Analytical theory for the voltammetry of the non-Nernstian catalytic mechanism at macro and microelectrodes: Interplay between the rates of mass transport, electron transfer and catalysis

Abstract An analytical theoretical treatment of the first-order catalytic mechanism with non-Nernstian electron transfer is presented for electrodes of different geometry and size. As a result, a general and rigorous expression for the transient current-potential response is obtained, applicable to any electrode size and to any electrochemical and chemical kinetics. From the general theoretical solution, the conditions under which the non-Nernstian catalytic mechanism reaches the steady state response are discussed and the corresponding analytical expression is derived. This has a very simple mathematical form, which holds for any electrode geometry as evidenced here for macroelectrodes, microhemispheres and microdiscs. The new analytical solutions reveal relevant analogies between the responses of the catalytic mechanism and a simple charge transfer, which enables us to establish simple procedures for the elucidation of the reversibility of the electrode reaction. The influence of the latter on the current-potential response of direct-current (normal pulse and cyclic voltammetries) and of differential (differential double pulse and square wave voltammetries) techniques are studied. Also, the dependence of the response on the catalytic kinetics and thermodynamics and on the electrode size are analyzed.