Butler-Volmer formalism

Figure 6.6. Gibbs energy profiles of the outer-sphere one-electron transfer process (4) in the Butler -Volmer formalism at electrode potential Ej (a) and electrode potential E2 (b).

If a Butler-Volmer formalism is assumed (see Eq. 1.101) for the sake of simplicity, the expression of the current-potential relationship can be rewritten as... 

In what follows, the Butler-Volmer formalism for the electrode kinetics will be assumed (unless otherwise indicated), so the expressions for the rate constants are (see Sect. 1.7.1) ... 

For the application of Eq. (6.191) to CV, the Butler-Volmer formalism has been used and the following changes are made ... 

The reductive and oxidative peaks shown in Fig. 7.21 are well resolved and the relative magnitude of the oxidative peak and the peak-to-peak separation increases with frequency. The theoretical reverse SWV voltammograms were fitted to the experimental data assuming both BV and MH models. As can be seen, with the Butler-Volmer formalism ( ) excellent fits are obtained between experimental and theoretical SWV curves such that the magnitude and separation of the reduction and... 

In the above equations, kIt(i/l and k(txh are the first-order heterogeneous rate constants (in s ) at potential Eh of a pulse sequence, for the electro-reduction and electro-oxidation reactions, respectively. It will be assumed that the potential dependence of the rate constants is in agreement with the Butler-Volmer formalism (see Eq. (1.101)), i.e.,... 

Comparing this equation with the following relation in the classical Butler-Volmer formalism (note that AQ0gj Aq 0et) ... 

Generally, the electrochemical rate constants are different for the surface-bound and solution-phase redox couples that, within the Butler-Volmer formalism, means they can have different values of the standard rate constant (fcg , fcg ), transfer coefficient (a °, and formal potential... 

A thorough discussion on the modified Butler-Volmer formalism followed here is described in [73]. 

The transfer of ions across immiscible electrolyte interfaces (ITIES) can be described by a similar Butler-Volmer formalism and involves resolvation of the transferred ions. The flux of ions can be measured by the electronic current in the external circuit generated at symmetrical reference electrodes reversible to one of the ions. 

The rate constants kf and k, in Equations 8.36 and 8.37 are given assuming Butler-Volmer formalism ... 

As discussed in Section 3.1.2 and illustrated in Figure 3.3, activation barriers and therefore rate constants for electrochemical elementary reactions vary with electrode potential. A method is introduced here to extrapolate typical DFT, surface slab evaluated activation barriers as a function of potential. This extrapolation takes advantage of the Butler-Volmer formalism [eqn (3.6)]. We first rewrite the reduction of a surface species A [eqn (3.42)] into the following two equations. 

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