A LATTICE MODEL DESCRIPTION OF AMPHIPHILIC MIXTURES .1. EQUILIBRIUM PROPERTIES

A three-component lattice model with unit-vector orientations at the lattice sites is presented. The model describes ternary mixtures of oil, water, and amphiphile, and in particular the microemulsion phase. The phase diagram of the model is derived using mean-field theory and simulation. It is shown that the results of Monte Carlo simulations of sufficiently large systems show remarkable agreement with experiment. In particular, the present model reproduces the mesoscopic order of the microemulsion phase. The structure of the microemulsion is understood in terms of the liquid-crystalline phases adjacent to it on the phase diagram and the nature of the phase transitions that occur between them. The behavior of the system when the ratio of oil to water is changed is investigated and the percolation threshold is described. A method for carrying out dynamical simulations is discussed.