Role of equation of state on studying surfactant adsorption kinetics

The adsorption kinetics of a surfactant is used to apply the equilibrium surface tension data gamma (C) for the determination of the adsorption isotherm and then to apply the dynamic surface tension gamma (t) on determining the controlling mechanism, the diffusivity, and/or the sorption rate constants. A concept for surfactants lacking low surface pressure data has been proposed (Hsu et al. Langmuir 1997, 13, 6204; 1999,15,1952): using only a limited range of equilibrium surface tension data to determine the adsorption isotherm can cause a mistake on determining the adsorption mechanism and diffusion coefficient. In this work, the above concept is extended: even though an isotherm describes the gamma (C) data well, it may describe the dynamic surface tension data incorrectly. An incorrect controlling mechanism and/or a diffusion coefficient with a significant error may result if only the gamma (C) data are applied on determining the adsorption isotherm and model parameters. A second set of equilibrium data, equation of state gamma(Gamma), is useful and necessary for studying the adsorption kinetics. A theoretical simulation and two examples (for surfactants with either cooperative or anticooperative adsorption) are presented in this article to illustrate this concept.