Adsorption kinetics of ionic surfactants with detailed account for the electrostatic interactions. I. No added electrolyte

The problem of diffusion-controlled adsorption from a non-micellar solution of an ionic surfactant in the absence of added electrolyte is solved analytically for the case of small deviations from equilibrium. For that purpose the electro-diffusion equations of the transport of surfactant ions and counterions are combined with the Poisson-Boltzmann equation for the electrical field. The resulting set of equations is linearized and Laplace transform is applied. Analytical expression for the Laplace image of the adsorption is obtained in terms of elementary functions. Simple formulae for the short-time and long-time asymptotics of adsorption and surface tension relaxation are derived. To illustrate the effect of the electrostatic interactions we calculated the theoretical dependence of the characteristic relaxation time on the bulk surfactant concentration and surface potential for aqueous surfactant solutions in contact with various non-aqueous phases (air, heptane, decane, petroleum ether) and two surfactants: SDS and DTAB. The general trend is that the electrostatic effects decelerate the process of adsorption, as it could be expected. The derived exact analytical expressions quantifying these effects can be directly applied for the interpretation of experimental data for the kinetics of ionic surfactant adsorption. The reliability of our approach is verified through a comparison with other available theories.