A Theoretical Analysis of Synergistic Effects in Mixed Surfactant Systems

Abstract

Synergistic effects in mixed binary surfactant systems have been investigated by analyzing the main contributions to the free energy of forming a mixed surfactant aggregate. We show that a nonlinear behavior of the critical micelle concentration (cmc) with respect to the surfactant composition of the aggregates is determined by a nonlinear behavior of the free energy per aggregated surfactant. It appears that synergistic effects are due mainly to entropic free energy contributions related with the surfactant headgroups. For a mixture of a monovalent ionic and a nonionic surfactant in the absence of added salt we obtain, entirely because of electrostatic reasons, a negative deviation from ideal behavior of the cmc vs the aggregate composition corresponding to an interaction parameter β ≈ −1, whereas β values on the order of −5 or even less can arise for mixtures of two ionic surfactants with the same charge number but with different hydrocarbon moieties. Moreover, we introduce a novel expression for the free energy of mixing aggregated surfactant headgroups with surrounding solvent molecules. Accordingly, synergistic effects arise as a result of different headgroup cross-section areas in mixtures of two nonionic surfactants with rigid headgroups. These effects are found to be rather small, with 0 > β > −1, when the difference in headgroup size is modest but can become more significant when the size difference is larger. In mixtures of an ionic and a nonionic surfactant with different headgroup cross-section areas the two contributions to synergistic effects always enhance one another and, hence, β values below −1 are obtained. Generally, the synergistic effects tend to increase with increasing asymmetry between the two surfactants.