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

- New theory of chronoamperometry at hemispheroidal electrodes
- Valid for oblate and prolate hemispheroids under limiting current conditions
- Rigorous semi-analytical formulae for Faradaic current density and current
- Highly accurate current values from numerically inverted Laplace transforms
- Suitable for experimental data analysis and validation of modelling methods

The recently described theory of potential step chronoamperometry at inlaid microdisk electrodes [L. K. Bieniasz, Electrochim. Acta 199(2016)1] is extended to hemispheroidal electrodes, assuming diffusional transport under limiting current conditions. Both oblate and prolate hemispheroids are discussed. The theory provides previously unknown, rigorous, complete, and explicit expressions for the concentration, the Faradaic current density, and the Faradaic current. The expressions are in the form of inverse Laplace transforms of infinite series involving spheroidal wave functions. Numerical Laplace transform inversion, applied to the series, yields highly accurate solution values. Hence, the present solutions are advantageous over formerly used low-accurate and/or heuristic approximations, for the purposes of experimental data analysis, and for testing of modelling/simulation techniques.