Derivation of a general kinetic equation for transfer-controlled adsorption at liquid interfaces using Statistical Rate Theory

Recently, Joos proposed a new kinetic model for transfer-controlled surfact ant adsorption at liquid interfaces. His model is general, in the sense tha t the change in interfacial tension is incorporated into adsorption rate de scriptions, and its governing kinetic equation can be reduced to various sp ecific expressions for individual situations, such as the Langmuir kinetic equation. Joos developed his kinetic model by simply drawing analogies betw een adsorption and electrode kinetics, where the rate expression was obtain ed by using conventional chemical reaction theory. In this paper, we presen t a quantum statistical formulation for surfactant adsorption kinetics. Wit h the assumption of excited states for molecular adsorption, we derive a ra te equation by using Statistical Rate Theory (SRT), which gives the express ion for transition probabilities from a first-order perturbation analysis o f the Schrodinger equation. This new derivation avoids using the principle of mass action and the law of Arrhenius-Eyring, and hence many empirical as sumptions in conventional chemical reaction theory are not needed for descr ibing adsorption kinetics. The resulting rate expression can be reduced to Joos's kinetic equation and hence serves as a confirmation of it. Simplifications of the general rate expression are also presented for speci fic interfacial situations of near equilibrium and far from equilibrium. A combination of these rate expressions with a surface tension-adsorption rel ation, e.g. the Frumkin equation, can result in equations that are experime ntally accessible. Future work will be concentrated on experimental investi gations that may provide further validation of the theory and estimates for the parameters used in the rate expressions, especially the symmetry facto r alpha. (C) 1998 Elsevier Science B.V. All rights reserved.