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 surfactant adsorption at liquid interfaces. His model is general, in the sense that the change in interfacial tension is incorporated into adsorption rate descriptions, and its governing kinetic equation can be reduced to various specific expressions for individual situations, such as the Langmuir kinetic equation. Joos developed his kinetic model by simply drawing analogies between adsorption and electrode kinetics, where the rate expression was obtained by using conventional chemical reaction theory. In this paper, we present a quantum statistical formulation for surfactant adsorption kinetics. With the assumption of excited states for molecular adsorption, we derive a rate equation by using Statistical Rate Theory (SRT), which gives the expression for transition probabilities from a first-order perturbation analysis of the Schrodinger equation. This new derivation avoids using the principle of mass action and the law of Arrhenius–Eyring, and hence many empirical assumptions in conventional chemical reaction theory are not needed for describing 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 specific interfacial situations of near equilibrium and far from equilibrium. A combination of these rate expressions with a surface tension–adsorption relation, e.g. the Frumkin equation, can result in equations that are experimentally accessible. Future work will be concentrated on experimental investigations that may provide further validation of the theory and estimates for the parameters used in the rate expressions, especially the symmetry factor α .