Lattice model for surfactants in solution

Abstract

A three-dimensional lattice model for surfactant mixtures is presented in this paper. We extend the spin-1 or Blume-Emery-Griffiths model to include orientational degrees of freedom for each molecule. The model is then applied to ternary mixtures of surfactant with equal amounts of water and oil, and to binary mixtures of surfactant and water. For each case, phase diagrams are calculated using both mean-field and Bethe approximations. One interesting feature of this model is that it can exhibit long-period lamellar phases even though a simple Hamiltonian, containing only nearest-neighbor interactions, is used. The model also produces a ‘‘disorder line,’’ which is thought to divide the disordered phase of the ternary mixture into a region of ordinary disordered fluid and a region of microemulsion.