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

We address the problem about the electro-diffusion-controlled adsorption fr om a submicellar solution of an ionic surfactant in the presence of a non-a mphiphilic electrolyte (salt). We consider a disturbance of the surfactant adsorption layer, which is damped by the electro-diffusive transport of sur factant ions, counterions and colons. The evolution of the electric double layer with time is theoretically examined. The counterion adsorption (bindi ng) is taken into account. Our purpose is to find the long-time asymptotic solution of the full electro-diffusion boundary problem. Assuming small per turbations the problem is linearized and a set of three differential operat or equations is obtained. In the asymptotic case of long times these differ ential equations reduce to hypergeometric equations, whose solutions, fortu nately, can be expressed in terms of elementary functions. As a result, exp licit expressions for the characteristic relaxation times of the adsorption s of surfactant ions and counterions are obtained. Next we determine the ch aracteristic relaxation time of surface tension, which is different from th e adsorption relaxation time because of a specific contribution from the dy namic 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 experimen tal finding that the addition of salt accelerates the relaxation of the sur face tension for the higher surfactant concentrations, but decelerates it f or the lower surfactant concentrations. The results could be also useful fo r a theoretical interpretation of the processes in foams and emulsions unde r dynamic conditions. (C) 1999 Elsevier Science B.V. All rights reserved.