Microscopic interpretation of electron transfer

This last expression shows that 10 and k0 both express the rate of an electrode reaction (independent of occ in this case). 

Exactly the same result is obtained by following identical reasoning, using the anodic instead of the cathodic reaction in (4.14). 

Some notions of the mechanism of electron transfer were given in Section 4.2. Any theory must be realistic and take into account the reorientation of the ionic atmosphere in mathematical terms. There have been many contributions in this area, especially by Marcus, Hush, Levich, Dog-nadze, and others5-9. The theories have been of a classical or quantum-mechanical nature, the latter being more difficult to develop but more correct. It is fundamental that the theories permit quantitative comparison between rates of electron transfer in electrodes and in homogeneous solution. 

what is the variation of the rate constant with potential The charge transfer coefficient, or, anodic or cathodic, is given by 

This is a form of the Tafel relation (Section 6.6) so long as the current is proportional to the rate constant. It is an example of a linear free energy relationship (a kinetic parameter, In A , varies linearly with a thermodynamic parameter, E). Substituting AG we get 

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