Lattice model of microemulsions

Abstract

A simple model of oil, water, and amphiphile, in which the third is favored energetically to sit between the other two, is studied in three dimensions via mean-field theory. Oil-rich, water-rich, disordered fluid, and lamellar phases exist. Phase diagrams show the progression from two-phase to three-phase to two-phase coexistence commonly observed in such systems. Three independent structure functions characterizing the disordered fluid are calculated to determine whether it can be identified with a microemulsion. It is found that the region in which this fluid phase exists can be divided into a part in which correlation functions decay monotonically at large distances, and another in which their decay is nonmonotonic. We identify the latter with the microemulsion. There is no phase transition between the two regions. In the microemulsion, the water-water structure function at low wave number has the form proposed by Teubner and Strey, with coefficients that we determine. The behavior of the structure functions along different thermodynamic paths, and for systems both balanced and not, is presented. Agreement with experiment is qualitatively good.