Statistical mechanics of microemulsions

Abstract

At low surfactant concentrations, an oil–water microemulsion may be represented as two immiscible continuum fluids, oil and water, dispersed in one another so as to form two interpenetrating, multiply connected regions, with the surfactant adsorbed at the interface between them. Scriven¹ has pointed out that as the oil/water ratio is increased, three types of structure will evolve in succession: starting from the oil-in-water emulsion to be expected at low oil content, there should be a smooth transition to a bicontinuous structure, in which neither phase can be said to surround the other, followed by a second transition to a water-in-oil emulsion when the oil content is sufficiently high. It seems likely, as Scriven suggests, that the phase diagrams reported for microemulsion systems involve all of these structures. Here we propose a statistical mechanical model for microemulsions, based on a simple procedure for generating random two-fluid geometries. Over certain ranges of the model parameters, the resulting free energy-composition surface shows regions where a bicontinuous phase may coexist with an oil-in-water and a water-in-oil emulsion; such three-phase equilibria have been observed experimentally². Our calculations also suggest a possible explanation of the very low interfacial tensions sometimes found between microemulsion phases.