Relative growth rate

In cyclic voltammetry, the Randles–Sevcik equation describes the effect of scan rate on the peak current i_p. For simple redox events such as the ferrocene/ferrocenium couple, i_p depends not only on the concentration and diffusional properties of the electroactive species but also on scan rate.

$i_p=0.4463nFAC{\left(\frac{nFvD}{RT}\right)}^{\frac{1}{2}}$

Or if the solution is at room temperature:

$i_p=268,600n^{\frac{3}{2}}A{D}^{\frac{1}{2}}C{v}^{\frac{1}{2}}$

• i_p = current maximum in amps
• n = number of electrons transferred in the redox event (usually 1)
• A = electrode area in cm²
• F = The Faraday Constant in C mol⁻¹
• D = diffusion coefficient in cm²/s
• C = concentration in mol/cm³
• ν = scan rate in V/s

For novices in electrochemistry, the predictions of this equation appear counter-intuitive, i.e. that i_p increases at faster voltage scan rates. It is important to remember that current, i, is charge (or electrons passed) per unit time. Therefore, at faster voltage scan rates the charge passed per unit time is greater, hence an increase in i_p, while the total amount of charge is the same.

Uses

Using the relationships defined by this equation, the diffusion coefficient of the electroactive species can be determined. Linear plots of i_p vs. ν^1/2 provide evidence for a chemically reversible redox process vs the cases where redox causes major structural change in the analyte. For species where the diffusion coefficient is known (or can be estimated), the slope of the plot of i_p vs. ν^1/2 provides information into the stoichiometry of the redox process.

See also

• On-line calculator for use of Randles–Sevcik equation:http://www.calctool.org/CALC/chem/electrochem/cv1