The role of charge separation in the response of electrochemical systems

Abstract

To elucidate the effect of charge layers on the behavior of electrochemical systems comprising microgeometries, we investigate microhemisphere and microdisc electrodes. A binary electrolyte is examined, consistent with virtually all battery and fuel–cell electrolytes. The transport–controlled current density response is shown to be governed by two dimensionless groups: the first group, δ, corresponds to a Debye length divided by the electrode radius, while the second, σ, characterizes the charge density on the electrode surface relative to the salt concentration. In many cases of practical interest, δ is very small, and the modelling equations approach a singularity; the resulting equation system is thus not amenable to numerical solution. We have used an asymptotic analysis to deal with this problem, so that our model calculations cover the full range of δ–values that are of interest. The asymptotics are given for more general electrode shapes, including hemispheres and discs.