Adsorption kinetics of ionic surfactants after a large initial perturbation. Effect of surface elasticity

This theoretical study is devoted to the relaxation of surface tension of a n ionic surfactant solution for submicellar concentrations. The effects of added nonamphiphilic electrolyte and counterion binding are taken into acco unt. We consider a large initial deviation from equilibrium, which is defin ed as the formation of a new interface: there is no adsorbed surfactant and electric double layer at the initial moment. Next, the surfactant solution and its interface are allowed to relax without any subsequent perturbation . The electrodiffusion equations, which describe the adsorption kinetics, a re nonlinear, and it is impossible to find a general analytical solution, e specially in the case of large initial deviations. Nevertheless, the proble m can be linearized in the asymptotic case of long times. The derived theor etical expressions show that the relaxation times in the cases of large and small initial perturbations are numerically close to each other. For that reason the relaxation time can be considered as a general kinetic property of the adsorption monolayer. The theory predicts also the slope of the expe rimental plot of dynamic surface tension vs inverse square root of time; th is makes the theory useful for interpretation of experimental data. The the oretical expressions involve the surface (Gibbs) elasticity, whose definiti on for adsorption monolayers of soluble ionic surfactants is discussed in d etail. The Gibbs elasticity of such monolayers is found to increase strongl y with the rise of salt concentration. The derived asymptotic expressions a re verified against an exact computer solution of the electrodiffusion prob lem, and excellent agreement is found.