Molecular-Thermodynamic Theory of Micellization of Multicomponent Surfactant Mixtures:  2. pH-Sensitive Surfactants

In article 1 of this series, we developed a molecular-thermodynamic (MT) theory to model the micellization of mixtures containing an arbitrary number of conventional (pH-insensitive) surfactants. In this article, we extend the MT theory to model mixtures containing a pH-sensitive surfactant. The MT theory was validated by examining mixtures containing both a pH-sensitive surfactant and a conventional surfactant, which effectively behave like ternary surfactant mixtures. We first compared the predicted micellar titration data to experimental micellar titration data that we obtained for varying compositions of mixed micelles containing the pH-sensitive surfactant dodecyldimethylamine oxide (C₁₂DAO) mixed with either a cationic surfactant (dodecyltrimethylammonium bromide, C₁₂TAB), a nonionic surfactant (dodecyl octa(ethylene oxide), C₁₂E₈), or an anionic surfactant (sodium dodecyl sulfate, SDS) surfactant. The MT theory accurately modeled the titration behavior of C₁₂DAO mixed with C₁₂E₈. However, C₁₂DAO was observed to interact more favorably with SDS and with C₁₂TAB than was predicted by the MT theory. We also compared predictions to data from the literature for mixtures of C₁₂DAO and SDS. Although the pH values of solutions with no added acid were modeled with only qualitative accuracy, the MT theory resulted in quantitatively accurate predictions of solution pH for mixtures containing added acid. In addition, the predicted degree of counterion binding yielded a lower bound to the experimentally measured value. Finally, we predicted the critical micelle concentration (cmc) of solutions of two pH-sensitive surfactants, tetradecyldimethylamine oxide (C₁₄DAO) and hexadecyldimethyl betaine (C₁₆Bet), at varying solution pH and surfactant composition. However, at the pH values considered, the pH sensitivity of C₁₆Bet could be neglected, and it was equivalently modeled as a zwitterionic surfactant. The cmc's predicted using the MT theory agreed well with the experimental cmc's and were found to be comparable to and sometimes better than the cmc's determined using the regular solution theory (RST), even though the empirical RST utilizes experimentally measured cmc's as an input. The MT theory presented here represents the first molecular-based quantitative description of the micellization behavior of mixtures of pH-sensitive surfactants and conventional surfactants, and allows qualitative and quantitative predictions of the micellization behavior of a variety of surfactant systems.