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

The kinetics of adsorption of charged nano particles or molecules to a char ged surface are modeled on the basis of a simple model that takes into acco unt, (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 b ased on the presence of a diffusion layer. Passing through the electric dou ble 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 th at takes into account the 'specific' lateral interactions too and that lead s in the equilibrium state to the Frumkin-Fowler-Guggenheim (FFG) equation. In the FFG model the activation energy due to specific lateral interaction s is assumed to be proportional to the equilibrium lateral interaction ener gy. The effect of the electrostatic interactions and the corresponding acti vation energy barriers for adsorption and desorption are considered to be a n additional part of the attachment-detachment step. The electrostatic pote ntial 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, fr om the known bare surface charge plus the effective charge contribution due to particle adsorption. As a result of this treatment the adsorption kinet ics are not only a function of the particle concentration and the surface c overage, but also of the surface charge, the particle charge and the salt c oncentration. The model is illustrated with some calculated results. The fi rst illustrations are based on the Langmuir model extended with electrostat ic interactions and show, for a given particle concentration and transport rate constant, the effects of salt concentration, surface charge and partic le charge on both the adsorption and desorption kinetics. The next illustra tions are based on the FFG model extended with electrostatics and the effec t of the specific lateral interactions on the adsorption kinetics of charge d and uncharged particles is shown. (C) 2001 Elsevier Science B.V. All righ ts reserved.