We have developed a simple off-lattice density functional theory and applied it to ternary water-oil-amphiphile mixtures. Our approach is based on mean field free energy functionals calculated from hard-sphere perturbation theory, to which is added a contribution arising from molecular association between the water-like and the amphiphilic species. This latter term is treated using the Wertheim theory for associating liquid mixtures, and it gives rise to a re-entrant binary phase diagram in a very natural way. The resulting ternary phase diagrams resemble experimental data both qualitatively and quantitatively. We also calculate the structure and free energy of interfaces between phases in this system, and show that the presence of amphiphile dramatically lowers the surface tension between the water-rich and oil-rich phases. This simple model contains many of the features of real microemulsion systems, and can be extended to study lamellar and other complex phases.
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