Butler-Volmer equation charge transfer coefficients

Hydrogen evolution, the other reaction studied, is a classical reaction for electrochemical kinetic studies. It was this reaction that led Tafel (24) to formulate his semi-logarithmic relation between potential and current which is named for him and that later resulted in the derivation of the equation that today is called "Butler-Volmer-equation" (25,26). The influence of the electrode potential is considered to modify the activation barrier for the charge transfer step of the reaction at the interface. This results in an exponential dependence of the reaction rate on the electrode potential, the extent of which is given by the transfer coefficient, a. 

For a given overpotential, the effective current density depends on the magnitude of the charge-transfer coefficient a as well as on the exchange current density iu. If the overpotential is high enough—that is, if either —(a Frj/RT) or (a Fr/)/RT > 1—then one of the partial current densities in the Butler-Volmer equation overrules the other ... 

In -> Butler-Volmer equation describing the charge transfer kinetics, the transfer coefficient a (or sometimes symbol jS is also used) can range from 0 to 1. The symmetrical energy barrier results in a = 0.5. Typically, a is in the range of 0.3 to 0.7. In general, a is a potential-dependent factor (which is a consequence of the harmonic oscillator approximation, see also - Marcus theory) but, in practice, one can assume that a is potential-independent, as the potential window usually available for determination of kinetic parameters is rather narrow (usually not more than 200 mV). 

Volmerian electrode reaction — This term has been used for electrode reactions in which the - charge transfer coefficient is constant. Reactions for which the latter is potential dependent were called non-volmerian. According to the - Marcus theory there is generally a potential dependence of the charge transfer coefficient, however that is usually very small. The terms Volmerian and non-volmerian refer to the classic Butler-Volmer theory (-> Butler-Volmer equation) where no potential dependence was assumed. See also -> Volmer. 

The values of the Tafel coefficients and j8c depend on the mechanism of the electrode reactions, which often consist of several elementary steps (Section 5.1). It is however not necessary to know the mechanism in order to apply the Butler-Volmer equation. Indeed, equation (4.36) describes the charge-transfer kinetics in a global, mechanism-independent fashion, making reference to three easily measured quantities t o, nd The formulae (4.37) and (4.38) then define the anodic and cathodic Tafel coefficients ... 

Equation 6 is referred to as the Butler-Volmer equation. Normally, for significant overpotentials, either one or the other of the two terms is dominant, so that the current-density exponentially increases with r, i.e. In i is proportional to 3tiF/RT in the case, for example, of appreciable positive t] values. Here the significance of Tafel s b coefficient (Equation 1) is seen b = dn/d In i = RT/3F for a simple, single-electron charge-transfer process. 

Below the limiting current density, mass transport as well as charge transfer determines the overall reaction rate. For T /p g - 1 the Butler-Volmer equation (34) reduces to (68), where g is the cathodic Tafel coefficient for the reaction of... 

Simplified Butler-Volmer Equation with Identical Charge Transfer Coefficient... 

For the equal charge transfer coefficient on the anode and cathode electrode, that is, Ua = Uc = a, the general Butler-Volmer equation (Equation 11.3) can be written as... 

Simplified Butler-Volmer Equation 3 Butler-Volmer Equation with Identical Charge Transfer Coefficients-sinh Simplification A very nice simplification can be made to the BV model if the anodic and cathodic charge transfer coefficients at the electrode are equivalent (i.e., Uc = a a). In this case, no approximation is needed, and a new form explicit in r] and mathematically equivalent to the original BV model can be written. This model is valid over all regions of the electrode polarization, as shown in Figure 4.25. 

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