# The Long-Time Chronoamperometric Current at an Inlaid Microband (or Laminar) Electrode

Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, UK

Received: 27 November 2012 / Revised: 20 December 2012 / Accepted: 21 December 2012 / Published: 4 January 2013

(This article belongs to the Special Issue Ultramicroelectrode Electrochemistry - Theory and Applications)

In this article, we derive an approximate asymptotic analytical expression for the long-time chronoamperometric current response at an inlaid microband (or laminar) electrode. The expression is applicable when the length of the microband is much greater than the width, so that the diffusion of the electrochemical species can be regarded as two-dimensional. We extend the previously known result for the diffusion-limited current response (Aoki, K. et al. J. Electroanal. Chem. 1987, 225, 19–32 and Phillips, C.G. J. Electroanal. Chem. 1992, 333, 11–32) to accommodate quasi-reversible reactions and unequal diffusion coefficients of the oxidant and the reductant. Comparison with numerical calculations validates the analytical expression, and we demonstrate that unequal diffusion coefficients can substantially change the current response. Finally, we discuss the form of the long-time current response for a one-step, one-electron redox reaction if the rate constants are modelled in the Butler–Volmer framework, and indicate the importance of choosing the width of the microband appropriately to allow accurate experimental determination of the standard kinetic rate constant and the electron transfer coefficient.

*Keywords:*chronoamperometry; two-dimensional; electrode; band; microband; lamina; voltammetry