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Lattice Models of Amphiphilic Assembly

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Book cover Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution

Part of the book series: NATO ASI Series ((ASIC,volume 369))

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Abstract

Very complex liquids such as self-assembled fluids present particular challenges and exhibit novel phenomena that distinguish them from simple or even more conventional complex liquids. Consequently, there are philosophical differences in ones approach to their study. For example, one is often more interested in the unveiling of some interesting phenomena or trend rather than calculation of some very detailed property. This is fortunate since it is still not really feasible to study a truly molecular theory.

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References

  1. The term is something of a misnomer, the molecules form large clusters or aggregates simply because of the particular balance of molecular energies.

    Google Scholar 

  2. Amphiphile from Greek roots amphi = both ends, philios = to love.

    Google Scholar 

  3. This aspect of these systems renders the self-avoiding surface models largely inapplicable to these situations.

    Google Scholar 

  4. Sometimes more than the three components, oil, water and amphiphile are added. Such components as salt or alcohol are termed cosurfactants and modulate the emulsion properties.

    Google Scholar 

  5. We emphasize that this is a highly schematic version of the phase diagram that is useful for theorists. Real phase-diagrams are considerably distorted from this picture. However, it is at present believed that these distortions arise from the fact that the solvent properties vary as a function of temperature. This diagram is from an article by H. T. Davis, J. F. Bodet, L. E. Scriven and W. G. Miller, on “Microemulsions and their Precursors,” in Physics of Amphiphilic Layers, J. Meunier, D. Langevin and N. Bociara, Spring-Verlag Proceedings in Physics 21 (1987).

    Google Scholar 

  6. The notation 232 have been used by some to designate the progression from oil-microemulsion to water-microemulsion two (2) phase equilibria via the Winsor three-phase equilibrium. S.-H. Chen, S. L. Chang, R. Strey, J. Samseth, and K. Mortensen,, J. Phys. Chem. 95, 7427 (1991)

    Article  Google Scholar 

  7. One of these (the Ising Model) is more tractable for analytical calculations. The other is more flexible in that it may be extended to become a cellular automaton, thereby describing dynamical phenomena.

    Google Scholar 

  8. B. Widom, Lattice Model of Microemulsions, J. Chem. Phys. 84, 6943 (1986)

    Article  ADS  Google Scholar 

  9. J. C. Wheeler and B. Widom, Phase Transitions and Critical Points in a Model Three Component System, J. Am. Chem. Soc. 40, 3064 (1968)

    Article  Google Scholar 

  10. K. A. Dawson, M. D. Lipkin, and B. Widom, Phase Diagram of a Lattice Microemulsion Model, J. Chem. Phys. 88, 5149 (1988)

    Article  ADS  Google Scholar 

  11. B. Widom, K. A. Dawson, and M. D. Lipkin, Hamiltonian and Phenomenological Models of Microemulsions,Physica 140A, 26 (1986).

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. A. Ciach and J. S. Høye, J. Chem. Phys. 90, 1222 (1989)

    Article  ADS  Google Scholar 

  14. A. Ciach, J. S. Høye, and G. Stell, J. Chem. Phys. 90, 1214 (1989)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. A. Ciach, J. S. Høye, and G. Stell J. Phys. A 21, L777 (1988)

    Article  ADS  Google Scholar 

  17. J. W. Halley, J. Chem. Phys. 88, 3313 (1988)

    Article  ADS  Google Scholar 

  18. M. Kahlweit and R. Strey, Langmuir 4, 499 (1988)

    Article  Google Scholar 

  19. G.M.Garneiro and M. Schick, J. Chem.Phys.89, 4638 (1988)

    Article  Google Scholar 

  20. T. P. Stockfisch and W. H. Shih, J. Phys. Chem. 92, 3292 (1988)

    Article  Google Scholar 

  21. K. Chen, C. Ebner, C. Jayaprakash and R. Pandid, Phys. Rev. A 38, 6240 (1988)

    Article  ADS  Google Scholar 

  22. K. Chen, C. Ebner, C. Jayaprakash and R. Pandid J. Phys. C 20, 1361 (1987)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. A. Robledo, Phys. Rev. A 36, 4067 (1987)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. S. A. Safran, D. Roux, and D. Andelman, Phys. Rev. Lett. 57, 491 (1986)

    Article  ADS  Google Scholar 

  27. M. Schick and W. H. Shih, Phys. Rev. B 341797(1986)

    Article  ADS  Google Scholar 

  28. Any interface in a lattice model possesses a “roughening” temperature above which is fluid-like, beneath which it is “flat” or crystalline-like. It is easy to prove that, above the roughening temperature, the lattice interface Hamiltonian is equivalent to a fluid Hamiltonian. In our discussions of microemulsion, the interface will always be a rough one, so the effects of the lattice on long length-scale properties are probably negligible. See, for example, Y. Levin and K. A. Dawson, Sine-Gordon Renormalization of the Orientational Roughening Transition, Phys. Rev. A 42, 3507 (1990). We should note, however, that such arguments are only technically valid for surfaces that do not deviate much from being planar. The large deviation case is not well understood.

    Google Scholar 

  29. K. A. Dawson, Spatially Frustrated Lattice Models, Phys. Rev. A 36, 3383 (1987).

    Article  ADS  Google Scholar 

  30. K. A. Dawson, B. L. Walker, and A. Berera, Accounting for Fluctuations in a Lattice Model of Microemulsions, Physica A 165, 320 (1990).

    Article  ADS  Google Scholar 

  31. K. A. Dawson, M. D. Lipkin, and B. Widom, Phase Diagram of a Lattice Microemulsion Model, J. Chem. Phys. 88, 5149 (1988)

    Article  ADS  Google Scholar 

  32. K. A. Dawson, Spatially Frustrated Lattice Models, Phys. Rev. A 36, 3383 (1987).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. K. A. Dawson, M. D. Lipkin, and B. Widom, Phase Diagram of a Lattice Microemulsion Model, J. Chem. Phys 88, 5149 (1988)

    Article  ADS  Google Scholar 

  35. K. A. Dawson, Spatially Frustrated Lattice Models, Phys. Rev. A 36, 3383 (1987).

    Article  ADS  Google Scholar 

  36. Y. Levin, C. J. Mundy, and K. A. Dawson, Renormalization of a Landau-Ginzburg-Wilson Theory of Microemulsion, Phys. Rev. A, in press.

    Google Scholar 

  37. S. A. Brazovskii, Sov. Phys.JETP 41, 85 (1978).

    ADS  Google Scholar 

  38. S. A. Chen,S. L. Chang, R. Strey,J. Samseth, K. Mortensen,J.Phys. Chem.95,7427(1991)

    Article  Google Scholar 

  39. S.-H. Chen, S.-L. Chang, and R. Strey, J. Chem. Phys. 93, 1907 (1990)

    Article  ADS  Google Scholar 

  40. E. W. Kaler, K. E. Bennett, H. T. Davis, and L. E. Scriven, J. Chem. Phys. 79, 5673 (1983)

    Article  ADS  Google Scholar 

  41. H. Saito and K. Shinoda, J. Colloid Interface Sci. 102, 647 (1970)

    Article  Google Scholar 

  42. C. Cabos and P. Delord, J. Appl. Cryst. 12, 502 (1979)

    Article  Google Scholar 

  43. M. Kolarchyk, S.-H. Chen, J. S. Huang, and M. W. Kim, Phys. Rev. A 29, 2054 (1984)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. B. H. Robinson, C. T. Toprakcioglu, J. C. Dore, and P. Chieux, J. Chem. Soc. Faraday Trans. 1 80, 13 (1984)

    Article  Google Scholar 

  46. S.-H. Chen, T. Lin and J. S. Huang, Physics of Complex Supermolecular Fluids, Exxon Monograph, S. A. Safran and N. A. Clark, Eds., Wiley and Sons, New York (1987).

    Google Scholar 

  47. K. A. Dawson, B. Walker, and A. Berera, Accounting for Fluctuations in a Lattice Model of Microemulsions, Physica A 165, 320 (1990).

    Article  ADS  Google Scholar 

  48. See, for example, A. Berera and K. A. Dawson, Low Temperature Analysis of Three-Phase Coexistence, Phys. Rev. Lett. 42, 3618 (1990)

    ADS  Google Scholar 

  49. K. A. Dawson, Interfaces Between Phases in a Lattice Model of Microemulsions, Phys. Rev. A 35, 1766 (1987).

    Article  ADS  Google Scholar 

  50. A. M. Cazabat, D. Langevin, J. Meunier A. Pouchelon,Critical Behavior in Microemulsions, Adv. Colloid Interface. Sci. 126,175 (1982)

    Article  Google Scholar 

  51. R. Aveyard, B. P. Binks, S. Clark and J. Mead, Interfacial Tension Minimum in Oil-Water-Surfactant Systems, J. Chem. Soc. Faraday Trans. 82, 125, (1986)

    Article  Google Scholar 

  52. J. R. Gunn and K. A. Dawson, Microscopic Model of Amhiphilic Assembly, J. Chem. Phys.91 6393 (1989)

    Article  ADS  Google Scholar 

  53. D. Guest, D. Langevin, and J. Meunier, Liquid interfaces: Role of the Fluctuations and Analysis of Ellipsometry and Reflectivity Measurements, J. Phys. (Paris). 48, 1819 (1987).

    Article  Google Scholar 

  54. J. R. Gunn and K. A. Dawson, Microscopic Model of Amhiphilic Assembly, J. Chem. Phys. 91, 6393 (1989).

    Article  ADS  Google Scholar 

  55. T. P. Hoar and J. H. Schulman, Nature 152, 102 (1943)

    Article  ADS  Google Scholar 

  56. J. H. Schulman, W. Stockenius, and L. M. Prince, Mechanism of Formation and Structure of Microemulsion by Electron Microscopy, J. Phys. Chem. 63, 1677 (1959)

    Article  Google Scholar 

  57. H. F. Eicke and J. Rehak, On the Formation of Water/Oil-Microemulsion, Helv. Chim. Acta 59, 2883 (1976).

    Article  Google Scholar 

  58. That the interface is typically non-wet is indicated by, for example, H. Kunieda and K. Shinoda, Correlation Between Critical Solution Phenomena and Ultralow interfacial Tensions in a Surfactant/Water!Oil System, Bull. Chem. Soc. Jpn. 55,1777 (1982).

    Article  Google Scholar 

  59. M. Kahlweit, R. Strey, M. Aratono, G. Busse, J. Jen, and K. V. Schubert, Tricriîical Points in H2O-Oil-Amphiphile Mixtures, J. Chem. Phys. 95, 2842 (1991)

    Article  ADS  Google Scholar 

  60. J. R. Gunn and K. A. Dawson, “A Lattice Model Description of Amphiphilic Mixtures. (I.) Equilibrium Properties,” J. Chem. Phys., in press.

    Google Scholar 

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

    Article  ADS  Google Scholar 

  62. M. Teubner and R. Strey, J. Chem. Phys. 87, 3195 (1987).

    Article  ADS  Google Scholar 

  63. S.-H. Chen, S.-L. Chang, and R. Strey, J. Chem. Phys. 93, 1907 (1990).

    Article  ADS  Google Scholar 

  64. See, for example, Monte Carlo Methods in Statistical Physics, K. Binder, ed. (Springer-Verlag, 1984).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  66. W. Jalur and R. Strey, J. Chem. Phys. 87, 3195 (1987).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  68. A. Ciach and J.S. Høye, J. Chem. Phys. 90, 1222 (1989)

    Article  ADS  Google Scholar 

  69. Dietrich Stauffer, Introduction to Percolation Theory, Taylor and Francis, London, 1985.

    Google Scholar 

  70. J. R. Gunn, C. M.Mcallum, and K. A. Dawson, A Dynamical Lattice Model Similation, Phys. Rev. A, in press; Y. Levin, C. Mundy, and K. A. Dawson, Relaxation Processes in Self-Assembled Systems (II), Phys. Rev. A, in press

    Google Scholar 

  71. J. Hardy, Y. Pomeau, and O. de Pazzis, J. Math. Phys. 14, 1746 (1973)

    Article  ADS  Google Scholar 

  72. J. Hardy, O. de Pazzis, and Y. Pomeau, Phys. Rev. A 3, 1949 (1976).

    Article  ADS  Google Scholar 

  73. U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56 1505 (1986)

    Article  ADS  Google Scholar 

  74. U. Frisch, D. d’Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet, Complex Systems 1, 648 (1987),

    Google Scholar 

  75. C. Appert and S. Zaleski, Phys. Rev. Lett. 64, 1 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  76. H. Chen, S. Chen, G.D. Doolen, Y.C. Lee, and H.C. Rose, Phys. Rev. A 40, 2850 (1989).

    Article  ADS  Google Scholar 

  77. D. d’Humières and P. Lallemand, Complex Systems 1, 598 (1987)

    Google Scholar 

  78. D. d’Humières, P. Lallemand, and G. Searby, Complex Systems 1, 632 (1987).

    Google Scholar 

  79. M.E. Colvin, A.J.C. Ladd, and B.J. Alder, Phys. Rev. Lett. 61, 381 (1988).

    Article  ADS  Google Scholar 

  80. D.H. Rothman and J.M. Keller, J. Stat. Phys. 52, 1119 (1988)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  81. G.W. Baxter and R.P. Behringer, Phys. Rev. A 42, 1017 (1990).

    Article  ADS  Google Scholar 

  82. M. Creutz, Phys. Rev. Lett. 50, 1411 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  83. M. Creutz, Ann. Phys. 167, 62 (1986).

    Article  ADS  Google Scholar 

  84. L. Onsager, Phys. Rev. 65, 117 (1944)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  85. B.M. McCoy and T.T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambridge, 1973).

    MATH  Google Scholar 

  86. D. Frenkel and M.H. Ernst, Phys. Rev. Lett. 63, 2165 (1989).

    Article  ADS  Google Scholar 

  87. K. Binder, Phys. Rev. A 25, 1699 (1982).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Chemistry, University of California, Berkeley, CA, 94720, USA

    K. A. Dawson

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  1. K. A. Dawson
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Editors and Affiliations

  1. Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Sow-Hsin Chen

  2. Corporate Research, Exxon Research and Engineering Company, Annandale, NJ, USA

    John S. Huang

  3. Dipartimento di Fisica, Università di Roma la Sapienza, Rome, Italy

    Piero Tartaglia

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Dawson, K.A. (1992). Lattice Models of Amphiphilic Assembly. In: Chen, SH., Huang, J.S., Tartaglia, P. (eds) Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution. NATO ASI Series, vol 369. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2540-6_13

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  • DOI: https://doi.org/10.1007/978-94-011-2540-6_13

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