Structure and phase equilibria of microemulsions

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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.