Derivation of a new equation for prediction of the thin layer depth of the extended-Langmuir model for dilute binary mixtures

General Adsorption Model to Describe Sigmoidal Surface Tension Isotherms of Binary Liquid Mixtures

Surface tension (σ) isotherms of liquid mixtures can be divided into Langmuir-type (L-type, including L_I- and L_II-type) and sigmoid-type (S-type, including S_I- and S_II-type). Many models have been developed to describe the σ-isotherms. However, the existing models can well describe the L-type isotherms, but not the S-type ones. In the current work, a thermodynamic model, called the general adsorption model, was developed based on the assumption of surface aggregation occurring in the surface layers, to relate the surface composition with the bulk one. By coupling the general adsorption model with the modified Eberhart model, a two-parameter equation was developed to relate the σ with the bulk composition. Its rationality was examined using the σ data of 10 binary mixtures. The results indicate that the new model can accurately describe the S- and L-type isotherms of binary liquid mixtures, showing a good universality. One advantage of the model is that its two parameters, i.e., the adsorption equilibrium constant (K) and the average aggregation number (n), can be estimated by linear fitting experimental σ data, thereby obtaining unique values. This model suggests that the S- and L_II-type isotherms arise from the surface aggregation (n ≠ 1). In addition, the standard molar Gibbs free energy of surface adsorption (ΔG̃_ad⁰) and the apparent surface layer thickness (τ) were analyzed for 10 binary mixtures. The ΔG̃_ad⁰ data suggest that the order of adsorption tendency is L_I-type ≫ S_I-type ≈ S_II-type > L_II-type, and the strong adsorption usually corresponds to large τ. This work provides a feasible model for describing the S-type isotherms and a better understanding of the surface properties of liquid mixtures.