Cottrell Equation

Last Updated: 5/7/19 by Tim Paschkewitz

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• cottrell,
• CA,
• chronoamperometry

1Cottrell Equation

There are many resources that describe the detailed background, derivation, and applications of this equation.   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, $O+ne\rightarrow R$ 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

$\displaystyle i(t)=\frac{nFAD_O^{1/2}C_O^*}{{\pi}^{1/2}t^{1/2}}$

where $i(t)$ is current, $n$ is the number of electrons transferred in the half reaction, $F$ is Faraday's Constant (96,485 C/mol) , $A$ is the area of the electrode,  $D_O$ is the diffusion coefficient, $C_O^*$ is the initial concentration, and $t$ is time.

Written in linear form,

$\displaystyle i(t)=nFAD_O^{1/2}C_O^*{\pi}^{-1/2}t^{-1/2}$

which has the form of $y=mx+b$, therefore,

$\displaystyle i(t)=mt^{1/2}$

where

$m=nFAD_O^{1/2}C_O^*{\pi}^{-1/2}$

In this linear form, a plot of $i(t) \:\text{vs.}\: t^{-1/2}$ 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.
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