The mass-action-law theory of micellization revisited.

Abstract

Among numerous definitions of the critical micelle concentration (CMC), there is one related to the constant K of the mass action law as CMC = K(1-n) (n is the aggregation number). In this paper, the generalization of this definition for multicomponent micelles and the development of the mass-action-law theory of micellization based on this definition and the analysis of a multiple-equilibrium polydisperse micellar system have been presented. This variant of the theory of micellization looks more consistent than the earlier one. In addition, two thermodynamic findings are reported: the stability conditions for micellar systems and the dependence of aggregation numbers on the surfactant concentrations. The growth of the monomer concentration with the total surfactant concentration is shown to be a thermodynamic rule only in the case of a single sort of aggregative particles or at adding a single surfactant to a mixture. The stability condition takes more complex form when adding a mixture of aggregative particles. For the aggregation number of a micelle, it has been deduced a thermodynamic rule obeying it to increase with the total surfactant concentration. However, if the monomer concentration increases slowly, the aggregation number increases much more slowly and the more slowly the more pronounced is a maximum corresponding to a micelle on the distribution hypersurface (curve in the one-component case). This forms grounding for the quasi-chemical approximation in the mass-action-law theory (the constancy of aggregation numbers).