The edge effect for planar electrodes

The edge effect function (expressing enhanced current due to diffusion across an edge) is determined for diffusion-limited, reversible, irreversible, and quasi-reversible forms of simple electron transfer following a potential step at a semi-infinite strip electrode. The derivation involves the application of Laplace and Fourier transforms and solution of the transformed problem by the Wiener-Hopf technique. The edge effect functions for the diffusion-limited, reversible, and irreversible cases are obtained explicitly; the Laplace transform of the edge effect function for the quasi-reversible case is obtained. The response of a planar electrode to a potential step can be viewed as a sum of (1) a contribution proportional to the area and immediately significant; (2) a contribution proportional to the perimeter and becoming significant over a longer time interval; (3) further contributions determined by more subtle geometric features and becoming significant at yet longer times. The area contribution is determined by the well-known shielded planar electrode model. The perimeter contribution is given by the results of this paper, which extend results for the diffusion-limited case first derived by Oldham [K.B. Oldham, J. Electroanal. Chem. 122 (1981), 1-17]. (C) 1997 Elsevier Science S.A.