Cottrell equation

https://doi.org/10.1351/goldbook.09069
Equation for diffusion current \(I_{\rm{d}}\) at time \(t\) at a large planar electrode in contact with a semi-infinite layer of unstirred solution containing excess supporting (inert) electrolyte and an electroactive substance of bulk concentration \(c\) when, at the instant \(t = 0\), the potential of the electrode is suddenly changed to a value at which a mass-transport limited electrochemical reaction occurs and the concentration of the electroactive species at the electrode is zero, \[I_{\rm{d}} = zFA{D^{1/2}}c/(\pi^{1/2} t^{1/2})\] where \(z\) is the electron number of an electrochemical reaction in the charge transfer step of the species (being positive for an oxidation and negative for a reduction), \(F\) the Faraday constant, \(A\) the electrode surface area, and \(D\) the diffusion coefficient of the electroactive substance.
Note: This equation shows that the current decays from an initial infinitely large value, is proportional to \(1/t^{1/2}\), and that no steady-state current (current independent of time) is ever achieved. In practice, diffusion-limited transport is eventually limited by convection.
Source:
PAC, 2020, 92, 641. 'Terminology of Electrochemical Methods of Analysis (IUPAC Recommendations 2019)' on page 650 (https://doi.org/10.1515/pac-2018-0109)