Mixed adsorption and surface tension prediction of nonideal ternary surfactant systems

To deal with the mixed adsorption of nonideal ternary surfactant systems, the regular solution approximation for nonideal binary surfactant systems is extended and a pseudo-binary system treatment is also proposed. With both treatments, the compositions of the mixed monolayer and the solution concentrations required to produce given surface tensions can be predicted based only on the γ-LogC curves of individual surfactants and the pair interaction parameters. Conversely, the surface tensions of solutions with different bulk compositions can be predicted by the surface tension equations for mixed surfactant systems. Two ternary systems: SDS/Hyamine 1622/AEO7, composed of homogeneous surfactants, and AES/DPCl/AEO9, composed of commercial surfactants, in the presence of excess NaCl, are examined for the applicability of the two treatments. The results show that, in general, the pseudo-binary system treatment gives better prediction than the extended regular solution approximation, and the applicability of the latter to typical anionic/cationic/nonionic nonideal ternary surfactant systems seems to depend on the combined interaction parameter, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathop {(\beta }\nolimits_{an}^s } + {\mathop \beta \nolimits_{cn}^s })/2 - {\mathop \beta \nolimits_{ac}^s }/4 $$\end{document}: the more it deviates from zero, the larger the prediction difference. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathop {(\beta }\nolimits_{an}^s } + {\mathop \beta \nolimits_{cn}^s })/2 - {\mathop \beta \nolimits_{ac}^s }/4 $$\end{document}→0, good agreements between predicted and experimental results can be obtained and both treatments, though differently derived, are interrelated and tend to be equivalent.