An ion-binding model for ionic surfactant adsorption at aqueous-fluid interfaces

Abstract

A simple ion-binding model is presented to quantify the equilibrium adsorption of ionic surfactants at aqueous-fluid interfaces. The proposed model adopts a triple layer structure for the interface: a plane of adsorbed surfactants (interface plane), a plane of partially dehydrated, contact-bound counterions (inner Helmholtz plane), and a plane of hydrated counterions (outer Helmholtz plane). An analytic expression for the surface tension is obtained as a function of the physicochemical parameters of the system. It generalizes the classical results of J.T. Davies and E.K. Rideal (Interfacial Phenomena, Academic Press, New York, 1963) as well as those, more recent, of R.P. Borwankar and D.T. Wasan (Chem. Eng. Sci., 1 (1986) 199). In the ion-binding model, the surface tension depends on the electrocapacitance in the layers closest to the interface and the distances between them, in addition to the surface charges on the planes. For the limiting case of a moderate concentration of surfactant, asymptotic formulae for the surface tension are derived. On a semilogarithmic graph of surface tension versus surfactant concentration in the presence of background electrolyte, the asymptotic slope approaches - kT(M t), where k is Boltzmann's constant, T is temperature, and (M t) is the surface concentration of total sites, M t, available for surfactant headgroups in the interface, the parentheses indicating concentration. In the case of no salt added, the asymptotic slope is −2 kT(M t). The asymptotic formulae also establish the influence on the surface tension of the equilibrium constants and the lateral interaction parameter, ω, in Frumkin's isotherm. The ion-binding model results are in good agreement with the surface and interfacial tension data for sodium dodecyl sulfate (SDS). Agreement with measured ξ-potentials is also found for SDS at the air-water boundary.