The dynamic adsorption of charged amphiphiles: The evolution of the surface concentration, surface potential, and surface tension

In this work the evolution of the surface concentration, surface potential, and surface tension for adsorption of a charged amphiphile at an interface is studied numerically. While the results are of interest for any amphiphi le, the simulations are performed for typical surfactant material parameter s. The surface potential is related at each time step to the instantaneous surface charge density determined by the surfactant surface concentration u sing the Gouy-Chapman model. The sublayer concentration at each time step i s a Boltzmann distribution in instantaneous equilibrium with the surface po tential. At equilibrium, the surfactant is assumed to obey the Davies adsor ption isotherm. The model is integrated first for diffusion-controlled adsorption? in which the surfactant diffuses to the sublayer and adsorbs onto the interface in local equilibrium according to the adsorption isotherm. In this limit, sinc e the equilibrium adsorption is strongly reduced by the repulsive electrost atic potential, the time required to deliver the surfactant by diffusion is also reduced. The greater the electrical repulsion, the faster the diffusi on-controlled adsorption at a given surfactant concentration. Because less surfactant adsorbs, the surface tension reduces less at equilibrium. Counte rions of greater valence than the surfactant are more effective at screenin g the surface potential. Equilibrium adsorption, surface tension reduction, and diffusion time scales increase. As the surfactant valence increases, s o does the repulsion; the opposite trends in surface tension and diffusion time scales are predicted. The model is also integrated including both diffusion and adsorption-desorp tion kinetic barriers. In experiment, adsorption-desorption kinetic barrier s have been shown to control the mass transfer of non-ionic surfactants at elevated bulk concentration. The ability of the interface to deplete the bu lk reduces with concentration. Therefore, diffusion time scales are reduced . In these regimes, adsorption-desorption kinetics can be rate determining. In simulation, the occurrence of the shift of the controlling mechanism fr om pure diffusion control at dilute concentration to mixed kinetic-diffusio n control at elevated concentration is strongly influenced by ionic strengt h and surfactant valence. As the electrostatic adsorption increases, kineti c barriers are apparent at lower concentrations. Finally, a simple time scale argument that has previously proven useful in predicting a priori the time required for diffusion-controlled absorption t o an interface for nonionic surfactant ad-sorption is extended to include e lectrostatic effects. (C) 1999 Academic Press.