A new class of interfacial tension isotherms for nonionic surfactants based on local self-consistent mean field theory: classical isotherms revisited

Abstract

In this paper we use purely local density functional theory for the conformation of surfactant tails to obtain analytical interfacial tension isotherms of liquid–fluid interfaces in the presence of nonionic surfactants. For illustration, we derive the interfacial tension isotherm for nonionic surfactants at the air–water or the oil–water interface based on the Self-Consistent Field (SCF) theory, originally developed to treat grafted polymer brushes. The obtained interfacial tension isotherm turns out to be universal for a broad range of surfactant concentrations. We provide a feasible route for derivation of a whole class of adsorption isotherms based on the SCF theory. Comparison is given between the derived SCF adsorption isotherm with the classical isotherms of Frumkin and van der Waals. It is shown that these classical isotherms can be obtained as particular cases of a general SCF local density functional, corresponding to rigid surfactant tails. The SCF theory is shown to account for the flexibility of the surfactant chains in the adsorbed monolayer which modifies the interaction term in the surface tension and the adsorption isotherms. We compare experimental data for the surface tension and the surfactant adsorption isotherms for a nonionic surfactant with the predictions of the new theoretical isotherm. Very good agreement between nonionic surfactant adsorption at the air–water interface, calculated from the surface tension isotherm and neutron reflectivity and ellipsometry data, is obtained.