A simple model for adsorption kinetics at charged solid–liquid interfaces

Abstract The kinetics of adsorption of charged nano particles or molecules to a charged surface are modeled on the basis of a simple model that takes into account, (1) the transport step from bulk solution to the subsurface layer and (2) the attachment–detachment step that is involved in the transfer of the particle from the subsurface to the adsorbed state. The transport step is based on the presence of a diffusion layer. Passing through the electric double layer is made part of the attachment–detachment step. The configuration part of the attachment–detachment step is based on either a kinetic model that leads to the Langmuir equation in the equilibrium situation, or one that takes into account the ‘specific’ lateral interactions too and that leads in the equilibrium state to the Frumkin–Fowler–Guggenheim (FFG) equation. In the FFG model the activation energy due to specific lateral interactions is assumed to be proportional to the equilibrium lateral interaction energy. The effect of the electrostatic interactions and the corresponding activation energy barriers for adsorption and desorption are considered to be an additional part of the attachment–detachment step. The electrostatic potential of the activated state for attachment–detachment is made proportional to the equilibrium surface potential at a given adsorbed amount. The Gouy–Chapman model is used to calculate the (smeared-out) surface potential from the known (smeared-out) overall surface charge density, that is to say, from the known bare surface charge plus the effective charge contribution due to particle adsorption. As a result of this treatment the adsorption kinetics are not only a function of the particle concentration and the surface coverage, but also of the surface charge, the particle charge and the salt concentration. The model is illustrated with some calculated results. The first illustrations are based on the Langmuir model extended with electrostatic interactions and show, for a given particle concentration and transport rate constant, the effects of salt concentration, surface charge and particle charge on both the adsorption and desorption kinetics. The next illustrations are based on the FFG model extended with electrostatics and the effect of the specific lateral interactions on the adsorption kinetics of charged and uncharged particles is shown.