Butler-Volmer equation large cathodic current

Equation (8.21) can be applied to different charge transfer processes both at the cathode and the anode by fitting different parameter values for a and I, to these processes. The approximation in Equation (8.21) for the Butler-Volmer equatiotf is much better than the Tafel approximation. The reason is that it is exact both for large cirrrents (in one of the directions) and for zero current. The equation can be used as an approximation for the Butler-Volmer equation in both current directions if a different pair of parameters values a and Iq ate used for each direction. 

Large Cathodic Current We have seen from Figure 6.7 that for the large negative values of overpotential r], the partial cathodic current density i approaches i, i i. For these conditions the Butler-Volmer equation (6.45) can be simplified. Analysis of Eq. (6.45) shows that when rj becomes more negative, the first exponential term in the equation (corresponding to the anodic partial current) decreases, whereas the second exponential term (corresponding to the cathodic partial reaction) increases. Thus, under these conditions. 

Physically, the reason for the dramatic difference between performances of cathode and anode active layers is the exchange current density ia at the anode the latter is 10 orders of magnitude higher than at the cathode [6]. Due to the large ia, the electrode potential r]a is small. The anode of PEFC, hence, operates in the linear regime, when both exponential terms in the Butler-Volmer equation can be expanded [178]. This leads to exponential variation of rja across the catalyst layer with the characteristic length (in the exponent)... 

Regarding catalyst aging. Darling and Meyers have proposed a mechanistic model, based on empirical parameters, of the Pt oxidation/dissolution in a PEMFC cathode, largely cited by experimentalists in subsequent papers. By using classical Butler-Volmer equations written in terms of the CL electrode potential and empirical parameters (e.g. symmetry factors, zero-exchange current and... 

Each reaction may be subdivided into further detailed reaction steps. The overall reaction follows a Butler-Volmer equation. For large cathodic overvoltages, reduction may become diffusion limited and thus might reach the potentially independent maximum current density j d as described in Equation 1.119 and in Figure 1.23 and as discussed again for metal dissolution with oxygen reduction in Section 1.14. 

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