AN ION-BINDING MODEL FOR IONIC SURFACTANT ADSORPTION AT AQUEOUS-FLUIDINTERFACES

A simple ion-binding model is presented to quantify the equilibrium ad sorption of ionic surfactants at aqueous-fluid interfaces. The propose d model adopts a triple layer structure for the interface: a plane of adsorbed surfactants (interface plane), a plane of partially dehydrate d, contact-bound counterions (inner Helmholtz plane), and a plane of h ydrated counterions (outer Helmholtz plane). An analytic expression fo r 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 Y ork, 1963) as well as those, more recent, of R.P. Borwankar and D.T. W asan (Chem. Eng. Sci., 1(1986) 199). In the ion-binding model, the sur face tension depends on the electrocapacitance in the layers closest t o the interface and the distances between them, in addition to the sur face charges on the planes. For the limiting case of a moderate concen tration of surfactant, asymptotic formulae for the surface tension are derived. On a semilogarithmic graph of surface tension versus surfact ant concentration in the presence of background electrolyte, the asymp totic 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 parent heses indicating concentration. In the case of no salt added, the asym ptotic slope is -2kT(M(t)). The asymptotic formulae also establish the influence on the surface tension of the equilibrium constants and the lateral interaction parameter, omega, in Frumkin's isotherm. The ion- binding model results are in good agreement with the surface and inter facial tension data for sodium dodecyl sulfate (SDS). Agreement with m easured zeta-potentials is also found for SDS at the air-water boundar y.