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Micelles, Membranes, Microemulsions, and Monolayers pp 395–426Cite as

Lattice Theories of Microemulsions

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Part of the book series: Partially Ordered Systems ((PARTIAL.ORDERED))

Abstract

Ideally, one would like to have a microscopic basis for a theory of microemulsions. Such a theory would begin with the constituents of the system and produce from their known properties the observed behaviors of microemulsions. There are difficulties of many kinds in such an approach. Of course, the description of constituents must be simplified radically in order to extract general behaviors from particular systems. This simplification is common to the theoretical description of most physical systems. There is an additional difficulty, however, which arises in the theoretical description of a microemulsion; this is the lack of agreement on its defining behaviors. It is prudent, then, for us to state at the outset those properties which we consider to be characteristic of microemulsions, and therefore to be encompassed by any theory of them.

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References

  1. B. M. Knickerbocker, C. V. Pesheck, H. T. Davis, and L. E. Scriven, J. Phys. Chem. 86, 393 (1982).

    Article  Google Scholar 

  2. M. Kahlweit, R. Strey, P. Firman, and D. Haase, Langmuir 1, 281 (1985).

    Article  Google Scholar 

  3. P. Firman, D. Haase, J. Jen, M. Kahlweit, and R. Strey, Langmuir 1, 718 (1985).

    Article  Google Scholar 

  4. M. Kahlweit, R. Strey, and D. Haase, J. Phys. Chem. 89, 163 (1985).

    Article  Google Scholar 

  5. M. Kahlweit, R. Strey, and P. Firman, J. Phys. Chem. 90, 671 (1986).

    Article  Google Scholar 

  6. See Chap. 10 of this volume.

    Google Scholar 

  7. There is a large literature reporting such results. Some examples are as follows: L. Auvray, J.-P. Cotton, R. Ober, and C. Taupin, J. Phys. Chem. 88, 4586 (1984).

    Google Scholar 

  8. M. Kotlarchyk, S.-H. Chen, J. S. Huang, and M. W. Kim, Phys. Rev. Lett. 53, 941 (1984).

    Article  ADS  Google Scholar 

  9. C. G. Vonk, J. F. Billman, and E. W. Kaler, J. Chem. Phys. 87, 3195 (1987).

    Article  Google Scholar 

  10. D. J. Lee, M. M. Telo da Gama, and K. E. Gubbins, J. Phys. Chem. 89, 1514 (1985)

    Article  Google Scholar 

  11. M. M. Telo da Gama and J. H. Thurtell, J. Chem. Soc. Faraday Trans. 2 82, 1721 (1986).

    Article  Google Scholar 

  12. J. C. Wheeler and B. Widom, J. Am. Chem. Soc. 90, 3064 (1968)

    Article  Google Scholar 

  13. B. Widom, J. Phys. Chem. 88, 6508 (1984).

    Article  Google Scholar 

  14. B. Widom, J. Chem. Phys. 84, 6943 (1986).

    Article  ADS  Google Scholar 

  15. For reviews, see P. Bak, Rep. Prog. Phys. 45, 587 (1982).

    Google Scholar 

  16. M. E. Fisher and D. A. Huse, in Melting, Localization, and Chaos, edited by R. K. Kalia and P. Vashista ( Elsevier, New York, 1982 ), p. 259.

    Google Scholar 

  17. W. Selke, Physics Rep. 170, 213 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  18. M. Schick and W.-H. Shih, Phys. Rev. B 34, 1797, (1986).

    Google Scholar 

  19. M. Schick and W.-H. Shih, Phys. Rev. Lett. 59, 1205 (1987).

    Article  ADS  Google Scholar 

  20. S. Alexander, J. Physique Lett. 39, Ll (1978).

    Google Scholar 

  21. K. Chen, C. Ebner, C. Jayaprakash, and R. Pandit, J. Phys. C 20, L361 (1987).

    Article  ADS  Google Scholar 

  22. Phys. Rev. A 38, 6240 (1988).

    Article  Google Scholar 

  23. Another variant of this model has been studied by T. P. Stockfish and J. C. Wheeler, J. Phys. Chem. 92, 3292 (1988).

    Google Scholar 

  24. J. W. Halley and A. J. Kolan, J. Chem. Phys. 88, 3313 (1988).

    Article  ADS  Google Scholar 

  25. Gerhard Gompper, Michael Schick

    Google Scholar 

  26. A. Ciach, J. S. Hoye, and G. Stell, J. Phys. A 21, L777 (1988).

    Article  ADS  Google Scholar 

  27. J. Chem. Phys. 90, 1214 (1989).

    Google Scholar 

  28. A. Ciach and J. S. Hoye, J. Chem. Phys. 90, 1222 (1990).

    Article  ADS  Google Scholar 

  29. G. Gompper and M. Schick, Chem. Phys. Lett. 163, 475 (1989).

    Article  ADS  Google Scholar 

  30. M. W. Matsen and D. E. Sullivan, Phys. Rev. A 41, 2021 (1990).

    Article  ADS  Google Scholar 

  31. K. A. Dawson and A. Kurtovic, J. Chem. Phys. 92, 5473 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  32. R. G. Larson, L. E. Scriven, and H. T. Davis, J. Chem. Phys. 83, 2411 (1985).

    Article  ADS  Google Scholar 

  33. R. G. Larson, J. Chem. Phys. 91, 2479 (1989).

    Article  ADS  Google Scholar 

  34. G. Gompper and M. Schick, Phys. Rev. Lett. 62, 1647 (1989).

    Article  ADS  Google Scholar 

  35. G. Gompper and M. Schick, Phys. Rev. B 41, 9148 (1990).

    Article  ADS  Google Scholar 

  36. G. Gompper and M. Schick, Phys. Rev. A 42, 2137 (1990).

    Article  ADS  Google Scholar 

  37. M. Blume, V. Emery, and R. B. Griffiths, Phys. Rev. A 4, 1071 (1971).

    Article  ADS  Google Scholar 

  38. D. Mukamel and M. Blume, Phys. Rev. A 10, 610 (1974).

    Article  ADS  Google Scholar 

  39. M. Schick and W.-H. Shih (unpublished).

    Google Scholar 

  40. J. D. Hirschfelder, D. Stevenson, and H. Eyring, J. Chem. Phys. 5, 896 (1937).

    Article  ADS  Google Scholar 

  41. G. R. Andersen and J. C. Wheeler, J. Chem. Phys. 69, 2082 (1978).

    ADS  Google Scholar 

  42. J. S. Walker and C. A. Vause, Phys. Lett. 79A, 421 (1980).

    Article  Google Scholar 

  43. R. E. Goldstein, J. Chem. Phys. 83, 1246 (1985).

    Article  ADS  Google Scholar 

  44. G. M. Carneiro and M. Schick, J. Chem. Phys. 89, 4638 (1988).

    Article  Google Scholar 

  45. For a review of transfer-matrix methods, see M. N. Barber in Phase Transitions and Critical Phenomena vol. 8, edited by C. Domb and J. L. Lebowitz ( Academic, New York, 1984 ) p. 145.

    Google Scholar 

  46. E. M. Müller-Hartmann and J.Zittartz, Z. Phys. B 27, 261 (1977) introduced the approximation used to supplement the transfer-matrix results.

    Google Scholar 

  47. We are indebted to H. T. Davis for this observation.

    Google Scholar 

  48. A second study of the model, Ref. 12 above, focussed on a small region of phase space in which a fourth phase, also disordered, appears. Although there were reasons to believe that this phase represented the microemulsion, the fact that it does only appear in a small region of phase space and is uncorrelated with the lyotropic phases makes this identification much less compelling than that in the text.

    Google Scholar 

  49. N. C. Bartelt and T. L. Einstein, J. Phys. A 19, 1429 (1986).

    Article  ADS  Google Scholar 

  50. M. E. Fisher and B. Widom, J. Chem. Phys. 50, 3756 (1969).

    Article  ADS  Google Scholar 

  51. J. Stephenson, J. Math. Phys. 11, 420 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  52. L. Auvray, J.-P. Cotton, R. Ober, and C. Taupin, J. Phys. Chem. 88, 4586 (1984).

    Article  Google Scholar 

  53. L. Auvray, J.-P. Cotton, R. Ober, and C. Taupin, Physica 136B, 281 (1986).

    Google Scholar 

  54. G. Gompper and M. Schick, Phys. Rev. Lett. 65, 1116 (1990).

    Article  ADS  Google Scholar 

  55. K. A. Dawson, Phys. Rev. A 35, 1766 (1987).

    Article  ADS  Google Scholar 

  56. B. Widom, Langmuir 3, 12 (1987).

    Article  Google Scholar 

  57. M. Kahlweit, R. Strey, D. Haase, and P. Firman, Langmuir 4, 785 (1988).

    Article  Google Scholar 

  58. Similar considerations have been applied to the solid/liquid interface by A. A. Chernov and L. V. Mikheev, Phys. Rev. Lett. 60, 2488 (1988).

    Article  ADS  Google Scholar 

  59. M. Robert and J. F. Jeng, J. Phys. France 49, 1821 (1988).

    Article  Google Scholar 

  60. N. Jan and D. Stauffer, J. Phys. France 49, 623 (1988).

    Article  Google Scholar 

  61. K. A. Dawson, B. L. Walker, and A. Berera, Physica A 165, 320 (1990).

    Article  ADS  Google Scholar 

  62. Y. Levin and K. A. Dawson, Phys. Rev. A 42, 1976 (1990).

    Article  ADS  Google Scholar 

  63. A. Berera and K. A. Dawson, Phys. Rev. A 42, 3618 (1990).

    Article  ADS  Google Scholar 

  64. B. Kahng, A. Berera, and K. A. Dawson, Phys. Rev. A 42, 6093 (1990).

    Article  ADS  Google Scholar 

  65. T. Hofsäss and H. Kleinert, J. Chem. Phys. 88, 1156 (1988).

    Article  ADS  Google Scholar 

  66. A. Hansen, M. Schick, and D. Stauffer, Phys. Rev. A 44, 3686 (1991).

    Article  ADS  Google Scholar 

  67. B. Widom, J. Chem. Phys. 90, 2437 (1989).

    Article  ADS  Google Scholar 

  68. B. Widom, private communication.

    Google Scholar 

  69. H. Kleinert, J. Chem. Phys. 84, 964 (1986).

    Article  ADS  Google Scholar 

  70. K. Chen, C. Jayaprakash, R. Pandit, and W. Wenzel, Phys. Rev. Lett. 65, 2736 (1990).

    Article  ADS  Google Scholar 

  71. G. Gompper, R. Holyst, and M. Schick, Phys. Rev. A43. 3157 (1991).

    Google Scholar 

  72. Gerhard Gompper, Michael Schick

    Google Scholar 

  73. D. Andelman, M. E. Cates, D. Roux, and S. A. Safran, J. Chem. Phys. 87, 7229 (1987).

    Article  ADS  Google Scholar 

  74. See also D. A. Huse and S. Leibler, J. Phys. France 49, 605 (1988).

    Article  Google Scholar 

  75. L. Golubovie and T. C. Lubensky, Europhys. Lett. 10, 513 (1989).

    Article  ADS  Google Scholar 

  76. Phys. Rev. A 41, 4343 (1990).

    Article  Google Scholar 

  77. S. A. Safran, D. Roux, M. E. Cates, and D. Andelman, Phys. Rev. Lett. 57, 491 (1986).

    Article  ADS  Google Scholar 

  78. D. Andelman, S. A. Safran, D. Roux, and M. E. Cates, Langmuir 4, 802 (1988).

    Article  Google Scholar 

  79. S. T. Milner, S. A. Safran, D. Andelman, M. E. Cates, and D. Roux, J. de Physique 49, 1065 (1988).

    Article  Google Scholar 

  80. P. G. de Gennes and C. Taupin, J. Phys. Chem. 86, 2294 (1982).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Sektion Physik der Ludwig-Maximilians-Universität München, 8000, München 2, Germany

    Gerhard Gompper

  2. Department of Physics, University of Washington, Seattle, Washington, 98195, USA

    Michael Schick

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  1. Gerhard Gompper
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  2. Michael Schick
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Editors and Affiliations

  1. Department of Chemistry and Biochemistry, University of California, 405 Hilgard Avenue, 90024-1569, Los Angeles, CA, USA

    William M. Gelbart

  2. Department of Physical Chemistry, Hebrew University, 91904, Jerusalem, Israel

    Avinoam Ben-Shaul

  3. CRPP, Domaine Universitaire, 33405, Talence Cedex, France

    Didier Roux

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© 1994 Springer-Verlag New York, Inc.

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Gompper, G., Schick, M. (1994). Lattice Theories of Microemulsions. In: Gelbart, W.M., Ben-Shaul, A., Roux, D. (eds) Micelles, Membranes, Microemulsions, and Monolayers. Partially Ordered Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8389-5_8

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  • DOI: https://doi.org/10.1007/978-1-4613-8389-5_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8391-8

  • Online ISBN: 978-1-4613-8389-5

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