A triangular lattice model for binary and ternary mixtures containing surfactants

The phase equilibria of ternary mixtures of water, oil and surfactants and binary mixtures of water and surfactants are studied using a triangular lattice-gas model that is an extension of the spin-1 Blume-Capel model with the addition of the orientational degrees of freedom for surfactants. The phase diagram of the model is investigated via Monte Carlo simulations in conjunction with the extrapolation technique of Ferrenberg and Swendsen combined with the finite-size scaling method of Lee and Kosterlitz. Five phases are found for ternary mixtures in the case of equal water and oil concentrations: a water-oil coexistence region, a lamellar phase, a liquid crystalline phase, which has the symmetry of a rhombic lattice, and an extended disordered phase, which is divided by a Lifshitz line into disordered fluid and microemulsion regions. In the limiting case of a binary mixture of water and surfactants, we found a rich phase diagram corresponding to a lamellar phase, a hexagonal phase and a disordered phase. which is again divided by a Lifshitz line into disordered fluid and structured fluid regions. The latter can be considered as the analogue of the microemulsion found for the ternary systems