Structure of droplet microemulsions in the semi-dilute regime

We derive a functional of the microemulsion droplets size distribution function by adding the entropic free energy of a system of polydisperse hard spheres to the Helfrich interfacial free energy of the amphiphilic film. The latter is minimized by a monodisperse system of spherical (independent) aggregates, at the equilibrium radius, while the former is minimized by a random distribution of droplet sizes. As a result the equilibrium droplet size distribution yields a mean radius that is smaller than the equilibrium radius of isolated droplets. A link with molecular parameters is established by using our microscopic model for ternary amphiphilic mixtures and a (mean-field) free energy functional of the density profiles [J. Chem. Phys. 109, 1152 (1998)] to calculate the parameters of the Helfrich interfacial free energy for a single droplet. The theoretical results are compared with small-angle neutron scattering data reported by Gradzielski et al. [Phys. Rev. E 53, 3900 (1996)].