Synergistic effects in mixtures of two identically charged ionic surfactants with different critical micelle concentrations

Expressions for the critical micelle concentration (cmc) and activity coefficients as functions of surfactant composition in mixtures of two identically charged monovalent ionic surfactants are derived from the nonlinear Poisson-Boltzmann (PB) theory. For the special case of no added salt, the simple expression cmc ^α = xcmcα1 + (1 - x)cmcα2 is deduced, where the exponential parameter α > 1 depends on the number of ionic species in a surfactant molecule as well as the curvature of the self-assembled interface. Theoretical predictions are compared with cmc values obtained with some different experimental techniques for mixtures of the two cationic surfactants didodecyldimethylammonium bromide (DDAB) and dodecyltrimethylammonium bromide (DTAB) in water and in the absence of added salt. It is demonstrated that the PB theory generates significantly better agreement with experimental data than predicted by ideal behaviour or the regular mixture theory. We find that maximum synergistic effects occur at a DDAB mole fraction in solution y = 0.005. According to the PB theory, this very low value of y corresponds to a mole fraction of DDAB in the self-assembled interfacial aggregates equal to x = 0.995. Moreover, our calculations of the surfactant composition in the self-assembled interfacial aggregates above cmc demonstrate that the transition from small micelles to large bilayer aggregates is found to consistently occur at a mole fraction of DDAB equal to about x = 0.41-0.42, irrespective of the surfactant molar ratio in solution. Experimental observations strongly support the fact that concentrations of free surfactant, as well as the surfactant composition in the self-assembled interfacial aggregates, may be accurately calculated from the non-linear Poison-Boltzmann theory. On the other hand, a micelle-to-bilayer transition induced by changes in surfactant mole fraction in the self-assembled interfacial aggregates is consistent with neither ideal surfactant behaviour nor synergistic behaviour according to the regular mixture theory.