Analytical expressions of the I–E–t curves of a CE process with a fast chemical reaction at spherical electrodes and microelectrodes

The paper reports analytical expressions for the voltammetric response (I–E curve) and concentration profiles of all the species participating in a CE process (B ⇄ C + ne− ⇄ D) with a fast chemical reaction corresponding to the kinetic steady state approximation applicable to spherical electrodes of any size. An additional approximation to obtain a simpler analytical expression for the I–E curve and compact expressions for the concentration profiles is proposed. From this approximation the spherical diffusion and reaction layers concepts for any value of the applied potential are established, and the limit cases (planar, microspherical and ultramicrospherical electrodes) and the particular cases (catalytic and E mechanisms) are obtained. Methods for determining the kinetic parameters of the chemical reaction from the limit current and from the half-wave potential are proposed. The two above I–E responses are compared with that obtained from a more severe approximation which gives rise to an independent of time I–E curve that can only be applied for a narrow interval of the microelectrode radius. All these equations include as particular cases those deduced in a previous paper under limit current conditions.