Adsorption relaxation for nonionic surfactants under mixed barrier-diffusion and micellization-diffusion control

Relaxation processes of surfactant adsorption and surface tension, which are characterized by two specific relaxation times, are theoretically investigated. We are dealing with fluid interfaces and small initial deviations from equilibrium. For surfactant concentrations below the critical micellization concentration (CMC), we consider adsorption under mixed barrier-diffusion control. General analytical expressions are derived, which are convenient for both numerical computations and asymptotic analysis. Series expansions for the short- and long-time limit are derived. The results imply that the short-time asymptotics is controlled by the adsorption barrier, whereas the long-time asymptotics is always dominated by diffusion. Furthermore, for surfactant concentrations above the CMC, adsorption under mixed micellization-diffusion control is considered. Again, a general analytical expression is derived for the relaxation of surfactant adsorption and surface tension, whose long- and short-time asymptotics are deduced. The derived equations show that at the short times the relaxation is completely controlled by the diffusion, whereas the long-time asymptotics is affected by both demicellization and diffusion. The micellar effect is manifested as an exponential (rather than square-root) decay of the perturbation. The derived expressions are applied to process available experimental data for the nonionic surfactant Triton X-100 and to determine the respective demicellization rate constant.