Bifurcation analysis and liquid-crystal phases in Landau-Ginzburg model of microemulsion

Landau-Ginzburg model for oil-water-surfactant mixtures with three order parameters is derived from the lattice vector model [Ciach, Hoye, and Stell, J. Phys. A 21, L777 (1988)]. In case of oil-water symmetry all the coupling constants are explicitly expressed in terms of surfactant volume fraction rho(s), temperature T, and a parameter gamma describing the strength of surfactant. The bifurcation line in the parameter space (rho(s),T) and the positions of the Lifshitz and the tricritical points are found for different values of gamma. The structure of the ordered phases below the bifurcation is determined. For growing surfactant concentration lamellar, double-diamond, simple cubic and face-centered phases are stable; the last one is followed by the tricritical point. For strong surfactants the ordered phases appear for rho(s) similar to 10%. We claim that the present model is suitable for weak as well as for strong surfactants. (C) 1996 American Institute of Physics.