Prediction of Critical Micelle Concentrations of Nonideal Ternary Surfactant Mixtures

Abstract

We present a method for predicting critical micelle concentrations (cmc's) of nonideal ternary surfactant mixtures based on the use of a molecular-thermodynamic theory to predict regular solution theory β interaction parameters for the component surfactant pairs. The ternary mixture cmc predictions, which are generated using experimental data only for the single surfactant cmc's, compare well with experimentally measured mixture cmc values for several ternary surfactant mixtures. The molecular-thermodynamic theory used to predict the β parameters is based on evaluating free-energy contributions to mixed micelle formation, and uses the molecular structures of the surfactants and the solution conditions as inputs. We also present a detailed derivation of the expression for the mixture cmc of ternary surfactant mixtures, comparing the pseudophase separation approximation for mixed micelles with the molecular-thermodynamic theory for mixed micelles. We show that if (i) the mixed micelle aggregation number is large, (ii) all the mixed micelles have the same optimal micellar composition, and (iii) regular solution theory is used to model the nonidealities of mixed micelle formation, then the ternary cmc predicted by the molecular-thermodynamic theory is equivalent to that calculated with the pseudophase separation approximation.