Heterogeneous electron transfer Butler-Volmer model

The two models most commonly applied to the heterogeneous electron transfer kinetics are the Butler-Volmer model, which is primarily a macroscopic approach... 

The Butler-Volmer formulation of electrode kinetics [16,17] is the oldest and least complicated model constructed to describe heterogeneous electron transfer. However, this is a macroscopic model which does not explicitly consider the individual steps described above. Consider the following reaction in which an oxidized species, Ox, e.g. a ferricenium center bound to an alkanethiol tether, [Fe(Cp)2]+, is converted to the reduced form, Red, e.g. [Fe(Cp)2], by adding a single electron ... 

In real (as opposed to model) electrochemical cells, the net current flowing will often be partly determined by the kinetics of electron transfer between electrode and the electroactive species in solution. This is called heterogeneous kinetics, as it refers to the interface instead of the bulk solution. The current in such cases is obtained from the Butler-Volmer expressions relating current to electrode potential [73,74,83,257,559]. We have at an electrode the process (2.18), with concentrations at the electrode/electrolyte interface cj q and cb,Oj respectively. We take as positive current that going into the electrode, i.e., electrons leaving it, which corresponds to the reaction (2.18) going from left to right, or a reduction. Positive or forward (reduction) current if is then related to the potential E by... 

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