Modeling Interfacial Tension in Liquid−Liquid Systems Containing Electrolytes

A comprehensive model has been developed for calculating the interfacial tension (σ) in liquid−liquid systems with or without electrolyte components. The model consists of an equation for computing the interfacial tension of two-liquidphase nonelectrolyte systems and an expression for the effect of the electrolyte concentration. The dependence of the interfacial tension on the electrolyte concentration was derived by combining the Gibbs equation with a modified Langmuir adsorption isotherm that represents the interfacial excess of the solute species. The Langmuir adsorption formalism was extended by introducing the effects of binary interactions between solute species (ions or molecules) on the interface. The equation for the interfacial tension of nonelectrolyte liquid−liquid systems was derived using a general thermodynamic framework that was empirically extended by introducing an effective interfacial area that is defined for each component and takes into account the effects of other components at the interface. The model was found to reproduce experimental data for a variety of liquid−liquid systems. In particular, the interfacial tension of ternary systems can be accurately predicted using parameters determined from only binary data. Furthermore, the interfacial tension model was coupled with a previously developed thermodynamic model to provide activity coefficients and equilibrium concentrations in coexisting liquid phases. This makes it possible to reproduce the effects of speciation and salting out or salting in. Because of the coupling of the thermodynamic model with interfacial tension calculations, the variation of σ with electrolyte concentration can be reasonably predicted even without introducing electrolytespecific parameters in the interfacial tension model. Thus, the model can be used to estimate the electrolyte effect on σ in the absence of experimental data. With regressed model parameters, the average deviations between the calculated results and experimental data were 0.50 mN·m−1 for 30 binary nonelectrolyte systems, 0.88 mN·m−1 for 23 ternary nonelectrolyte systems, and 0.16 mN·m−1 for 26 systems with ionic components.