Modeling of Surface Tension Isotherms with an Extremum for Binary Liquid Mixtures

Anomalous (or aneotropic) surface tension (σ) isotherms with a distinct extremum (minimum or maximum) have been reported for numerous binary liquid mixtures, yet a feasible model for describing such aneotropic behavior remains lacking. In this work, by coupling the surface aggregation adsorption (SAA) model with the modified Eberhart equation (a nonlinear mixing rule), an equation for describing the aneotropic isotherms was developed that relates σ to the bulk composition via three parameters, i.e., the adsorption equilibrium constant (K), the average aggregation number (n), and the specific interaction parameter (λ). Approaches for estimating the three parameters (λ, n, and K) were established, which can yield unique and well-defined values. In addition, a single-parameter (λ) equation relating the surface composition to σ was established, enabling the prediction of the surface composition from experimental σ data. The validity of the model equations was verified using the aneotropic σ data of four binary mixtures reported in the literature, where two mixtures exhibit a minimum and two a maximum in surface tension. This work provides a feasible model for describing aneotropic isotherms and a better understanding of the surface adsorption of liquid mixtures.