A New Theory of Potential Step Chronoamperometry at a Microdisk Electrode: Complete Explicit Semi-Analytical Formulae for the Faradaic Current Density and the Faradaic Current

A novel theory is presented, of potential step chronoamperometry at a microdisk electrode, assuming a purely diffusional transport under limiting current conditions. The theory provides previously unknown, rigorous, complete, and explicit expressions for the concentration, the Faradaic current density, and the Faradaic current. The microdisk is considered as a limiting case of an oblate microhemispheroidal electrode, when the smallest radius of the hemispheroid tends to zero. The method of separation of variables in the Laplace space is used, resulting in two spheroidal differential equations. The concentration of the depolarizer, the Faradaic current density, and the Faradaic current, are then expressed as inverse Laplace transforms of infinite series involving spheroidal wave functions. Numerical Laplace transform inversion, applied to the series, yields highly accurate solution values. The series are also amenable to analytical examinations. Hence, the present solutions should be preferred over formerly used low-accurate and/or heuristic approximations, for the purposes of experimental data analysis, and for the testing of modelling/simulation techniques. The formula derived for the concentration can also be used to develop a theory of chronoamperometry at oblate microhemispheroidal electrodes.