Equivalence between Microelectrodes of Different Shapes: Between Myth and Reality

Abstract

Diffusion and diffusion coupled with homogeneous and/or heterogeneous kinetics are investigated at microelectrodes under conditions of steady-state (disk or hemisphere) or quasi-steady-state (hemicylinder and band) diffusion, in order to search for the possible existence of equivalence relationships between these electrodes of different shapes. The goal of this work is to answer the following question : Is it possible to extract sound kinetic and thermodynamic information from experimental voltammograms obtained at a disk or a band microelectrode, using theories or simulations performed respectively at a would-be equivalent hemispherical or a hemicylindrical microelectrode ? It is shown that no true equivalence exists for either pair (band/hemicylinder or disk/hemisphere). Despite the fact that there is no true equivalence, there are time domains where the pair components may become equivalent. This occurs at short times for both sets when planar diffusion prevails and in the quasi-steady-state regime for the band/hemicylinder pair, provided that no slow homogeneous kinetic steps are considered and that different rate constants are considered at each electrode (see text). Conversely, no equivalence exists between disk and hemisphere electrodes in the steady-state domain except for the already noted Nernstian electron transfer mechanism. Under all other kinetic situations, the disk and hemisphere electrodes are not equivalent. The fundamental physicochemical reasons for this major difference between the two microelectrodes pairs are discussed.