Mixtures of water, oil, and surfactant often form microemulsions where tiny drops of oil (or water) are dispersed in a matrix of water (or oil). A microemulsion is a partially-ordered fluid in which the surfactant molecules exist in an oriented layer at the boundary between the continuous phase and the discontinuous phase. This work proposes a molecular-thermodynamic model that is useful for calculating a variety of phase diagrams observed in microemulsion-forming systems.
The model is based on a revised form of Widom's abstract representation of a microemulsion; that representation provides a procedure for calculating essential contributions to the configurational entropy. In Widom's representation, all molecules are difunctional dumbbells such that all the hydrophilic ends are situated together in some lattice sites and all the lipophilic ends are situated together in other sites. A form of Guggenheim's quasichemical theory is used to evaluate the combinatorial contributions that correspond to Widom's picture. Chemical association of surfactant molecules and physical interactions are also taken into account. Minimization of the Gibbs energy yields a distribution function for representing micelle sizes.
Calculated ternary phase diagrams are in good agreement with experimental results. Different types of diagrams can be obtained upon changing physically significant model parameters. A study of how these parameters affect phase behavior provides insight on microemulsion stability.