Models of electrochemical electron transfer kinetics

In studying the activation polarization (overpotential, t ) of an electrode interface, 

This relation is termed the Tafel equation. The Tafel equation essentially describes the observed current density at a given electrode potential (potentiostatic mode) or, equivalently, yields the observed electrode potential at a given current density (galvanostatic mode). 

Single-electron transferring across electrified interfaces are traditionally characterized as either outer- or inner-sphere processes according to whether or not they are accompanied in a concerted manner with the formation or the breaking of chemical bonds. Outer-sphere reactions therefore solely involve the reorganization of the outer solvent sphere after the electron transfer has occurred. There are only very few truly outer-sphere reactions known to date such as [23] 

Consider a simple outer-sphere half-cell reaction process 

The Butler-Volmer (BV) approximation is the simplest approach to model and capture the essential features of the empirical Tafel equation. It considers an electrochemical half-cell reaction as an activated process, with the forward and backward reaction rates following an Arrhenius type law according to 

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