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 i onic and nonionic surfactants at the aqueous solution-air interface. A surf ace equation of state is developed by treating the adsorbed surfactant mole cules as a two-dimensional gaslike monolayer consisting of hard disks inter acting through attractive van der Waals interactions and repulsive electros tatic interactions, The hard-disk areas are calculated using known bond len gths and angles in the case of surfactants having compact hydrophilic heads and a Monte Carlo simulation approach in the case of surfactants having fl exible, polymer-like hydrophilic heads. Attractive van der Waals interactio ns between the surfactant hydrocarbon tails are treated as a purturbation t o the hard-disk repulsions using an expansion in surfactant surface concent ration truncated at second order. The corresponding second-order virial coe fficients are calculated using detailed molecular information about the sur factant species present in the monolayer, Electrostatic interactions are as sumed to form an additive contribution to the surface pressure and are calc ulated in the context of the Poisson-Boltzmann model distribution for the i ons present in the aqueous phase. The resulting surface equation of state f or the surfactant mixture is therefore molecularly based and does not conta in experimentally determined parameters. We utilize this theoretical surfac e equation of state, along with a recently developed theoretical descriptio n of the bulk mixed surfactant solution behavior, to predict the mixed surf actant solution-air surface tension and surface concentration and compositi on as a function of the total bulk surfactant concentration and solution co mposition, both below and above the critical micelle concentration of the s urfactant mixture. We also compare these theoretical predictions to availab le experimentally measured surface tensions of single surfactant aqueous so lutions of sodium dodecyl sulfate (SDS), dodecyl maltoside (C(12)Maltoside) , and dodecyl hexa(ethylene oxide) (C12E6), as well as of binary surfactant aqueous solutions of SDS-C(12)Maltoside and SDS-C12E6. The predicted adsor bed surfactant surface concentration and composition for the SDS-C(12)Malto side mixture are also compared to available experimentally measured values obtained recently using neutron scattering. In all cases, the theoretical p redictions are found to be in good agreement with the experimental values.