Cottrell Equation
Last Updated: 5/7/19 by Tim Paschkewitz
1Cottrell Equation
There are many resources that describe the detailed background, derivation, and applications of this equation.
Bard, A. J.; Faulkner, L. A.  Electrochemical Methods: Fundamentals and Applications, 2nd ed. Wiley-Interscience: New York, 2000.
Kissinger, P.; Heineman, W. R.  Laboratory Techniques in Electroanalytical Chemistry, 2nd ed. Marcel Dekker, Inc: New York, 1996.
Wang, J.  Analytical Electrochemistry, 3rd ed. John Wiley & Sons, Inc.: Hoboken, NJ, 2006. Here, we present just a snippet to get you started.
Kissinger, P.; Heineman, W. R.  Laboratory Techniques in Electroanalytical Chemistry, 2nd ed. Marcel Dekker, Inc: New York, 1996.
Wang, J.  Analytical Electrochemistry, 3rd ed. John Wiley & Sons, Inc.: Hoboken, NJ, 2006. Here, we present just a snippet to get you started.
The Cottrell equation describes the current response, in time, as a function of a step in potential. For the general half-reaction, and starting from the concentration profile with linear diffusion and assigning appropriate boundary conditions, the current-time response observed during an instantaneous potential step experiment is
where is current, is the number of electrons transferred in the half reaction, is Faraday's Constant (96,485 C/mol)
Wikipedia - Faraday Constant
, is the area of the electrode, is the diffusion coefficient, is the initial concentration, and is time.
Written in linear form,
which has the form of , therefore,
where
In this linear form, a plot of will indicate deviations from linearity, which suggest that the electrochemical reaction is coupled to other processes such as kinetic limitations or molecular/chemical changes such as ligand association or dissociation or geometric rearrangements.
2References
- Bard, A. J.; Faulkner, L. A.  Electrochemical Methods: Fundamentals and Applications, 2nd ed. Wiley-Interscience: New York, 2000.
- Kissinger, P.; Heineman, W. R.  Laboratory Techniques in Electroanalytical Chemistry, 2nd ed. Marcel Dekker, Inc: New York, 1996.
- Wang, J.  Analytical Electrochemistry, 3rd ed. John Wiley & Sons, Inc.: Hoboken, NJ, 2006.