TY - JOUR
T1 - An integral equation approach to the study of the steady state current at surface microelectrodes
AU - Bender, Michael A.
AU - Stone, H. A.
N1 - Funding Information:
HAS would like to thank Dr. Christopher Phillips of Imperial College, London, both for bringing this class of transport problems to his attention and for his suggestions during the course of the work, and Prof. John Newman of UC Berkeley for bringing the work of Baker and Verbrugge to his attention. MAB is grateful to the Rowland Fund at Harvard University for generous support of this undergraduate research. HAS gratefully acknowledges support from an NSF-Presidential Young Investigator Award (CTS-8957043). Both authors would like to thank Prof.. D.G.M. Anderson for helpful conversations. We thank Dr. D.R. Baker for bringing to our attention the examination by Nisancio~lu and Newman of the large K limit.
PY - 1993/6/1
Y1 - 1993/6/1
N2 - An efficient and accurate numerical procedure using integral equation methods is described for solving steady state microelectrode transport problems. The approach is applicable to the general case of an arbitrarily shaped planar electrode, including both surface and bulk reactions. In this work, results for the electrode current are presented for typical values of the dimensionless surface and bulk reaction constants for (1) the common case of an isolated disc-shaped microelectrode imbedded in an insulating plane substrate and (2) two identical disc-shaped microelectrodes at arbitrary separations in an insulating plane. The numerical results for the isolated disc problem are in excellent agreement with both the recent asymptotic approximations of Phillips and a new four-term expansion derived herein for conditions which are surface-reaction limited. For the more typical diffusion-limited reaction conditions studied by Phillips, a numerically based correction to the asymptotic series is proposed, thereby extending the range of utility of the analytical approximation. Overall, the numerical method allows straightforward investigation of mixed boundary value problems and is applicable to other surface transport problems, e.g. microelectrode rings or arrays of circular microelectrodes, for which characterization of the mass transport process for the two-disc configuration is a first step.
AB - An efficient and accurate numerical procedure using integral equation methods is described for solving steady state microelectrode transport problems. The approach is applicable to the general case of an arbitrarily shaped planar electrode, including both surface and bulk reactions. In this work, results for the electrode current are presented for typical values of the dimensionless surface and bulk reaction constants for (1) the common case of an isolated disc-shaped microelectrode imbedded in an insulating plane substrate and (2) two identical disc-shaped microelectrodes at arbitrary separations in an insulating plane. The numerical results for the isolated disc problem are in excellent agreement with both the recent asymptotic approximations of Phillips and a new four-term expansion derived herein for conditions which are surface-reaction limited. For the more typical diffusion-limited reaction conditions studied by Phillips, a numerically based correction to the asymptotic series is proposed, thereby extending the range of utility of the analytical approximation. Overall, the numerical method allows straightforward investigation of mixed boundary value problems and is applicable to other surface transport problems, e.g. microelectrode rings or arrays of circular microelectrodes, for which characterization of the mass transport process for the two-disc configuration is a first step.
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U2 - 10.1016/0022-0728(93)80222-4
DO - 10.1016/0022-0728(93)80222-4
M3 - Article
AN - SCOPUS:0002537651
SN - 0022-0728
VL - 351
SP - 29
EP - 55
JO - Journal of Electroanalytical Chemistry
JF - Journal of Electroanalytical Chemistry
IS - 1-2
ER -