Buttler-Volmer equation

The current-voltage curve (5.11) is then transformed to the Buttler-Volmer equation. 

They are obtained in two steps from the Buttler-Volmer equation (5.19) combined with (5.18). The B-V equation is valid only for current densities close to j = 0. In... 

Tafel plots have been used successfully for evaluation of slow electrochemical reactions at metal electrodes. Their application to electrochemical sensors is somewhat limited because of the mass transport boundary condition imposed by the nature of the Buttler-Volmer equation. Nevertheless, because it is simple and inexpensive, it should be always tried as the first approach, but bearing in mind its limitations. 

Based on the thermodynamics, the Tafel plot was later found to be a simplified Buttler-Volmer equation when AE is larger than about 116 mV/n, (Bard and Faulkner 1980), where n, is the number of electrons involved in the rate-determining step (not necessarily equal to the number of electrons involved in one reactant molecule) and it is 1 for the ORR. For the ORR, the OCV is already more than 180 mV lower than the thermodynamic voltage the activation overpotential AE, will be even higher when there is a current flow. So, the activation overpotential AE, for the ORR should follow the Tafel relationship. Based on the thermodynamics, the Tafel relationship is... 

The second expression for the current I f) must reveal the growth mechanism and, as an illustration, we consider the case of direct attachment of ions from the bulk of the electrolyte to the periphery of the two-dimensional cluster. The rate-determining step is supposed to be the ions transfer across the electric double layer. Then the current /i(0 is given by the Buttler-Volmer equation ... 

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