Structure and phase equilibria of microemulsions

Abstract

We present a simple phenomenological model to describe the phase equilibria and structural properties of microemulsions. Space is divided into cells of side ξ; each cell is filled with either pure water or oil. Surfactant molecules are presumed to form an incompressible fluid monolayer at the oil–water interface. The monolayer is characterized by a size-dependent bending constant K(ξ), which is small for ξ≥ξK, the de Gennes–Taupin persistence length. The model predicts a middle-phase microemulsion of structural length scale ξ≊ξK which coexists with dilute phases of surfactant in oil and surfactant in water. (These phases have ξ≊a, a being a molecular length.) On the same ternary phase diagram, we find also two regions of two-phase equilibrium involving upper- and lower-phase microemulsions that coexist with either almost pure water or oil. At low temperatures and/or high values of the bare bending constant, K0≡K(a), the middle-phase microemulsion may be entirely precluded by separation to a lamellar phase, whereas at high temperature and/or low values of K0, there is a first-order transition between a disordered microemulsion and a lamellar phase. In the absence of spontaneous curvature the phase diagram is oil–water symmetric. It may be asymmetrized by: (i) spontaneous curvature in the middle phase or (ii) a difference between the free energy of the two dilute phases. If the asymmetry is sufficiently large, the three-phase region disappears.