Ginzburg-Landau theory of aqueous surfactant solutions

A simple two order-paraIneter 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 K is found to depend only on the orientational profile of a flat bilayer.