Apparent binding degree of a counterion and micellar composition in cationic and nonionic surfactant mixed solutions at CMC

The Gibbs-Duhem equation of an ionic aggregate is obtained, considering the activity coefficient of the aggregate due to the interaction between the aggregate ion and its diffusion layer. The equation is applied to mixtures of cationic and nonionic surfactants. The critical micelle concentrations of the cationic an nonionic surfactant mixtures were measured in the presence of inorganic salt with the same counterion. The logarithm of the CMC of the mixture gives a linear relationship versus the logarithm of the counterion concentration for a constant molar ratio of the two surfactants. The apparent binding degree of the counterion and the fraction of the nonionic surfactant in the mixed micelle were obtained from the CMC data using the Gibbs-Duhem equation. The binding degree which is obtained by the Corrin-Harkins equation is apparent. The apparent binding degree increases with the decrease in the counterion concentration. The behavior of a parent binding degree is different from that of the real binding degree obtained by potentiometry. These facts are explained by our definition of the apparent binding degree of the counterion. (C) 2001 Academic Press.