Critical micelle concentrations and interaction parameters of aqueous binary surfactant:ionic surfactant mixtures

A relationship between the critical micelle concentration (CMC) and the surfactant's composition in the bulk phase that supercedes Rubingh's method is derived for aqueous mixtures of ionic surfactants by considering the interaction between a micellar ionic aggregate and the diffusion layer around it. To test this approach we measured the CMCs of solutions of cationic surfactant mixtures and also of alkylammonium dodecanesulfonate mixtures. In the absence of controlled concentration of the counterion, the CMCs do not fit Clint's equation, but CMCs measured at a constant counterion concentration fit it approximately. The interaction parameter in the theory of regular solutions is obtained from the relationship between the micellar and bulk compositions. The values of the interaction parameter and the concentration exponent change with the hydrophobicity of the counterion in mixtures of alkylammonium dodecanesulfonates. The micellar composition of dodecylammonium chloride and dodecyltrimethylammonium chloride mixtures depends very little on the counterion concentration. The interaction energy between the ammonium and trimethylammonium groups of the cationic surfactants is about -0.05kT on average and depends on the concentration of the counterion.