From micelles to microemulsion droplets: Size distributions, shape fluctuations, and interfacial tensions

Abstract

We present a theoretical description of the aggregation equilibrium of nonswollen and water-swollen micelles in oil (or vice versa). While we specialize on spherical, noninteracting aggregates, we treat the competition between phase separation, dissolution in monomers and formation of micelles with variable extent of swelling. The present model is based on an interfacial free energy of the surfactant monolayer which includes stretching and bending contributions. This free energy allows one to desribe both, the macroscopic interface in a two-phase system and the internal interface surrounding the aggregates on equal footing. The extent of swelling of the micelles at the CMC is determined by the bending energy of the saturated surfactant monolayer. Increasing the splay modulus or decreasing the spontaneous curvature favors swollen micelles (microemulsion droplets) and ultralow interfacial tensions. We present explicit results for the size distributions of the aggregates and interfacial tensions. Considering shape fluctuations of the aggregates we conclude that spherical micelles may be stabilized by small interfacial tension alone, while stability of strongly swollen microemulsion droplets requires a finite splay modulus of the monolayer.