Computational Study of Chronoamperometry at Rectangular Microelectrodes

Abstract

Three (space) dimensional diffusion to a rectangular microelectrode of length l and width w, embedded in an infinite coplanar insulator is simulated with boundary conditions for a chronoamperometric experiment. An alternating direction implicit finite difference method (Douglas-Gunn algorithm) utilizing a problem adapted grid is used to solve the diffusion equation. Current transients are computed for different values of the dimensionless length parameter L ¼ l/w, starting with L ¼ 1, i.e., a square electrode. Edge effects at the four sides of the rectangular electrode as well as the vertex effect contribute to the total current. With increasing L the transients approach the behavior of a microband electrode transient, where diffusion is essentially two dimensional. The breakdown of the two dimensional diffusion approach with decreasing values of L is analyzed and quantified. This serves as a guideline for analyzing transients measured with electrodes where the condition l » w is not fulfilled.

Reference values of the chronoamperometric response at cylindrical and capped cylindrical electrodes

“…Thus, if a whisker electrode is longer than 100 times its radius, it would be reasonable to use known current functions appropriate to a cylinder, which can simplify calculations. Similar behaviour was observed for planar rectangular microelectrodes of length l and width w; with increasing ratio l/w the current approaches that of a band electrode of length l [50].…”

Theory of square, rectangular, and microband electrodes through explicit GPU simulation

“…Current theoretical literature on microbands is split in the use of dimensionless co-ordinates -some, such as Aoki et al [22][23][24][25] and Streeter et al [7], use Eq. (2), whereas Britz et al [26] and Strutwolf [27] use Eq. (3).…”

“…To this author's knowledge, only two works of three-dimensional analysis of rectangular (non pseudo-infinite) microband electrodes exist -that of Strutwolf [27], and of Woodvine et al [31].…”

Electrochemical random-walk theory

“…Previous methods for tackling three dimensional Fickian diffusion have either relied on explicit finite difference calculation of uncomplicated geometries, which result in large simulation times due to the unstable nature of the discretisation method [6,15]. The alternating direction implicit finite difference method in three dimensions has also been used, but can suffer from oscillation and stability issues depending on the algorithm method used [31][32][33]. Boundary element simulation can be mathematically complex for this work, and finite element simulation can suffer from poor accuracy [7].…”