Randles–Ševčík equations

https://doi.org/10.1351/goldbook.09143
Equations describing the peak current \(I_{\rm{p}}\) in linear scan voltammetry and cyclic voltammetry as a function of the amount concentration, \(c_{\rm{0}}\), of electroactive species in bulk solution. For a reversible charge transfer: \[I_{\rm{p,rev}} = k\,z\,F\,A\,c_0 (z\,F\,D\nu/RT)^{1/2}\] for irreversible charge transfer: \[I_{\rm{p,irrev}} = k^{\prime}(\alpha z^{\prime})^{1/2} zFA{c_0}(FD\nu/RT)^{1/2}\] where \(k\) and \(k^{\prime}\) are numerical constants, \(\alpha\) is the charge transfer coefficient (usually assumed to be close to 0.5), \(z\) the electron number of an electrochemical reaction, \(z^{\prime}\) the number of electrons transferred before the rate determining step, \(F\) the Faraday constant, \(R\) the gas constant, \(T\) the thermodynamic temperature, \(A\) the electrode surface area, \(D\) the diffusion coefficient, and \(\nu\) the scan rate.
Notes:
  1. For \(A\) in \(\pu{cm2}\), \(D\) in \(\pu{cm2 s-1}\), \(\nu\) in \(\pu{cm2 s-1}\), and \(c_{0}\) in \(\pu{mol cm-3}\), and \(I_{\rm{p}}\) in \(A\).
  2. At \(T = \pu{298.15 K}\), for reversible charge transfer \(k = 0.446\), and for irreversible charge transfer, \(k^{\prime} = 0.496\).
Source:
PAC, 2020, 92, 641. 'Terminology of Electrochemical Methods of Analysis (IUPAC Recommendations 2019)' on page 677 (https://doi.org/10.1515/pac-2018-0109)