Adsorption kinetics of ionic surfactants with detailed account for the electrostatic interactions: effect of the added electrolyte

Abstract

We address the problem about the electro-diffusion-controlled adsorption from a submicellar solution of an ionic surfactant in the presence of a non-amphiphilic electrolyte (salt). We consider a disturbance of the surfactant adsorption layer, which is damped by the electro-diffusive transport of surfactant ions, counterions and coions. The evolution of the electric double layer with time is theoretically examined. The counterion adsorption (binding) is taken into account. Our purpose is to find the long-time asymptotic solution of the full electro-diffusion boundary problem. Assuming small perturbations the problem is linearized and a set of three differential operator equations is obtained. In the asymptotic case of long times these differential equations reduce to hypergeometric equations, whose solutions, fortunately, can be expressed in terms of elementary functions. As a result, explicit expressions for the characteristic relaxation times of the adsorptions of surfactant ions and counterions are obtained. Next we determine the characteristic relaxation time of surface tension, which is different from the adsorption relaxation time because of a specific contribution from the dynamic diffuse electric double layer. The thermodynamic parameters, entering the formula for the relaxation time, are expressed for various surfactant adsorption isotherms, those of Henry, Langmuir, Freundlich, Frumkin and van der Waals. The theory gives a quantitative interpretation of the experimental finding that the addition of salt accelerates the relaxation of the surface tension for the higher surfactant concentrations, but decelerates it for the lower surfactant concentrations. The results could be also useful for a theoretical interpretation of the processes in foams and emulsions under dynamic conditions.