Phase diagram of a lattice model for ternary mixtures of water, oil, and surfactants

We study a lattice model for a three-component system of water, oil, and surfactants in two dimensions. Large-scale Monte Carlo simulations were performed to obtain the phase equilibria for a wide range of temperatures and surfactant concentrations. We show that this model has a rich phase behavior, and both microemulsion and liquid crystalline phases were found. The phase behavior is consisent with that of a real system, and is in qualitative agreement with the model of Gompper and Schick [Phys. Rev. Lett. 62, 1647 (1989)], which is based on three-body interactions