Advertisement

Models for Transport and Relaxation in Glass Forming and Complex Fluids: Universality?

  • Thomas A. Vilgis

Abstract

The question whether most properties of glasses and the glass transition phenomenon behave with universal features or not has been disputed for many years. The use of the technical term “universality” for glasses is, however, to be understood in a different way compared to the case of phase transitions in statistical mechanics, for instance. In this latter field the physical situation is simple: Most of the scaling properties of critical quantities, such as the order parameter, the correlation length etc. and all the critical exponents depend on the order parameter dimension and the spatial dimension of the Euclidian space rather than on the details of the materials or the precise form of the interaction energy [1, 2]. It is well known, for example, that the critical properties, i.e. the behavior of the material near a critical point, of the (ferromagnetic) Ising model are identical to those of the lattice gas, the binary mixture, or the binary polymer blend. What is of course different in all cases and depends strongly on all details of the material is the critical temperature itself. The precise value of the critical point for the Ising model depends on the lattice type and is, in general, not known exactly for three dimensions [2, 3]. However, this critical point will be different from that of the binary mixture (at the critical composition, which corresponds to the zero field Ising model) or the polymer blend. In the latter case, the coupling constant even depends on the length of the polymers and all non-universal properties will also be molecular-weight dependent.

Keywords

Glass Transition Coordination Number Diffusion Constant Relaxation Function Random Phase Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols and Abbreviations

E

energy

F

force

KWW

Kohlrausch Williams-Watts

MMC

mode-mode coupling

TIG

theorists ideal glass

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amit DJ (1984) Field theory, the renormalization group, and critical phenomena. World Scientific, SingaporeGoogle Scholar
  2. 2.
    Itzykson C, Drouffe JM (1989) Statistical field theory. Cambridge University Press, CambridgeGoogle Scholar
  3. 3.
    Parisi G (1978) Statistical field theory. Benjamin Cummings, New YorkGoogle Scholar
  4. 4.
    Brawer S (1985) Relaxations in liquids and glasses. Am Cer Soc Columbus, OhioGoogle Scholar
  5. 5.
    Bueche F (1962) Physical properties of polymers. Interscience, New YorkGoogle Scholar
  6. 6.
    Ferry JD (1980) Viscoelastic properties of polymers. Wiley, New YorkGoogle Scholar
  7. 7.
    Jäckle J (1986) Rep Prog Phys, 49: 171CrossRefGoogle Scholar
  8. 8.
    Fredrickson GH (1988) Ann Adv Phys Chem, 39: 149Google Scholar
  9. 9.
    Leutheusser E (1984) Phys Rev A29: 2765Google Scholar
  10. 10.
    Götze W (1991) in JP Hansen, D Levesque, J Zinn-Justin (eds) Liquids, freezing, and the glass transition. Elsevier, AmsterdamGoogle Scholar
  11. 11.
    Schilling R (1993) this volumeGoogle Scholar
  12. 12.
    Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, OxfordGoogle Scholar
  13. 13.
    Bässler H (1987) Phys Rev Lett, 58: 767CrossRefGoogle Scholar
  14. 14.
    Richert R, Bässler H (1990) J Phys: Cond Matter 2: 2273CrossRefGoogle Scholar
  15. 15.
    Sillescu H (1992) private communicationGoogle Scholar
  16. 16.
    Boon JP, Yip S (1980) Generalized hydrodynamics. McGraw-Hill, New YorkGoogle Scholar
  17. 17.
    Williams G, Watts DC (1970) Trans Farad Soc 66: 80CrossRefGoogle Scholar
  18. 18.
    Blumen A, Klafter J, Zumofen G (1986) in I. Zoschke-Gränacher (ed) Optical spectroscopy of glasses. Reidel, DordrechtGoogle Scholar
  19. 19.
    di Marzio EA, Sanchez I (1986) in J Klafter, RJ Rubin, MF Schlesinger (ed) Transport and relaxation in random materials. World Scientific, SingaporeGoogle Scholar
  20. 20.
    Donth EJ (1981) Glasübergang, Akademie Verlag der DDR, BerlinGoogle Scholar
  21. 21.
    Donth EJ (1991) Non Cryst Solids, 131: 204CrossRefGoogle Scholar
  22. 22.
    Kirkpatrick TR, Tirumalai D (1989) Phys Rev A, 40: 1045CrossRefGoogle Scholar
  23. 23.
    Angell CA (1985) J Non-Cryst Solids, 73: 1CrossRefGoogle Scholar
  24. 24.
    Stillinger FH (1988) J Chem Phys 89: 6461CrossRefGoogle Scholar
  25. 25.
    Sethna JP (1988) Europhys Lett 6: 529CrossRefGoogle Scholar
  26. 26.
    Yonezawa F, Ninomia T (1983) Topological disorder in condensed matter, Springer Verlag, BerlinGoogle Scholar
  27. 27.
    Zallen R (1980) The Physics of Amorphous Solids. Wiley, New YorkGoogle Scholar
  28. 28.
    O’Connor NPT, Ball RC (1992) Macromolecules, in pressGoogle Scholar
  29. 29.
    Edwards SF, Evans KE (1982) JCS, Farad II 78:113CrossRefGoogle Scholar
  30. 30.
    Edwards SF, Vilgis TA (1985) in D Adler, H Fritzsche (eds) The physics of disordered materials. Plenum Press, New YorkGoogle Scholar
  31. 31.
    Edwards SF, Vilgis TA (1987) in T Kirste, F Pynn, Scaling in disordered systems. North-Holland, AmsterdamGoogle Scholar
  32. 32.
    Brereton MG (1992) Prog Coll & Polym Sci, in pressGoogle Scholar
  33. 33.
    Edwards SF, Vilgis TA (1986) Physica Scripta, T13: 7CrossRefGoogle Scholar
  34. 34.
    Spohn H (1992) Dynamics of interacting particles. Springer Verlag, BerlinGoogle Scholar
  35. 35.
    Hess W (1988) Macromolecules, 21: 2620CrossRefGoogle Scholar
  36. 36.
    Rickyazen G (1980) Green functions in condensed matter. Academic Press, LondonGoogle Scholar
  37. 37.
    Statman D, Chu B (1984) Macromolecules, 17: 1537CrossRefGoogle Scholar
  38. 38.
    Edwards SF (1985) Brit Polym J, 17: 122CrossRefGoogle Scholar
  39. 39.
    de Gennes PG (1972) Phys Lett 38A: 339Google Scholar
  40. 40.
    Mandelbrot B (1982) The fractal geometry of nature. Freeman, San FranciscoGoogle Scholar
  41. 41.
    O’Shaugnessy B, Procaccia I (1985) Phys Rev Lett 54: 455CrossRefGoogle Scholar
  42. 42.
    Alexander S, Orbach R (1982) J Phys Lett (France) 43: L625Google Scholar
  43. 43.
    Klafter J, Zumofen G, Blumen A (1991) J Phys A, 24: 4835CrossRefGoogle Scholar
  44. 44.
    Weiss GH, Rubin RJ (1983) Adv Chem Phys 52: 363CrossRefGoogle Scholar
  45. 45.
    Köhler J, Blumen A (1987) J PhysGoogle Scholar
  46. 46.
    Derrida B (1981) Phys Rev B 24: 2613CrossRefGoogle Scholar
  47. 47.
    Mezard M, Parisi G, Virasoro MV, Spin glass theory and beyond. World Scientific, SingaporeGoogle Scholar
  48. 48.
    Alexander S, Bernasconi J, Schneider W, Orbach R, Rev Mod Phys 53: 175Google Scholar
  49. 49.
    Bordewijk P (1975) Chem Phys Lett, 33: 1371Google Scholar
  50. 50.
    Palmer RG, Stein DL, Abrahams E, Anderson PW (1984) Phys Rev Lett 53: 958CrossRefGoogle Scholar
  51. 51.
    Rammal R, Toulouse G, Virasoro VM (1986) Rev Mod PhysGoogle Scholar
  52. 52.
    Vilgis TA (1987) J Stat Phys 47: 133CrossRefGoogle Scholar
  53. 53.
    Schreckenberg M, Zittarz J (1986) in Heidelberg colloquium on glassy dynamics. Springer Verlag, BerlinGoogle Scholar
  54. 54.
    Ogielsky A, Stein DL (1985) Phys Rev Lett 55: 1634CrossRefGoogle Scholar
  55. 55.
    Vilgis TA (1988) J Phys C 21: L299CrossRefGoogle Scholar
  56. 56.
    Edwards SF (1981) Ann NY Acad Sci, 371: 210Google Scholar
  57. 57.
    Edwards SF (1972) in AJ Chrompff, S, Newman, Polymer networks. Plenum Press, New YorkGoogle Scholar
  58. 58.
    Negele JW, Orland H (1988) Quantum statistical systems. Addison-Wesley, New YorkGoogle Scholar
  59. 59.
    Vilgis TA, Benmouna M, Benoit H (1991) Macromolecules, 24: 4481CrossRefGoogle Scholar
  60. 60.
    de Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, IthacaGoogle Scholar
  61. 61.
    Hansen JP, MacDonald IM (1990) Theory of simple liquids. Academic Press, New YorkGoogle Scholar
  62. 62.
    Deutsch HP, Binder K (1992) Europhys Lett 18: 667CrossRefGoogle Scholar
  63. 63.
    Schweizer K (1992) preprintGoogle Scholar
  64. 64.
    Bengtzelius U, Götze W, Sjölander A (1984) J Phys C 17: 5915CrossRefGoogle Scholar
  65. 65.
    Lovesey SW (1984) Theory of neutron scattering. Clarendon Press, OxfordGoogle Scholar
  66. 66.
    Vilgis TA (1990) J Phys: Cond Matter, 2: 3667CrossRefGoogle Scholar
  67. 67.
    Vilgis TA (1993) Phys Rev B, in pressGoogle Scholar
  68. 68.
    de Dominicis C, Orland H, Lainee J (1985) J Phys Lett (France) 46: L463Google Scholar
  69. 69.
    Angell CA 1991 J Non-Cryst Solids, 191: 13CrossRefGoogle Scholar
  70. 70.
    Ngai KL (1991) J Non-Cryst Solids, 131: 86Google Scholar
  71. 71.
    Böhmer R, Angell CA (1992) preprintGoogle Scholar
  72. 72.
    Böhmer R, Ngai KL, Angell CA, Plazek DJ (1993) J Chem Phys 99: 4201CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Thomas A. Vilgis

There are no affiliations available

Personalised recommendations