The replacement of Fick's laws by a formulation involving semidifferentiation

Abstract

The mathematical operation of semidifferentiation enables the concentration of an electroactive species at the surface of an electrode to be related straightforwardly to the faradaic current density. This relationship holds irrespective of the degree of reversibility of the electrode reaction and is not restricted to diffusion-controlled situations. This concept provides an improved starting point for the prediction of voltammetric relationships, compared with the classical Fick's law approach, in that only one additional condition (representing the electrical signal applied to the cell) is needed to characterize the experiment. This contrasts with the classical approach in which a number of simultaneous partial differential equations need to be solved. In addition, as illustrated in the examples cited, the greater simplicity of the new approach permits a generalization of voltammetric concepts and suggests improved experimental techniques. Specifically, we have uncovered a novel method of elucidating electrochemical kinetics.