Critical micelle concentrations of ternary surfactant mixtures: Theoretical prediction with user-friendly computer programs and experimental design analysis

We studied the behavior of an aqueous ternary surfactant mixture composed of a nonionic surfactant and two anionic surfactants which differ in both surfactant hydrophobic tail length and surfactant hydrophilic head structure. We used an experimental design program to calculate the critical micelle concentrations (CMCs) of this ternary surfactant mixture over the entire range of solution compositions. As inputs, the experimental design methodology requires the values of the ternary surfactant mixture CMCs for a limited subset of solution compositions which is determined by the experimental design program. We showed that this subset of ternary surfactant mixture CMC values can either be measured experimentally or predicted theoretically. The theoretical CMCs were predicted by a series of userfriendly computer programs which are based on molecular-ther-modynamic theories describing single and mixed micelle formation. The experimental design program generated two surfaces describing the ternary surfactant mixture CMCs over the entire solution composition range—one based on the experimentally measured subset of CMC values, and the other based on the theoretically predicted CMC values for the same subset of solution compositions. We found that these two CMC surfaces agree very well, thus demonstrating the utility of the computerassisted molecular-thermodynamic modeling as a predictive tool in surfactant mixture characterization and design.