Equations of state and adsorption isotherms of low molecular non-ionic surfactants

After a brief analysis of the three most widely used equations of state and adsorption isotherms, (those of van der Waals, Frumkin and Helfand–Frisch–Lebowitz with second virial coefficient) we analyze the definitions and the values of the main adsorption parameters (adsorption constant Ks, minimum area per molecule α and interaction constant β) and derive new expressions for some of them. Since it turned out that all three adsorption isotherms perform rather poorly, when used to interpret adsorption data, we applied also three more general equations—one was derived for localized adsorption long ago, but we had to derive two new equations for non-localized adsorption. We subject all 6 equations—the simple ones and the three generalized, to rigorous numerical analysis and discussion of the results. Our overall conclusion is that in some cases all equations can describe qualitatively the observed phenomena, but only the new equation of state, proposed by us for non-localized adsorption on fluid interface (and the respective adsorption isotherm), lead to correct quantitative description of the adsorption and the related parameters. In Appendix A we analyze the shortcomings and the source of errors in the fitting procedures.