A model microemulsion

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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.