The Symmetry Factor in Electrode Kinetics

Bockris JO M, Gochev A. Temperature dependence of the symmetry factor in electrode kinetics. J Electroanal Chem 1986 214 655-74. 

In Section 1.4 it was assumed that the rate equation for the h.e.r. involved a parameter, namely the transfer coefficient a, which was taken as approximately 0-5. However, in the previous consideration of the rate of a simple one-step electron-transfer process the concept of the symmetry factor /3 was introduced, and was used in place of a, and it was assumed that the energy barrier was almost symmetrical and that /3 0-5. Since this may lead to some confusion, an attempt will be made to clarify the situation, although an adequate treatment of this complex aspect of electrode kinetics is clearly impossible in a book of this nature and the reader is recommended to study the comprehensive work by Bockris and Reddy. ... 

Here kf and kb are the adsorption and desorption constants when 9 —> 0. The derivation of the equation above is similar to establishment of the Butler-Volmer kinetic law for electrochemical electron transfer reactions, where the symmetry factor, a, is regarded as independent from the electrode potential. Similarly, in the present case, the symmetry factor, a, is assumed to be independent of the coverage, 9. 

The symmetry factor P is obviously a central entity in electrodics and a fundamental quantity in the theoretical treatment of charge transfer at surfaces, particularly in relating electrode kinetics to solid-state physics. 

In many simple electrode reactions, the symmetry factor P is found to be close to one-half, and this value is usually assumed in the kinetic analysis of complex reactions. If this is substituted into Eq. 35E, we obtain ... 

The Tafel slope for this mechanism is 2.3RT/PF, and this is one of the few cases offering good evidence that P = a, namely, that the experimentally measured transfer coefficient is equal to the symmetry factor. A plot of log i versus E for the hydrogen evolution reaction (h.e.r.), obtained on a dropping mercury electrode in a dilute acid solution is shown in Fig. 4F. The accuracy shown here is not common in electrode kinetics measurements, even when a DME is employed. On solid electrodes, one must accept an even lower level of accuracy and reproducibility. The best values of the symmetry factor obtained in this kind of experiment are close to, but not exactly equal to, 0.500. It should be noted, however, that the Tafel line is very straight that is, P is strictly independent of potential over 0.6-0.7 V, corresponding to five to six orders of magnitude of current density. 

The determination of the numerical value of the symmetry factor p is a thorny problem in electrode kinetics. We might start with the conclusion namely, that it is common practice to use the value of P 0.5 in the study of electrode reactions. It is hard to come up with a satisfactory theory showing why this should be so, but there seems to be some good experimental evidence that it is, at least in a large number of experimental systems. 

Chapter 2, by B. E. Conway, deals with a curious fundamental but hitherto little-examined problem in electrode kinetics the real form of the Tafel equation with regard to the temperature dependence of the Tafel-slope parameter 6, conventionally written as fe = RT/ aF where a is a transfer coefficient. He shows, extending his 1970 paper and earlier works of others, that this form of the relation for b rarely represents the experimental behavior for a variety of reactions over any appreciable temperature range. Rather, b is of the form RT/(aH + ctsT)F or RT/a F + X, where and as are enthalpy and entropy components of the transfer coefficient (or symmetry factor for a one-step electron transfer reaction), and X is a temperature-independent parameter, the apparent limiting... 

In Section 1.4.4 we describe some typical examples of outer-sphere electron transfer kinetics, with particular emphasis on the variation of the transfer coefficient (symmetry factor) with the electrode potential (driving force). 

Figure 2. Working diagram showing how the linear free-energy relationship, common in electrode process kinetics, arises from changes in electrode potential. is a symmetry factor. An extreme case of an anharmonic oscillator energy profile is shown in schematic form (cf. Ref. 25). This representation assumes changes in V affect only the energy of electrons in the initial state at the Fermi level.

The kinetic parameters required to characterize an electrode reaction are reaction order, rate constant or exchange current density, symmetry factor, stoichiometric coefficient. and the standard heat and entropy of activation. These basic parameters can be measured using electrochemical techniques, some of which are discussed in this chapter. The interested reader is referred to refs. [ 1-12] for a detailed discussion of the various electrochemical and physicochemical techniques available at present to charaeterize the electrode surfaces and the electrochemical reactions. 

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