An Analytic Solution for the Microdisk Electrode and Its Use in the Evaluation of Charge‐Transfer Rate Constants

A simple analytic expression is developed for the current‐potential relationship of a stationary disk electrode. The analysis involves the coupling of the steady‐state diffusion equation with a Butler‐Volmer boundary condition on the electrode surface; the solution is exact if a large excess of inert supporting electrolyte is present. Analytic formulas are derived that allow one to determine how small the disk electrode must be to extract kinetic information from the electrochemical system. In addition, we show that the current distribution is uniquely governed by one dimensionless parameter. The kinetic parameters of a copper‐deposition process are calculated as an illustration of the method. We demonstrate experimentally the utility of microdisks for high‐rate plating studies and the importance of the potential scan rate in electro‐deposition studies; to use our analytic solution, the scan rate must be fast enough to avoid deposit buildup on the electrode, yet slow enough to obtain pseudosteady‐state transport rates.