Model systems Cottrell

Along with a group of models that have shown themselves useful, their particular normalisations will be presented. The first model, the Cottrell system, will also serve to introduce the concept of the Nernst diffusion layer. 

The Cottrell equation was developed in 1903 by solving a simple model system for chronoamperometry at a large electrode and at high overpotential [F.G. Cottrell, Z. Physik. Chem. 42 (1903) 385]. 

While the Cottrell system might be regarded as the simplest possible model with a Dirichlet boundary condition (that is, in which boundary concentrations are specified), the constant current case is the simplest possible for the Neumann boundary condition, in which a concentration gradient is specified at the boundary. This model can also be called the chronopotentiometric experiment since here, the current is given and it is the electrode potential that is measured against time. Mathematically this model is defined by the usual (2.33), here with the boundary conditions... 

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