Net-average curvature model for solubilization and supersolubilization in surfactant microemulsions

In this work, we propose a mathematical model to reproduce the solubilization, equivalent droplet radius, interfacial tension, and phase transitions of anionic surfactant microemulsions by scaling the curvature of the surfactant membranes to the electrolyte concentration required to obtain an optimum microemulsion formulation. At optimum formulation, equal amounts of oil and water are cosolubilized in a bicontinuous media that has a zero net curvature. Our first modeling approach is to use a single curvature term (inverse of an equivalent spherical droplet ratio) which proves to be inadequate as the system transitions to a bicontinuous microemulsion (supersolubilization), where the micelles become swollen and are no longer spherical. Later we introduce two curvature terms (net and average curvature) to interpret bicontinuous microemulsion behavior. The scaling constant (L), which has a length scale, was obtained for sodium dihexyl sulfosuccinate microemulsions with styrene, trichloroethylene, and limonene. This scaling constant (L) is shown to be independent of the oil type, temperature, surfactant, or additive concentration. We use this net-average curvature model to reproduce selected published data. We also compare the scaling constants (L values) for the different microemulsion systems studied, finding that this parameter is proportional to the length of the extended tail of the surfactant and reflects the surfactant solubilization potential. Additionally, the model was modified to account for palisade micellar solubilization. Finally, we introduce the interfacial rigidity concept to reproduce the interfacial tension of these systems.