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 o f a nonionic surfactant and two anionic surfactants which differ in both su rfactant hydrophobic tail length and surfactant hydrophilic head structure. We used an experimental design program to calculate the critical micelle c oncentrations (CMCs) of this ternary surfactant mixture over the entire ran ge of solution compositions. As inputs, the experimental design methodology requires the values of the ternary surfactant mixture CMCs for a limited s ubset of solution compositions which is determined by the experimental desi gn program. We showed that this subset of ternary surfactant mixture CMC va lues can either be measured experimentally or predicted theoretically. The theoretical CMCs were predicted by a series of user-friendly computer progr ams which are based on molecular-thermodynamic theories describing single a nd mixed micelle formation. The experimental design program generated two s urfaces describing the ternary surfactant mixture CMCs over the entire solu tion composition range-one based on the experimentally measured subset of C MC values, and the other based on the theoretically predicted CMC values fo r the same subset of solution compositions. We found that these two CMC sur faces agree very well, thus demonstrating the utility of the computer-assis ted molecular-thermodynamic modeling as a predictive tool in surfactant mix ture characterization and design.