Prediction of equilibrium surface tension and surface adsorption of aqueous surfactant mixtures containing zwitterionic surfactants

A theoretical framework is developed for the treatment of electrostatic eff ects associated with the adsorption of zwitterionic surfactants, either as a single species or when mixed with ionic or nonionic surfactants, at the a ir-aqueous solution interface. A notable advantage of this theoretical fram ework is that it can be used to predict the interfacial properties of aqueo us mixtures that contain any number of surfactant components without utiliz ing any experimental information about the mixed surfactant systems. Electr ostatic effects are modeled by assuming that the charges located on the pol ar heads of the various adsorbed surfactant molecules form multiple, two-di mensional charge layers located at different positions within the monolayer . This model, combined with a Gouy-Chapman description of the diffuse layer , including a Stern layer of counterion steric exclusion, is then used to e valuate the electrostatic contribution to the surface pressure. Nonelectros tatic effects are incorporated by treating the adsorbed surfactant molecule s as a two-dimensional gaslike monolayer consisting of hard disks interacti ng through attractive van der Waals interactions. The hard-disk areas are c alculated using known bond lengths and angles of the surfactant molecules. The attractive van der Waals interactions between the surfactant hydrocarbo n tails are treated as a perturbation to the hard-disk repulsions using an expansion in surfactant surface concentration truncated at second order. Th e resulting surface equation of state is combined with a bulk chemical pote ntial model to predict the surface tension and surface concentration and co mposition of aqueous solutions containing various types of surfactants and their mixtures. We then compare these theoretical predictions to experiment al measurements of aqueous solutions containing ii) the nonionic surfactant dodecyl maltoside (C(12)Maltoside), the zwitterionic surfactant dodecyl be taine (C(12)Betaine), and the anionic surfactant sodium dodecyl sulfate (SD S), (ii) the binary surfactant mixtures of C(12)Maltoside-C(12)Betaine and C(12)Betaine-SDS, and (iii) the ternary surfactant mixture of C(12)Maltosid e-C(12)Betaine-SDS. In all cases, the theoretical predictions are found to be in good agreement with the experimental results.