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 amphiphile, the simulations are performed for typical surfactant material parameters. The surface potential is related at each time step to the instantaneous surface charge density determined by the surfactant surface concentration using the Gouy–Chapman model. The sublayer concentration at each time step is a Boltzmann distribution in instantaneous equilibrium with the surface potential. At equilibrium, the surfactant is assumed to obey the Davies adsorption 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, since the equilibrium adsorption is strongly reduced by the repulsive electrostatic potential, the time required to deliver the surfactant by diffusion is also reduced. The greater the electrical repulsion, the faster the diffusion-controlled adsorption at a given surfactant concentration. Because less surfactant adsorbs, the surface tension reduces less at equilibrium. Counterions of greater valence than the surfactant are more effective at screening the surface potential. Equilibrium adsorption, surface tension reduction, and diffusion time scales increase. As the surfactant valence increases, so 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–desorption kinetic barriers. In experiment, adsorption–desorption kinetic barriers have been shown to control the mass transfer of non-ionic surfactants at elevated bulk concentration. The ability of the interface to deplete the bulk 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 from pure diffusion control at dilute concentration to mixed kinetic–diffusion control at elevated concentration is strongly influenced by ionic strength and surfactant valence. As the electrostatic adsorption increases, kinetic barriers are apparent at lower concentrations. Finally, a simple time scale argument that has previously proven useful in predicti