Advertisement

Landau Theory of Wetting Transitions

  • E. H. Hauge
Part of the NATO ASI Series book series (NSSB, volume 174)

Abstract

An interface between two coexisting bulk phases costs free energy1. The macroscopic surface tension is nothing but this excess free energy per unit area. Suppose now that three bulk phases coexist. A natural question is then: Are all three interfaces stable against the intension of a macroscopic layer of the third phase ? If every interfacial tension is less than the sum of the other two, the answer is yes. One could express this by saying that none of the bulk phases wet the interface between the other two. (There might be a wetting layer of microscopic thickness. In that case one could reasonably call the interface partially wet.) On the other hand, if the triangular inequality does not hold for the three tensions, one of the interfaces will be completely wet by the third phase. In 1977 Cahn predicted2 that for suitably chosen systems there should be a (interfacial) phase transition between states of partial and complete wetting at a temperature below bulk criticality. This prediction has since been verified experimentally3.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    As an excellent basic reference, see J. S. Rowlinson and B. Widom, The Molecular Theory of Capillarity (Clarendon, Oxford, 1982).Google Scholar
  2. 2.
    J. W. Cahn, J. Chem. Phys. 66, 3667 (1977)ADSCrossRefGoogle Scholar
  3. C. Ebner and W. F. Saam, Phys. Rev. Lett. 38, 1486 (1977).ADSCrossRefGoogle Scholar
  4. 3.
    The transition was first seen by M. R. Moldover and J. W. Cahn, Science 207, 1073 (1980)ADSCrossRefGoogle Scholar
  5. since then a number of groups have studied the wetting transition experimentally in various contexts. For references, see the review by D. E. Sullivan and M. M. Telo da Gama, Ref. 6.Google Scholar
  6. 4.
    L. M. Landau and E. M. Lifshitz: Course of Theoretical Physics, Vols. 5 and 9Google Scholar
  7. E. M. Lifshitz and L. P. Pitaevskii: Statistical Physics, Part 1 (3rd ed.) & 2 (Pergamon, Oxford, 1980).Google Scholar
  8. 5.
    J. D. van der Waals, Z. Phys. Chem. 13, 657 (1894)Google Scholar
  9. J. D. van der Waals, English translation in J. Stat. Phys. 20, 197 (1979).CrossRefGoogle Scholar
  10. 6.
    Early work is reviewed in R. Pandit, M. Schick and M. Wortis, Phys. Rev. B 26, 5112 (1982)ADSGoogle Scholar
  11. For an introductory survey, see E. H. Hauge in Fundamental problems in Statistical Mechanics VI, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1985)Google Scholar
  12. Statics and dynamics are reviewed by P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985)ADSCrossRefGoogle Scholar
  13. The most comprehensive review is that by D. E. Sullivan and M. M. Telo da Gama, in Fluid Interfacial Phenomena, C. A. Croxton, ed. (Wiley, New York, 1986).Google Scholar
  14. 7.
    R. Pandit and M. Wortis, Phys. Rev. B 25, 3236 (1982).MathSciNetGoogle Scholar
  15. 8.
    E. Brézin, B. I. Halperin and S. Leibler, J. Physique 44, 75 (1983).Google Scholar
  16. 9.
    P. C. Hemmer and J. L. Lebowitz in Phase Transitions and Criticalb Phenomena, Vol. 5B, C. Domb and M. S. Green, eds. (Academic, New York, 1976) pp 107–203.Google Scholar
  17. 10.
    D. E. Sullivan, Phys. Rev. A 25, 1669 (1982).ADSCrossRefGoogle Scholar
  18. 11.
    R. Lipowsky, Phys. Rev. Lett. 52, 1429 (1984)ADSCrossRefGoogle Scholar
  19. S. Dietrich and M. Schick, Phys. Rev. B 31, 4718 (1985) and 33, 4952 (1986)ADSCrossRefGoogle Scholar
  20. C. Ebner, W. F. Saarn and A. K. Sen, Phys. Rev. B 31, 6134Google Scholar
  21. D.M. Kroll, R. Lipowsky and R. K. P. Zia, Phys. Rev. B 32, 1862 (1985).MathSciNetADSGoogle Scholar
  22. 12.
    E. Brézin, B. I. Halperin and S. Leibler, Phys. Rev. Lett. 50, 1387 (1983)ADSCrossRefGoogle Scholar
  23. R. Lipowsky, D. M. Kroll and R. K. P. Zia, Phys. Rev. B 27, 4499 (1983);ADSCrossRefGoogle Scholar
  24. E. H. Hauge and K. Olaussen, Phys. Rev. B 32, 4766 (1985).ADSCrossRefGoogle Scholar
  25. 13.
    K. Binder, D. P. Landau and D. M. Kroll, Phys. Rev. Lett. 56, 2272 (1986).ADSCrossRefGoogle Scholar
  26. 14.
    E. H. Hauge, Phys. Rev. B 33, 3322 (1986).ADSCrossRefGoogle Scholar
  27. 15.
    D. M. Kroll and T. F. Meister, Phys. Rev. 31, 392 (1985)ADSCrossRefGoogle Scholar
  28. P. Tarazona, U. Martini Bettolo Marconi and R. Evans, to be published.Google Scholar
  29. 16.
    D. M. Kroll and G. Gompper, to be published.Google Scholar
  30. 17.
    G. Forgacs, H. Or land and M. Schick, Phys. Rev. B 33, 95 (1986).ADSCrossRefGoogle Scholar
  31. 18.
    T. Aukrust and E. H. Hauge, Phys. Rev. Lett. 54, 1814 (1985).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • E. H. Hauge
    • 1
  1. 1.Institutt for teoretisk fysikkUniversitetet i Trondheim, NTHTrondheim-NTHNorway

Personalised recommendations