Isotropic Phases of Self-Assembled Amphiphilic Aggregates

An account is given of recent theoretical and experimental progress in understanding isotropic phases of amphiphilic molecules in solution. The viewpoint is mainly that of equilibrium statistical mechanics, but with some discussion of dynamical features, such as viscoelasticity. We start by discussing spherical and anisometric micelles, especially rigid rod micelles, and their interactions with each other and with perturbing fields. Flexible worm-like micelles are next considered, emphasising their length distribution and its kinetics; their linear (and, briefly, nonlinear) visco-elasticity; tracer diffusion, including anomalous diffusion; and the role of equilibrium crosslinks. The aggregation of amphiphiles into bilayers is then discussed. The elastic curvature energy of bilayers is used to account for the stability of the sponge phase (L$_{3}$). Scaling laws for dilution of this phase are given, and its unusual symmetry pointed out. The role of edge- and line-defects in the sponge phase is outlined, along with preliminary ideas concerning its dynamical properties. Finally, the possible stability of other isotropic bilayer phases, containing equilibrium vesicles and/or onion-like structures, is briefly examined.