Cottrell equation, potential step methods

The Cottrell equation is derived from Pick s second law of diffusion (Section 1.5) and predicts the variation of the current in time, when a potential step is applied under conditions of large overpotential. For this equation to be valid the current must be limited by diffusion of the analyte to the electrode surface, and thus the solution has to be unstirred. The overpotential at which the reaction is driven must be large enough to ensure the rapid depletion of the electroactive species (O) at the electrode surface, such that the process would be controlled by the diffusion to the electrode. This equation is most often applied to potential step methods (e.g., chronoamperometry see Chapter 11) ... 

We describe here that the redox oligomer wires fabricated with the stepwise coordination method show characteristic electron transport behavior distinct from conventional redox polymers. Redox polymers are representative electron-conducting substances in which redox species are connected to form a polymer wire.21-25 The electron transport was treated according to the concept of redox conduction, based on the dilfusional motion of collective electron transfer pathways, composed of electron hopping terms and/or physical diffusion.17,18,26-30 In the characterization of redox conduction, the Cottrell equation can be applied to the initial current—time curve after the potential step in potential step chronoamperometry (PSCA), which causes the redox reaction of the redox polymer film ... 

In practice two methods are used for stationary planar electrodes in quiescent solution chronoamperometry and chronopotentiometry. By use of an electroactive species whose concentration, diffusion coefficient, and n value are known, the electrode area can be calculated from the experimental data. In chronoamperometry, the potential is stepped from a value where no reaction takes place to a value that ensures that the concentration of reactant species will be maintained at essentially zero concentration at the electrode surface. Under conditions of linear diffusion to a planar electrode the current is given by the Cottrell equation [Chapter 3, Eq. (3.6)] ... 

Double-potential step chronoamperometry This method was proposed in 1965 by Schwarz and Shain [18] for the investigation of follow-up reactions especially for the mechanism. During the first potential pulse the product B is produced at a stationary electrode under diffusion-controlled conditions for a timed interval tp. During this interval substance B diffuses into the solution and simultaneously undergoes a chemical reaction. Then, the potential is suddenly switched to a value where B is converted back into A. The backward current indicates the amount of B which has not reacted and can be related to the rate constant kf. The forward current-time dependence is given by the Cottrell equation... 

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