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

Abstract

An essential characteristic and common feature of certain amphiphilic systems is the existence of the special two-dimensional membrane-like structure of their local order. As seen in previous chapters, these amphiphilic systems can be considered with good approximation as true bidimensional surfaces, at scales larger than their thickness (≈ 10–20Å). Consequently, many of their properties can be related to the geometrical, mechanical and statistical characteristics of simple fluctuating surfaces, independently of the details of their internal structure. Examples are provided by vesicles and lamellar phases, in which the two-dimensional membrane-like structure characterizes the whole system, and by fluid middle-phase isotropic microemulsions [1], whose properties can be understood in terms of the local sheet-like order. Among the extraordinary wealth of phases encountered in lyotropic (ternary, quaternary …) systems, the lamellar phases occupy a surprisingly large place in the phase diagrams [1]. Their importance also relies on their observed coexistence with less ordered phases (microemulsions) [2,3] or more ordered structures (e.g., hexagonal or cubic phases) [4] which place them in a unique intermediary position (and structure) (see Sec. 1.4.2). In the following, we will call under the generic name “membrane” all systems presenting a two-dimensional membrane-like structure in their local order.

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References

  1. P. Ekwall, Adv. Liq. Cryst. 1,1 (1975).

    Google Scholar 

  2. D. Roux, Ph.D. Thesis (1984), Bordeaux.

    Google Scholar 

  3. Physics of Amphiphiles: Micelles, Vesicles and Microemulsions, V. Degiorgio and M. Corti, eds. (North Holland, Amsterdam, 1985).

    Google Scholar 

  4. J. Charvolin and A. Tardieu, Solid State Phys. 48 209 (1978), F. Seitz and D. Turnbull, eds.

    Google Scholar 

  5. D. Sornette and N. Ostrowsky, J. de Physique 45 265 (1984).

    Article  Google Scholar 

  6. J. Fröhlich, The Statistical Mechanics of Surfaces, Lecture Notes in Physics 216 151 (1985).

    Google Scholar 

  7. Statistical Mechanics of Membranes and Surfaces, D. R. Nelson, T. Piran and S. Weinberg, eds., Fifth Jerusalem Winter School (World Scientific, Singapore, 1987).

    Google Scholar 

  8. P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1985), 2nd edition.

    Google Scholar 

  9. A. M. Polyakov, Nucl. Phys. B 268 406 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  10. P. Orland, Phys. Rev. Lett. 59 2393 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  11. W. Helfrich, Z. Naturforsch 28c 693 (1973).

    Google Scholar 

  12. H. J. Deuling and W. Helfrich, Biophys. J. 16 861 (1976)

    Google Scholar 

  13. H. J. Deuling and W. Helfrich, J. de Physique 37 1335 (1976).

    Google Scholar 

  14. R. M. Servuss, W. Harbich and W. Helfrich, Biochem. Biophys. Acta 436 900 (1976).

    Google Scholar 

  15. S. B. Hladky and D. W. R. Gruen, Biophys. 38 251 (1982).

    Article  Google Scholar 

  16. M. A. Peterson, J. Math. Phys. 26 711 (1985).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. W. Helfrich, in Physics of Defects (Les Houches, Session XXXV, 1980), R. Balian et al. eds. (North Holland, Amsterdam, 1981).

    Google Scholar 

  18. F. Brochard, P. G. De Gennes and P. Pfeuty, J. de Physique 37 1099 (1976).

    Article  Google Scholar 

  19. H. Engelhardt, H. P. Duwe and E. Sackmann, J. de Physique Lett. 46 L-395 (1985).

    Google Scholar 

  20. J. F. Faucon, M. D. Mitov, P. Méléard, I. Bivas and P. Bothorel, J. de Physique 50 2389 (1989).

    Article  Google Scholar 

  21. H. P. Duwe, J. Kaes and E. Sackmann, J. de Physique 51, 945 (1990).

    Article  Google Scholar 

  22. M. Mutz and W. Helfrich, J. de Physique 51, 991 (1990).

    Article  Google Scholar 

  23. F. Brochard and J. F. Lennon, J. de Physique 36, 1035 (1975).

    Article  Google Scholar 

  24. F. C. Larche, J. Appell, G. Porte, P. Bassereau and J. Marignan, Phys. Rev. Lett. 56, 1700 (1986).

    Article  ADS  Google Scholar 

  25. J.-M. de Meglio, M. Dvolaitzky, L. Léger and C. Taupin, Phys. Rev. Lett. 54, 1686 (1976).

    Article  Google Scholar 

  26. F. Nallet, D. Roux and J. Prost, Phys. Rev. Lett. 62 276 (1989).

    Google Scholar 

  27. F. Nallet, D. Roux and J. Prost, J. de Physique 50, 3147 (1989).

    Google Scholar 

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

    Article  Google Scholar 

  29. Ordering in Two Dimensions, S. K. Sinha, ed. (North Holland, 1982).

    Google Scholar 

  30. D. R. Nelson, in Fundamental Problems in Statistical Mechanics V, E. G. D. Cohen, ed. (North Holland, Amsterdam, 1985).

    Google Scholar 

  31. L. Peliti and S. Leibler, Phys. Rev. Lett. 54, 1690 (1985).

    Article  ADS  Google Scholar 

  32. D. Sornette, Thèse d’état, Université de Nice (1985).

    Google Scholar 

  33. W. Helfrich, J. de Physique 46, 1263 (1985).

    Google Scholar 

  34. W. Helfrich, J. de Physique 48 285 (1987).

    Google Scholar 

  35. D. Förster, Europhys. Lett. 4, 65 (1987).

    Article  ADS  Google Scholar 

  36. F. David and E. Guitter, Europhys. Lett. 5, 709 (1988).

    Article  ADS  Google Scholar 

  37. H. Kleinert, J. Stat. Phys. 56 227 (1989b)

    Google Scholar 

  38. H. Kleinert, Phys. Lett. A 138 201 (1989a)

    Google Scholar 

  39. H. Kleinert, Phys. Rev. Lett. 58, 1915 (1987).

    Google Scholar 

  40. D. R. Nelson and L. Peliti, J. de Physique 48, 1085 (1987).

    Article  Google Scholar 

  41. F. David, E. Guitter and L. Peliti, J. de Physique 48, 2059 (1987).

    Article  Google Scholar 

  42. Y. Kantor and D. R. Nelson, Phys. Rev. A 35, 4020 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  43. D. Sornette, J. Phys. Condens. Matter 1 1905 (1989)

    Google Scholar 

  44. D. Sornette, in Physics of Amphiphilic Layers,Les Houches, J. Meunier, D. Langevin and N. Boccara, eds. (Springer-Heidelberg, 1987).

    Google Scholar 

  45. L. Golubovic and T. C. Lubensky, Phys. Rev. B 39 12110 (1989).

    Article  ADS  Google Scholar 

  46. P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).

    Article  ADS  Google Scholar 

  47. S. Dietrich, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (1987).

    Google Scholar 

  48. V. L. Pokrovsky and A. L. Tapalov, Theory of Incommensurate Crystals, Soviet Scientific Reviews, Physics 1 (Harwood, 1984).

    Google Scholar 

  49. J. Villain, in Structures et Instabilités, C. Godrèeche, ed. (Les éditions de Physique, 1986).

    Google Scholar 

  50. M. E. Fisher and D. S. Fisher, Phys. Rev. B 25 3192 (1982).

    Google Scholar 

  51. S. G. J. Mochrie, A. R. Kortan, R. J. Birgeneau and P. M. Horn, Z. Phys. B 62 79 (1985).

    Article  ADS  Google Scholar 

  52. J. N. Israelachvili, Intermolecular and Surface Forces, With Applications to Colloidal and Biological Systems (Academic Press, 1985).

    Google Scholar 

  53. J. Mahanty and B. W. Ninham, Dispersion Forces (Academic Press, London, 1976).

    Google Scholar 

  54. B. V. Derjaguin, Y. I. Rabinovich and N. V. Churaev, Nature 272 313 (1978).

    Article  ADS  Google Scholar 

  55. S. Nir, Progress. Surf. Sci. 8 1 (1976).

    Article  ADS  Google Scholar 

  56. R. Kjellander and S. Marcelja, Chemica Scripta 25 1 (1985).

    Google Scholar 

  57. D. F. Evans and B. W. Ninham, J.Phys. Chem. 90 226 (1986).

    Article  Google Scholar 

  58. N. Ostrowsky and D. Sornette, Colloids and Surfaces 14 231 (1985).

    Google Scholar 

  59. J. N. Israelachvili and D. Sornette, J. de Physique 46 2125 (1985).

    Article  Google Scholar 

  60. W. Helfrich, Z. Naturforsch 33a 305 (1978).

    ADS  Google Scholar 

  61. L. J. Lis, M. McAllister, N. Fuller, R. P. Rand, and V. A. Parsegian, Biophys. J. 37 657 (1982).

    Google Scholar 

  62. W. Helfrich and R. M. Servuss, Il Nuovo Cimento 3D 137 (1984).

    Article  ADS  Google Scholar 

  63. P. Nozières, Course at Collège de France, Paris (1984), unpublished.

    Google Scholar 

  64. D. Sornette and N. J. Ostrowsky, J. Chem. Phys. 84 4062 (1986).

    Article  ADS  Google Scholar 

  65. D. Sornette, Europhys. Lett. 2 715 (1986).

    Article  ADS  Google Scholar 

  66. P. G. de Gennes, Physics of Liquid Crystals (Oxford Unitersity Press, Oxford, 1974).

    Google Scholar 

  67. D. Sornette, J. de Physique 48 151 (1987).

    Google Scholar 

  68. O. Parodi, in Colloides et Interfaces, Les éditions de Physique, A. M. Cazabat and M. Veyssié, eds. (1984).

    Google Scholar 

  69. M. Kléman, Points, Lignes, Parois dans les Fluides Anisotropes et les Solides Cristallins, 1 Les éditions de physiques (1977).

    Google Scholar 

  70. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).

    Article  ADS  Google Scholar 

  71. A. Caillé, C.R.A.S. (Paris) 274, 891 (1972).

    Google Scholar 

  72. R. Ribotta and G. Durand, J. de Physique 38 179 (1977).

    Article  Google Scholar 

  73. G. Grinstein and R. A. Pelcovitz, Phys. Rev. Lett. 47, 856 (1981).

    Article  ADS  Google Scholar 

  74. G. Grinstein and R. A. Pelcovitz, Phys. Rev. A 26 915 (1982).

    Article  ADS  Google Scholar 

  75. C. R. Safinya, E. B. Sirota, D. Roux, and G. S. Smith, Phys. Rev. Lett. 62 1134 (1989).

    Article  ADS  Google Scholar 

  76. C. R. Safinya, D. Roux, G. S. Smith, S. K. Sinha, P. Dimon, N. A. Clark and A. M. Bellocq, Phys. Rev. Lett. 57, 2718 (1986).

    Article  ADS  Google Scholar 

  77. D. Roux and C. R. Safinya, J. de Physique 49 307 (1988).

    Article  Google Scholar 

  78. W. Janke and H. Kleinert, Phys. Lett. A 117, 353 (1986).

    Article  ADS  Google Scholar 

  79. W. Janke and H. Kleinert, Phys. Rev. Lett. 58 144 (1987).

    Article  ADS  Google Scholar 

  80. W. Janke, H. Kleinert and Meinhart, Phys. Lett. B 217, 525 (1989).

    Article  ADS  Google Scholar 

  81. G. Gompper and D. M. Kroll, Europhys. Lett. 9, 59 (1989).

    Article  ADS  Google Scholar 

  82. R. Lipowsky and B. Zielinska, Phys. Rev. Lett. 62 1572 (1989).

    Article  ADS  Google Scholar 

  83. S. Leibler and A. Maggs, Phys. Rev. Lett. 63 406 (1989).

    Article  ADS  Google Scholar 

  84. P. G. de Gennes, J. Chem. Phys. 48, 2257 (1968).

    Article  ADS  Google Scholar 

  85. J. Villain and P. Bak, J. de Physique 42 657 (1981).

    Article  Google Scholar 

  86. M. E. Fisher, J. Stat. Phys. 34, 667 (1984).

    Article  ADS  MATH  Google Scholar 

  87. R. Lipowsky and S. Leibler, Phys. Rev. Lett. 56 2541 (1986).

    Article  ADS  Google Scholar 

  88. R. Lipowsky and M. Fisher, Phys. Rev. B 36 2126 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  89. D. Sornette, J. Phys. C 20 4695 (1987).

    Article  ADS  Google Scholar 

  90. N. Ostrowsky and D. Sornette, Chemica Scripta 25 108 (1985).

    Google Scholar 

  91. K. G. Wilson, Sci. Am. 241 (August issue), 158 (1979).

    Article  Google Scholar 

  92. J. Bricmont, A. El. Mellouke and J. Fröehlich, J. Stat. Phys. 42, 743 (1986).

    Article  ADS  Google Scholar 

  93. E. Brézin, B. I. Halperin and S. Leibler, Phys. Rev. Lett. 50 1387 (1983)

    Google Scholar 

  94. E. Brézin, B. I. Halperin and S. Leibler, J. de Physique 44, 775 (1983).

    Google Scholar 

  95. D. S. Fisher and D. A. Huse, Phys. Rev. B 32 247 (1985).

    Article  ADS  Google Scholar 

  96. S. Leibler and R. Lipowsky, Phys. Rev. B 35 7004 (1987).

    Article  ADS  Google Scholar 

  97. Physics of Amphiphilic Layers, L. Meunier, D. Langevin and N. Boccara, eds. (Springer-Heidelberg, 1987).

    Google Scholar 

  98. R. Lipowsky, Europhys. Lett. 7, 255 (1989).

    Article  ADS  Google Scholar 

  99. F. David, Europhys. Lett. 6, 603 (1988).

    Article  ADS  Google Scholar 

  100. R. F. Kayser, Phys. Rev. A 33 1948 (1986).

    Article  ADS  Google Scholar 

  101. Y. Kantor and D. R. Nelson, Phys. Rev. Lett. 58 2774 (1987); Y. Kantor and D. R. Nelson, Phys. Rev. A 36 4020 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  102. J. Aronovitz and T. C. Lubensky, Phys. Rev. Lett. 60 2634 (1988).

    Article  ADS  Google Scholar 

  103. M. Paczusky, M. Kardar and D. R. Nelson, Phys. Rev. Lett. 60 2638 (1988).

    Article  ADS  Google Scholar 

  104. Y. Kantor, M. Kardar and D. R. Nelson, Phys. Rev. A 35 3056 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  105. M. Kardar and D. R. Nelson, Phys. Rev. Lett. 58, 1289 (1987).

    Article  ADS  Google Scholar 

  106. J. Aronovitz, L. Golubovic and T. C. Lubensky, J. de Physique 50 609 (1989).

    Article  Google Scholar 

  107. J. Toner, Phys. Rev. Lett. 62, 905 (1989).

    Article  ADS  Google Scholar 

  108. D. Roux and C. Coulon, J. de Physique 47, 1257 (1986).

    Article  Google Scholar 

  109. E. A. Evans and V. A. Parsegian, Proc. Natl. Acad. Sci. 83, 7132 (1986).

    Google Scholar 

  110. S. Chandrasekar, Rev. Mod. Phys. 15 1 (1943).

    Article  ADS  Google Scholar 

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Sornette, D., Ostrowsky, N. (1994). Lamellar Phases: Effect of Fluctuations (Theory). 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_5

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