J. Phys. II France
Volume 2, Numéro 9, September 1992
Page(s) 1725 - 1744
DOI: 10.1051/jp2:1992230
J. Phys. II France 2 (1992) 1725-1744

Ginzburg-Landau theory of aqueous surfactant solutions

G. Gompper and Stefan Klein

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

(Received 26 May 1992, accepted 15 June 1992)

A simple two order-parameter Ginzburg-Landau theory for binary mixtures of water and amphiphile is introduced. The amphiphile concentration is described by a scalar, the orientational degrees of freedom of the amphiphile by a vector order parameter. Phase diagrams are calculated by minimizing the free energy functional. Several ordered lyotropic phases of lamellar, hexagonal, inverse hexagonal, and cubic structure exist. Phase diagrams show the sequence of ordered phases with increasing amphiphile concentration commonly observed in such systems. Several scattering intensities characterizing the disordered phase are calculated. They clearly show the tendency for bilayer or micelle formation. Finally, the elastic bending constants of surfactant bilayers are determined. The bending modulus $\kappa$ is found to depend only on the orientational profile of a flat bilayer.

61.20G - 61.25E - 64.60C

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