A theoretical analysis of synergistic effects in mixed surfactant systems

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 beta approximate to -1, whereas beta 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 > beta > -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, beta values below -1 are obtained. Generally, the synergistic effects tend to increase with increasing asymmetry between the two surfactants.