Microemulsions: theoretical estimates of droplet sizes and size distributions

Abstract

After a brief introduction on general properties of microemulsions, this paper presents an expression for the Gibbs energy of a water in oil (W/O) microemulsion containing a range of droplet sizes. Droplets are partitioned in categories, j, where j is the number of surfactant molecules per droplet. The Gibbs energy takes into account: the amounts and chemical potentials of the constitutents of the dispersion medium and of the droplets, including the adsorption layers, the interfacial tension, the bending stress and the concentration of droplets of type j. The droplets of all sizes are in a mass-action equilibrium with single molecules in the water and/or oil regions. — A few necessary parameters are taken from experiments with the system: water, cyclohexane, sodium dodecylsulphate (SDS), 1-pentanol, and NaCl. — The concentration of droplets of type j can then be expressed in their radius, a _j , their surface tension and its dependence on curvature, and known constants (such as kT and parameters pertaining to the electrical double layer) both for saturated (Winsor II equilibria) and unsaturated microemulsions. — The size distributions are found to be fairly wide, the width increasing with increasing average droplet size.