THERMAL FLUCTUATIONS AND PHASE-EQUILIBRIUM IN MICROEMULSIONS

We construct a simple coarse-grained model and use it to study global phase behavior of ensembles of fluid membranes. This model is an improvement over previous phenomenological models of Talmon and Prager, de Gennes and co-workers, Widom, and more recently of Safran and co-workers. We show here that there is necessarily an entropic contribution, missing in all previous theories, to the coarse-grained free energy whose physical origin is the same as that of Helfrichs entropic repulsion stabilizing lamellar multimembrane phases. The inclusion of this steric entropy in the previous phenomenological studies is essential if they are to be used in the study of periodic phases in microemulsions and analogous surfactant systems. Thus the model enables us to obtain, in a unified way, phase diagrams containing both uniform and periodic phases in microemulsions and in binary systems of nonionic surfactant bilayers in a single solvent. Mean-field theory for this model yields rich phase diagrams containing dilute, random bicontinuous, lamellar, columnar, and an antiferromagnetic phase that may correspond to a droplet crystal or to a plumbers nightmare. The model depends on two phenomenological parameters related to strengths of steric entropy and softening of membrane rigidity. We discuss the sensitivity of phase diagrams (in particular the existence of the middle-phase microemulsion) to values of these parameters. We find that the existence of a realistic middle phase (with structural length scale much larger than the molecular length scale) crucially depends on the presence of steric entropy. The model reproduces the experimentally observed four-phase equilibria among uniform phases in microemulsions. © 1990 The American Physical Society.