Prediction of critical micelle concentrations and synergism of binary surfactant mixtures containing zwitterionic surfactants

We present a simplified ''working model'' of a recently developed molecular-thermodynamic theory of mixed surfactant solutions which can be utilized to predict critical micelle concentrations (cmc's) and synergism of binary surfactant mixtures in which one of the surfactants is zwitterionic. Given (i) the chemical structures of the hydrophilic heads and the hydrophobic tails of the surfactants, (ii) the cmc's of the pure surfactants, and (iii) the solution conditions such as temperature and the concentration of added salt, the model can predict the beta(A beta) interaction parameter characterizing synergism in mixed micelle formation and the mixture cmc as a function of solution composition. The model considers electrostatic interactions as the main contribution to synergism in mixed micelle formation, initially accounting for these interactions at an approximate level. The model applies only to surfactants; with linear hydrocarbon tails and neglects synergism due to steric interactions between the surfactant heads or due to the packing of the surfactant tails in the micellar core. The simplified working model is further examined in the context of a more rigorous treatment of the electrostatic interactions, and the electrostatic approximations underlying the simplified model are evaluated and shown to be reasonable. The model predictions are compared to experimental mixture cmc data and to beta(A beta) interaction parameters extracted from experimental measurements. Zwitterionic surfactants often exhibit specific interactions when mixed with anionic or cationic surfactants, because zwitterionic surfactants that can donate a proton can acquire a negative charge, while those that can accept a proton can acquire a positive charge. Although the simplified working model does not explicitly account for this specificity, the predictions agree reasonably well with experimental data for mixtures in which the zwitterionic surfactant acquires a partial charge opposite to that of the ionic surfactant with which it is mixed.