Butler-Volmer model

The voltammograms at the microhole-supported ITIES were analyzed using the Tomes criterion [34], which predicts ii3/4 — iii/4l = 56.4/n mV (where n is the number of electrons transferred and E- i and 1/4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufficient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler-Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. 

The example treated above is of appreciable relevance for several parts of this chapter, as will be seen later. The potential dependence of c 0 and Cr can be derived explicitly if it is known how kf depends on E. As an illustration in Fig. 2(a), c 0 vs. E curves are given assuming the commonly accepted Butler—Volmer model... 

In the phenomenological Butler-Volmer model (BV) [28, 29], the effect of the applied potential E on the energy of the transition state is assumed to be between that of the oxidized and reduced states, although no molecular description of the activation process is proposed. Accordingly, the activation energies for the reduction and oxidation reactions can be written as ... 

In this section, both approaches will be compared in chronoamperometry under limiting current conditions at spherical electrodes and microelectrodes. As is well known, for spherical electrodes and taking into account the Butler-Volmer model, the value of the diffusion-controlled reduction current at large overpotentials, e B is given by the following expression (see Eq. (2.147) of Sect. 2.5.2) ... 

The two models most commonly applied to the heterogeneous electron transfer kinetics are the Butler-Volmer model, which is primarily a macroscopic approach... 

Although such terms as Butler-Volmer equation or Butler-Volmer expression or Butler-Volmer kinetics or Butler-Volmer model are widely used in the literature, see e.g., Refs, [ii-xii], its definition is ambiguous and even the name is questionable in the light of the historical facts [viii, xiii, xiv]. 

IMPLICATIONS OF THE BUTLER-VOLMER MODEL FOR THE ONE-STEP, ONE-ELECTRON PROCESS... 

Implications of the Butler-Volmer Model for the One-Step, One-Electron Process 99... 

In the case of surface-bound redox couples the asymmetric Marcus-Hush model needs to be used since the Butler-Volmer model has been found inappropriate for the description of the voltammetry of these systems [9]. 

FIGURE 8.21 Plot of the electrochemical cell current given by the Butler-Volmer model as a funetion of the difference of eleetrode potential with the equilibrium potential (eleetrode overpotential). and /g refer to the forward and baekward eurrents, respectively. 

There are two approaches to modeling the SOFC electrochemistry at the mesoscale an elementary kinetics-based model and a modified Butler-Volmer model. In the elementary kinetics-based model, the electrochemical reactions of the SOFC are modeled exactly, whereas in the modified Butler-Volmer model, the phenomenological Butler-Volmer equation is solved based on the local Faradaic current density. 

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