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Impedance of a Micro-Disk Microelectrode

For the macroelectrode, one can use the Warburg impedance to describe the diffusion coefficient. This Demonstration shows the analytical solution for the diffusional impedance of a micro-disk electrode. It is a function of frequency, kinetics, concentration, and the radius of the microelectrode.

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The equivalent circuit for an electrochemical cell with the micro-disk electrode as a working electrode is given by this diagram:
= electrolyte resistance
= charge transfer resistance
= double layer capacitance
= diffusional impedance
The diffusional impedance can be simulated by the finite-element method (FEM) or by the finite-difference method (FDM). [1] formulates the analytical expression for the real and the imaginary parts of the diffusional impedance:
,
,
where
= radius of microelectrode,
= diffusion coefficient,
= angular frequency.
The numeric values of the functions and are given in this Demonstration; you can vary the parameters , , and to investigate the diffusional impedance .
References
[1] M. Fleischmann and S. Pons, "The Behavior of Microdisk and Microring Electrodes. Mass Transport to the Disk in the Unsteady State: The AC Response," Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 250(2), 1988 pp. 277–283.
[2] M. Keddam, N. Portail, D. Trinh, and V. Vivier, "Progress in Scanning Electrochemical Microscopy by Coupling with Electrochemical Impedance and Quartz Crystal Microbalance," ChemPhysChem, 10(18), 2009 pp. 3175–3182.
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