Predicting micellar solution properties of binary surfactant mixtures

The widespread use of surfactant mixtures in practical surfactant applications motivates the need for a comprehensive predictive theory that will improve our fundamental understanding of the behavior of these complex systems and facilitate the design and optimization of new surfactant mixtures. With this in mind, we have combined a molecular model of mixed micellization with a thermodynamic framework to predict a broad spectrum of solution properties of mixed surfactant systems. The molecular model accounts for micellar mixing nonidealities resulting from electrostatic and steric interactions between the surfactant hydrophilic heads and from packing of surfactant hydrophobic tails of unequal lengths in the micellar core. In particular, we describe in detail a rigorous treatment of electrostatic interactions that enables the theory to quantitatively predict properties for binary mixtures containing nonionic, anionic, cationic, and zwitterionic surfactants, including the critical micelle concentration (cmc) of the mixture; the beta interaction parameter; the micelle and monomer compositions; the monomer concentration; and the micelle shape, size, and size distribution. The inputs to the theory are the pure surfactant chemical structures and the solution conditions, including the total surfactant concentration and composition, the temperature, and the type and concentration of added salt. We compare theoretical predictions to experimental measurements of mixture cmc values, micelle compositions, and micelle aggregation numbers for anionic/nonionic, cationic/cationic, anionic/cationic, and ionic/zwitterionic surfactant mixtures, and analyze the results in terms of the various free-energy contributions to mixed micellization. We also correlate synergism in fundamental predicted properties to experimentally measured synergism in practical surfactant performance characteristics such as dishwashing, soil removal, and emulsification.