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Elastic Properties of Interfaces in a Ginzburg-Landau Theory of Swollen Micelles, Droplet Crystals and Lamellar Phases

Using a Ginzburg-Landau free energy for oil-water-surfactant mixtures, we show that the Helfrich Hamiltonian describes the free energy of the amphiphilic monolayers at the oil/water interface, and calculate the bending rigidity, the saddle splay modulus and the spontaneous radius of curvature. The results are used to discuss the phase diagram obtained from Landau theory, which contains a lamellar phase, a hexagonal phase of cylinders, and a droplet crystal. It is found that the interaction of the monolayers plays an important role in stabilizing the lamellar phase.