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In [[electrochemistry]], the '''Cottrell equation''' describes the change in [[electric current]] with respect to time in a controlled potential experiment, such as  [[chronoamperometry]]. Specifically it describes the current response when the potential is a step function. It was derived by [[Frederick Gardner Cottrell]] in 1903.<ref>F.G. Cottrell, Z. Phys. Chem. 42 (1903), p. 385.</ref> 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 reaction|"diffusion controlled."]]  The Cottrell equation describes the case for an electrode that is planar but can also be derived for spherical, cylindrical, and rectangular geometries by using the corresponding [[Laplace's equation|laplace operator]] and boundary conditions in conjunction with [[Fick's_laws_of_diffusion#Fick.27s_second_law|Fick's second law of diffusion]].<ref>Bard, A. J.; Faulkner, L. R. “Electrochemical Methods.  Fundamentals and Applications” 2nd Ed.  Wiley, New York. 2001. ISBN 0-471-04372-9</ref>

:<math> i = \frac {nFAc_{j}^{0}\sqrt{D_{j}}}{\sqrt{\pi t}} </math>

where,
:i = current, in unit A
:n = number of electrons (to reduce/oxidize one molecule of analyte j, for example)
:F = [[Faraday constant]], 96,485 C/mol
:A = area of the (planar) electrode in cm<sup>2</sup>
:c<sub>j</sub><sup>0</sup> = initial concentration of the reducible analyte j in mol/cm<sup>3</sup>;
:D<sub>j</sub> = [[Fick's law of diffusion|diffusion coefficient]] for species j in cm<sup>2</sup>/s
:t = time in s.
Deviations from linearity in the plot of i vs t<sup>-1/2</sup> sometimes indicate that the redox event is associated with other processes, such as association of a [[ligand]], dissociation of a ligand, or a change in geometry.  

In practice, the Cottrell equation simplifies to 
:''i'' = kt<sup>-1/2</sup>, where k is the collection of constants for a given system (n, F, A, c<sub>j</sub><sup>0</sup>, D<sub>j</sub>).

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

The ratio i<sub>p</sub>/(scan rate)<sup>1/2</sup>, where i<sub>p</sub> is the peak current, is sometimes referred to as the "current function."

== See also ==
* [[Voltammetry]]
* [[Electroanalytical Methods]]
* [[Sand Equation]]

==References==
<references/>

[[Category:Electrochemical equations]]