Incorporating electrode kinetics into the convolutive modeling of reactions at planar, cylindrical and spherical electrodes

Convolutive modeling provides a valuable alternative to digital simulation as a means of predicting the outcome of a voltammetric experiment, for comparison with the laboratory version. Methods based on either of two conjugate functions are described, differing in the direction that the convolution takes. Other than the requirement of uniform accessibility of the electrode surface, convolutive modeling places few restrictions on the range of experiments that may be modeled. The electrode reaction may have any degree of reversibility and may, or may not, be coupled to a first-order chemical process. The diffusivities of the reactant and product may be equal or unequal. The current may be the controlled electrical variable, or the current may be monitored in an experiment in which the potential is controlled. A range of experimental techniques is addressed in this article, including current-reversal chronopotentiometry and cyclic voltammetry without and with a following chemical reaction. Algorithms are reported for each of the two convolution routes. Examples treated in detail include both planar and spherical diffusion fields. The heterogeneous rate constant was varied in all instances, reversible, quasi-reversible, and near-irreversible cases bring considered. Differences between the predictions of the two routes was found to be insignificant, both of the theoretical voltammograms agreeing excellently with analytical formulas, where these are available for comparison. In the case of quasi-reversible cyclic voltammetry, the prediction of the convolutive model was evaluated by global analysis: the input parameters were recovered with only minor discrepancies. (C) 2001 Elsevier Science Ltd. All rights reserved.