Theoretical and experimental investigation of the equilibrium oil-water interfacial tensions of solutions containing surfactant mixtures

A molecular-thermodynamic theory is developed to model the adsorption of surfactant mixtures at the oil-water interface. The use of experimentally determined parameters is minimized by utilizing a theoretical description that is based on the molecular characteristics of the surfactants. Specifically, the adsorbed surfactant molecules are modeled as a two-dimensional nonideal gaslike monolayer of hard disks exhibiting no attractive interactions of the van der Waals type due to the compatibility of the surfactant alkyl tails and the nonpolar oil phase. In addition, electrostatic effects associated with the presence of charges in the surfactant polar heads are modeled as an additive contribution to the surface pressure, which is calculated using a Gouy-Chapman based description of the diffuse layer, including a Stern layer of counterion steric exclusion. As such, the surface equation of state contains no experimentally determined parameters. In cases when the surfactant molecules partition extremely into either the oil phase or the aqueous phase, the adsorption isotherm contains only one experimentally determined parameter for each single surfactant component considered, which can be determined from a single interfacial tension measurement on each single surfactant solution. In cases when the partitioning of the surfactant molecules between the oil phase and the aqueous phase must be accounted for, the oil-water partition coefficient of each surfactant component in the mixture is required and can be determined from two interfacial tension measurements on each single surfactant solution. A notable advantage of the resulting theory is that the interfacial properties of the mixed surfactant solution can be predicted without conducting any additional measurements on the mixed surfactant system. The predictions made using this theory include the interfacial tension and the interfacial concentration and composition as a function of the total bulk surfactant concentration and composition and the oil-water volume ratio, for a solution containing any number of surfactant components below the critical micelle concentration. To test the theoretical predictions; we have measured the decane-water interfacial tensions of (i) the nonionic surfactant dodecyl hexa(ethylene oxide) (C12E6), (ii) the ionic surfactant sodium dodecyl sulfate (SDS), and (iii) binary surfactant mixtures of C12E6 and SDS. To further test the validity of the theory, we have also compared the predicted hexadecane-water interfacial tensions of binary mixtures of the nonionic surfactants dodecyl di(ethylene oxide) (C12E2) and dodecyl octa(ethylene oxide) (C12E8) with experimental values reported in the literature. In all the cases examined, the theoretically predicted interfacial tensions compare favorably with the experimentally measured values.