Prediction of Equilibrium Surface Tension and Surface Adsorption of Aqueous Surfactant Mixtures Containing Ionic Surfactants

We report results of a theoretical study of the adsorption of mixtures of ionic and nonionic surfactants at the aqueous solution−air interface. A surface equation of state is developed by treating the adsorbed surfactant molecules as a two-dimensional gaslike monolayer consisting of hard disks interacting through attractive van der Waals interactions and repulsive electrostatic interactions. The hard-disk areas are calculated using known bond lengths and angles in the case of surfactants having compact hydrophilic heads and a Monte Carlo simulation approach in the case of surfactants having flexible, polymer-like hydrophilic heads. Attractive van der Waals interactions between the surfactant hydrocarbon tails are treated as a purturbation to the hard-disk repulsions using an expansion in surfactant surface concentration truncated at second order. The corresponding second-order virial coefficients are calculated using detailed molecular information about the surfactant species present in the monolayer. Electrostatic interactions are assumed to form an additive contribution to the surface pressure and are calculated in the context of the Poisson−Boltzmann model distribution for the ions present in the aqueous phase. The resulting surface equation of state for the surfactant mixture is therefore molecularly based and does not contain experimentally determined parameters. We utilize this theoretical surface equation of state, along with a recently developed theoretical description of the bulk mixed surfactant solution behavior, to predict the mixed surfactant solution−air surface tension and surface concentration and composition as a function of the total bulk surfactant concentration and solution composition, both below and above the critical micelle concentration of the surfactant mixture. We also compare these theoretical predictions to available experimentally measured surface tensions of single surfactant aqueous solutions of sodium dodecyl sulfate (SDS), dodecyl maltoside (C 12 Maltoside), and dodecyl hexa(ethylene oxide) (C 12 E 6 ), as well as of binary surfactant aqueous solutions of SDS−C 12 Maltoside and SDS−C 12 E 6 . The predicted adsorbed surfactant surface concentration and composition for the SDS−C 12 Maltoside mixture are also compared to available experimentally measured values obtained recently using neutron scattering. In all cases, the theoretical predictions are found to be in good agreement with the experimental values.