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Cottrell equation

Electrochemical reactions can be limited in multiple ways. The two main limitations are potential and diffusion.

The potential is the driving force of a reaction, which is described by the Nernst Equation.  If the potential is high enough to drive a reaction, another problem occurs: Depletion.

The reaction occurring at the electrode consumes an active species in front of the electrode. This active species is then depleted and is missing for the reaction to occur. New active species is transported to the electrode by diffusion. Now the diffusion is determining the current flowing at the electrode.

The change of the current due to depletion and diffusion after a potential step is described by the Cottrell equation:

Here I is the current, z the number of transferred electrons, F the Faraday constant, A the surface area of the electrode, c* is the bulk concentration, D the diffusion coefficient and t the time.

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