A model microemulsion

Abstract

The microemulsion model of de Gennes et al., which is a modified version of the earlier model of Talmon and Prager, is modified further by imposing a microscopic cell-size cutoff. Two free-energy minima compete and lead to a composite free-energy surface consisting of two intersecting sheets. The microemulsion phase arises from one sheet and the oil- and water-rich phases with which it may be in equilibrium arise from the other. The Schulman condition, according to which the surfactant-film pressure equals the oil–water interfacial tension, is found to hold to good approximation in the middle-phase microemulsion that contains comparable amounts of oil and water. The oil- and water-filled domains in that microemulsion are found to be about 75–80 Å across. That phase is of such high osmotic compressibility that it would be opalescent or turbid due to fluctuations of composition. The model shows a range of phase equilibria like that seen in experiment, including two- and three-phase equilibria, critical points, and critical endpoints. The critical points are tricritical, and each is associated with a locus of second-order transitions.