Butler—Volmer equation, application

This is the most commonly employed form of the Butler -Volmer equation as it does not involve the unmeasurable surface concentration terms. It must be remembered, however, that equation (1.35) is only applicable under the conditions where [0]0 [O ] and [R]0 =t- [R ]- We must now examine this equation in some detail, as its form dictates the nature of a number of electrochemical techniques for exploring reaction mechanisms. 

On application of an overpotential rj, the Gibbs energy of the electron-transfer step changes by eo[r) — Afa rj), where Afa(rj) is the corresponding change in the potential fa at the reaction site. Consequently, rj must be replaced by [rj — Afa r )] in the Butler-Volmer equation (5.13). 

The Butler-Volmer equation (Eq. 7.23) is a relation for current density, i, as a function of the overpotential, TJ, applicable from TJ = 0 to the value of the overpotential... 

Mann RF, Amphlett JC, Peppley BA, Thurgood CP (2(K)6) Application of Butler-Volmer equations in the modelling of activation polarization for PEM fuel cells. J Power Sources 161 775-781... 

The Butler-Volmer equation, together with Equation (3.19), allows the prediction of the current-voltage characteristics of a galvanic or an electro chemical cell. In applications where the current density is high (or the over potential is high), the exponential law of the Butler-Volmer equation implies that 77 can be approximated by a constant value independent of j. Relation (3.19) can then be written in its simplified form (Fig. 3.5) ... 

The current-voltage curves corresponding to these processes are depicted in Fig. 5.1. As the net current across the metal/solution interface is zero the potential Ep assumed by the particle under stationary conditions is given by the point of intersection of the two i(E) curves. At this potential the anodic and cathodic currents are equal and their value corresponds to iR. The latter defines the overall reaction rate. Both the mixed potential Ep and the reaction current iR may be evaluated from electrokinetic theory. Application of the Butler-Volmer equation to reaction (5.2) gives for the reaction rate V the expression... 

In the given form, the Butler-Volmer equation is applicable rather broadly, for flat model electrodes, as well as for heterogeneous fuel cell electrodes. In the latter case, concentrations in Eq. (2.13) are local concentrations, established by mass transport and reaction in the random composite structure. At equilibrium,/f = 0, concentrations are uniform. These externally controlled equilibrium concentrations serve as the reference (superscript ref) for defining the equilibrium electrode potential via the Nernst equation. 

This is the original Butler-Volmer equation. It has, however, rather limited applicability. It should be used only when electrode potential and all concentrations are uniform. Such conditions are barely encountered in fuel cell electrodes. 

The reason why so much attention is devoted to the Butler-Volmer equation and to the exponential dependence of current on potential is interesting to note. First of all, many electrochemical experiments, particularly the fundamental ones, are carried out in the region where the influence of transport control from the solution side is purposely avoided. One simply calculates what the limiting current will be (see below) and then makes one s experiments in the situation when the currents examined are much less than the limiting current, so that the Butler-Volmer equation is applicable. 

This is the most common form of the Butler-Volmer equation. It is applicable to electrode reactions whose rate is entirely limited by charge transfer at the interface. This process is sometimes called activation control, the corresponding overpotential is then called the activation overpotential. 

Application of the Butler-Volmer equation to the rate-determining step (l-59c) yields for the anodic dissolution... 

Another gassing current calculation approach for PV applications was developed by Filler et al. [25]. Cnrrent is usually small in PV applications and gassing is the major loss during charging therefore, the Butler-Volmer equation can be modified and normalized to define the gassing current ... 

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

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