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# Cottrell equation

In electrochemistry, the Cottrell equation describes the change in electric current with respect to time in a controlled potential experiment, such as chronoamperometry. For a simple redox event, such as the ferrocene/ferrocenium couple, the current measured depends on the rate at which the analyte diffuses to the electrode. That is, the current is said to be "diffusion controlled." The Cottrell equation describes the case for an electrode that is planar.

i = nFAcoO(DO)1/21/2t1/2

Where

n = number of electrons
F = Faraday constant, 96,500 coulombs/mole
A = area of the (planar) electrode in units cm2
coO = initial concentration of the reducible analyte O with units molarity
DO = diffusion coefficient for species O in units cm2/s
t = time in s

Deviations from linearity in the plot of i vs t-1/2 sometimes indicate that the redox event is associated with other processes, such as assocition of a ligand, dissociation of a ligand, or a change in geometry.

In practice, the Cottrell equation simplifies to

i = kt-1/2, where k is the collection of constants for a given system (n, F, A, coO, DO).

Furthermore, (scan rate)1/2 is used in place of t-1/2. Typical scan rates are in the range 20 to 2000 mV/s.

## References

1. ^ Bard, A. J.; Faulkner, L. R. “Electrochemical Methods. Fundamentals and Applications” 2nd Ed. Wiley, New York. 2001. ISBN 0-471-04372-9