Critical micelle concentration and partition coefficient of mixed micelles: Analysis of ternary systems based on Markov chain model and simple mixture model

Abstract

When two or more surfactants are mixed, the mixed system exhibits improved performance compared with a single surfactant system in solution. The Markov chain model can analyze the critical micelle concentration (CMC) of mixed micelles, yielding results similar to those of a simple mixture model, which is typically referred to as the “regular solution theory”. In this study, two hypotheses were tested: (1) the Markov chain model for ternary systems can be simplified by approximating the association constant of surfactants i and j as Kij = Kji and (2) the quasi-simple ternary mixture model, that is, a simple mixture model analogous to the Markov chain model, helps interpret the interaction parameter of the simple mixture model that can describe the partition coefficient of the binary mixed micelle. Equations were derived for (1) the Markov chain model for ternary systems by assuming Kij = Kji and (2) the interaction parameter of the simple mixture model that can describe the partition coefficient of the binary mixed micelle. The models were compared with the experiment data, and the derived equations described the data of the CMC and partition coefficient well.