Transfer coefficient, Butler-Volmer model

Both the frequency of the well and its depth cancel, so that the free energy of activation is determined by the height of the maximum in the potential of mean force. The height of this maximum varies with the applied overpotential (see Fig. 13). To a first approximation this dependence is linear, and a Butler-Volmer type relation should hold over a limited range of potentials. Explicit model calculation gives transfer coefficients between zero and unity there is no reason why they should be close to 1/2. For large overpotentials the barrier disappears, and the rate will then be determined by ion transport. 

Simplified Butler-Volmer Equation 3 Butler-Volmer Equation with Identical Charge Transfer Coefficients-sinh Simplification A very nice simplification can be made to the BV model if the anodic and cathodic charge transfer coefficients at the electrode are equivalent (i.e., Uc = a a). In this case, no approximation is needed, and a new form explicit in r] and mathematically equivalent to the original BV model can be written. This model is valid over all regions of the electrode polarization, as shown in Figure 4.25. 

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