Modeling of the surfactant adsorption to the water-oil interfaces

A model that describes the adsorption of an ionic surfactant to an oil-water interface in the presence of an aqueous electrolyte that shares a common cation with the surfactant was developed, solved numerically, and evaluated with experimental interfacial tension data. The model includes algorithms for three processes: (i) the distribution of surfactant molecules between the interfacial and aqueous phases, (ii) the association of counter-ions with the charged interface, and (iii) the equation of state for the interface that defines the relationship between interfacial composition and interfacial tension. In defining distribution of surfactant between the aqueous and interfacial phases, both the chemical and electrical energies of phase transfer were considered. Calculation of the electrical energy of transfer requires calculating the electrical potential at the interface. In this study, the potential was calculated with both a double layer model (i.e., Gouy-Chapman model) and a triple layer model (i.e., Stern layer model) for ion distribution at and near the interface. The chemical energy of transfer is a measure of the non-ideal chemical interactions at the interfacial and in the aqueous phases and is equal to the ratio of surfactant activity coefficients in both phases. The relationship between the interfacial composition and interfacial tension was defined by the Gibbs equation assuming that only the activity of surfactant at the interface changes with composition at the interface. The overall model was solved numerically and related ionic strength and surfactant dose to interfacial tension, and interfacial surfactant concentration. The model was trained with laboratory and literature data, using a minimum number of adjustable parameters. The data collected in the laboratory consists of measured oil-water interfacial tension for a number of surfactants (all linear alkyl sulfates) at defined ionic strengths regulated with NaCl, with trichloroethylene (TCE) as the representative oil. A major part of this study was characterizing the ratio of surfactant activity coefficients for the interfacial and aqueous phases (i.e., the chemical energy of transfer). Two unique algorithms to describe this ratio were invoked and evaluated. The first algorithm was a simple exponential two-parameter empirical equation. The second was derived based on the Redlich-Kister expansion for describing excess energy. The calculated trend in the chemical energy of transfer was consistent with the trends predicted by both algorithms.