Cottrell Equation for the Potential-Step Experiment

The Cottrell equation in electrochemistry gives the current to a planar electrode in the potential-step experiment. This Demonstration shows the dependence of the current on the time, concentration, and diffusion coefficient.

where is the diffusion coefficient (/s), is the concentration in bulk solution (mM), is the surface area of the electrode (), is Faraday’s constant, is the time (s), and is the number of electrons transferred.

The graphic on the left shows that the current of the electrode is inversely proportional to ; the current decays quickly for a short time and tends to a limiting value with increasing time.

This phenomenon can be explained by the concentration profile (right), since the current is related to at . Initially, is very large, so the current is large. As time increases, the concentration near the electrode surface is consumed and decreases. The filling part of the concentration profile represents the Nernst diffusion layer , which is the distance when the concentration consumed is about 80%.