09069 IUPAC Gold Book - Cottrell equation 10.1351/goldbook.09069 09069 current 1 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. 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. electrode https://goldbook.iupac.org/terms/view/09060 electrode surface area https://goldbook.iupac.org/terms/view/09074 electron number of an electrochemical reaction https://goldbook.iupac.org/terms/view/09063 PAC, 2020, 92, 641. 'Terminology of Electrochemical Methods of Analysis (IUPAC Recommendations 2019)' on page 650 (https://doi.org/10.1515/pac-2018-0109) https://goldbook.iupac.org/terms/view/09069/html https://goldbook.iupac.org/terms/view/09069/json https://goldbook.iupac.org/terms/view/09069/plain Citation: 'Cottrell equation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.09069 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-06-29T13:26:16+00:00