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Cottrell Equation

Last Updated: 5/7/19 by Tim Paschkewitz

  • CA,
  • chronoamperometry,
  • cottrell
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  1. Cottrell Equation
  2. References

1Cottrell Equation

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) Wikipedia - Faraday Constant , 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}
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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