A model for membranes, vesicles and micelles in amphiphilic systems

We present a microscopic model for the aggregates of amphiphilic molecules, based on a simple density functional approximation for the free energy. The different molecular aggregates are described as self-structured density distributions at the relative minima of the grand potential energy. We search for these structures with planar and spherical geometries, and obtain the phase diagram for bilayer membranes, and the curvature energies for vesicles and different types of micelles. The study of a global phase diagram, to get the density of micelles and isolated amphiphilic molecules, at equilibrium with free membranes, requires me link between two description levels of micelles: as self-structured density distributions, or as molecular clusters in the solution of amphiphilic molecules in water. This is done with the help of a simple harmonic model which provides an appropriate choice of the configurational unit cell for micelles.