E. Abrahams, and P. W. Anderson, Phys. Rev. Lett. 53, 958 (1984).
62. A. T. Ogielski, Phys. Rev. B 32, 7384 (1985).
63. P. K. Dixon, L. Wu, S. Nagel, B. D. Williams, and J. P. Carini, Phys. Rev. Lett. 65, 1108 (1990).
64. A. Patkowski, W. Steffen, G. Meier, and E. W. Fischer, J. Non-Cryst. Solids 172-174, 52 (1994).
65. R. Zorn, A. Arbe, J. Colmero, B. Frick, D. Richter, and V. Buchenan, Phys. Rev. E 52, 781 (1995).
66. B. Frick, Prog. Colloid Polym. Sci. 80, 164 (1989).
67. D. Bikto, S. N. Coppersmith, R. L. Leheny, N. Meron, S. R. Nagel, and T. F. Rosenbaum, J. Res. Natl. Inst. Stand. Tech. 102, 207 (1997);
68. N. Menon and S. R. Nagel, Phys. Rev. Lett. 74, 1230 (1995);
69. R. L. Leheny and S. R. Nagel, Europhys. Lett. 39, 447 (1997).
70. C. A. Angell, J. Res. Natl. Inst. Stand. Technol. 102, 171 (1997).
71. D. S. Fisher, Phys. Rev. Lett. 56, 416 (1986).
72. V. S. Dotzenko, J. Phys. C 18, 6023 (1985).
73. S. F. Edwards and K. E. Evans, J. Chem. Soc., Faraday Trans. 2 78, 113 (1983);
74. S. F. Edwards and T. A. Vilgis, in The Physics of Disordered Materials, edited by D. Adler and H. Fritzsche (Plenum, New York, 1985).
75. J. P. Bouchaud, L. Cugliandolo, J. Kurchan, and M. Mezard, Physica A 226, 243 (1996).