Synergistic effects in mixtures of an anionic and a cationic surfactant

Synergistic effects in mixtures of an anionic and a cationic surfactant have been theoretically investigated. We derive an explicit expression far the critical micelle concentration (cmc) as a function of the aggregate composition from the Poisson-Boltzmann mean field theory and, thus, demonstrate that the conspicuously large synergistic effects that have been experimentally observed can be rationalized without the need of invoking any specific interactions between the surfactant headgroups. The simple relation beta = -4 epsilon (el/kTelNzT) is derived, i.e.,the "interaction parameter" beta is directly related to the electrostatic free energy contribution epsilon (el) for the pure surfactant, implying, among other things, that the magnitude of beta decreases vith increasing cmc for the pure surfactant in agreement with experimental observations. We furthermore demonstrate that the aggregate composition is close to equimolar composition (x(1) = 0.5) at cmc in almost the entire regime of overall surfactant compositions and that the free monomer concentration of the surfactant in excess is generally much larger than the corresponding quantity for the surfactant in deficit.