标题： 共面周期电极在受限空间中的特性：二维扩散的情况 显示英文标题

标题： Properties of coplanar periodic electrodes in confined spaces: Case of two-dimensional diffusion

摘要： 电极的周期性配置，特别是微电极的周期性配置，自微加工技术出现以来就引起了人们的兴趣。 在本报告中，推导了适用于任何有限高度和二维对称性的周期性单元（或任何可以周期性扩展的单元）的理论。 在此单元中的扩散方程被求解，并得到了以傅里叶系数表示并作为任意电流密度函数的浓度分布。 从这个基本结果出发，推导出了一组相当普遍的性质，因为它们不假设诸如可逆电极反应（当电流循环时能斯特方程有效）之类的限制。 这些性质包括：水平平均值和浓度的（加权）总和，它们与净电流和单元中物质的积累有密切关系。 推导出的性质可以用来解释收集效率和极限电流的定性方面，预测反电极上的浓度以及由极端极化电极上物质耗尽引起的非线性，并估计在电位控制实验中电流达到稳态所需的时间。 理论结果通过解析和数值方法在电极交错阵列的具体情况下进行了说明。 显示英文摘要

摘要： 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 two-dimensional 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 non-linearities 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.