Properties of coplanar periodic electrodes in confined spaces: Case of twodimensional diffusion
Abstract
Periodic configurations of electrodes, in particular of microelectrodes, have been of interest since the advent of microfabrication. In this report, theory which is common to any periodic cell (or any cell that can be extended periodically) with finite height and twodimensional symmentry was derived. The diffusion equation in this cell was solved and the concentration profile was obtained in terms of its Fourier coefficients and as a function of an arbitrary current density. From this base result, a set of properties were derived which are fairly general, since they don't assume restrictions such as reversible electrode reactions (Nernst equation valid when current circulates). These properties involve: horizontal averages and (weighted) sum of concentrations, both with a close connection to the net current and accumulation of species in the cell. The derived properties allow: to explain qualitative aspects of collection efficiency and limiting currents, to predict the concentration on counter electrodes and nonlinearities caused by depletion of species at extremely polarized electrodes, and to estimate the time required by the current to reach steady state in potential controlled experiments. The theoretical results are illustrated analytically and numerically for the concrete case of interdigitated array of electrodes.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 arXiv:
 arXiv:1802.00120
 Bibcode:
 2018arXiv180200120G
 Keywords:

 Physics  Chemical Physics
 EPrint:
 v2: Preprint version, 26 pages, 4 figures