Electrode symmetry factor

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. ... 

Figure 8. Dependence of the symmetry factor a on the free energy of the transition for the reaction of hydrogen ion discharge on a metal electrode.

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 3.12. Potential energy profiles for the concerted and stepwise mechanism in the case of a thermal reductive process (E is the electrode potential for an electrochemical reaction and the standard potential of the electron donor for a homogeneous reaction) and variation of the rate constant and the symmetry factor when passing from the concerted to the stepwise mechanism. 

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. 

Figure 8-7 shows the anodic and cathodic polarization curves observed for a redox couple of hydrated titanium ions Ti /Ti on an electrode of mercury in a sulfuric add solution the Tafel relationship is evident in both anodic and cathodic reactions. FYom the slope of the Tafel plot, we obtain the symmetry factor P nearly equal to 0.5 (p 0.5). 

Another important aspect of the Marcus theory has also been systematically investigated with organic molecules, namely the quadratic, or at least the non-linear, character of the activation-driving force relationship for outer sphere electron transfer. In other words, does the transfer coefficient (symmetry factor) vary with the driving force, i.e. with the electrode... 

Thickness of thin layers, measured by ellipsometty, 1148,1151 Thin layer cells, 1146 adsorption in, 1103 in electrode kinetics, 1103 Ihiophcnol, adsorption, 979 Thirsk, clectrodcposition, 1310 Thompson, G. P., 1455 Thompson, J. J 1057, 1455 Throwing power, 1112 Throwing power, electrodeless, 1376 Titanium carbide, as dectrocatalyst, 1287 Transfer coefficient and symmetry factor, 1186, 1529... 

In practice, one often has cases where the course of the cathodic and anodic current densities across the electrode with change of overpotential is symmetrical (except for the signs for the same numerical value of T)). It will be seen in the next section that this is so if the symmetry factor, P, is exactly 0.50. More often, the anodic and cathodic curves are nearly symmetrical. However, sometimes they are importantly and even dramatically different. For example, the anodic current is oxidizing and could provoke... 

There is therefore one essential conclusion from the comparison of electrodic e-i junctions and semiconductor n-p junctions The symmetry factor P originates in the atomic movements that are a necessary condition for the charge-transfer reactions at electrode/electrolyte interfaces. Interfacial charge-transfer processes that do not involve such movements do not involve this factor. By understanding this, ideas on P become a tad less underinformed. Chapter 9 contains more on this subject. 

At the outset, recall how the symmetry factor was introduced (Section 8.2.4). The charge-transfer reaction was roughly pictured as the jump of an electron acceptor toward the electrode during which, somewhere en route, an electron jumped to the particle and completed its job of electro-nation. Representing the energy of the system... 

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. 

When the symmetry factor was introduced by Volmer and Erdey-Gruz in 1930, it was thought to be a simple matter of the fraction of the potential that helps or hinders the transfer of an ion to or from the electrode (Section 7.2). A more molecularly oriented version of the effect of P upon reaction rate was introduced by Butler, who was the first to apply Morse-curve-type thinking to the dependence of theenergy-dis -tance relation in respect to nonsolvent and metal—hydrogen bonds. 

Notice that in n-electron multistep electrode reactions, n kinetic parameters, rate coefficients, kh and transfer coefficients or symmetry factors, oth corresponding to each elementary step can be defined. However, these quantities are not directly accessible by experiment. 

The main catalytic influence of the nature of the electrode material is through the adsorption of intermediates of complex electrode reactions. Hortiuti and Polanyi [58] suggested that the activation energy of an electrode reaction should be related to the heat of adsorption of adsorbed intermediates by a relationship of the form of the Br0nsted rule in homogeneous solutions. This corresponds to a vertical shift of the potential energy curves by an amount j3Aif°ds with (5 a symmetry factor as discussed in Sect. 6.4 and depicted in Fig. 12. 

Bockris JO M, Nagy Z (1973) Symmetry factor and transfer coefficient a source of confusion in electrode kinetics. J Chem Edu 50 839M3... 

Let us follow the work by Wang and Nowick256 on electrode kinetics of Pt, 02/Ce02 (doped) which was indeed invoking the model mechanism given by Eqs. (163) and (164). If the transfer step is assumed to be rate determining and the symmetry factors are set to 1/2,... 

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. 

Although Eqs. 4D and 5D look similar, the transition from one to the other is by no means trivial and is the subject of detailed discussion later. Here we shall limit ourselves to a brief discussion of two points. First, the charge on the particle z, which appears in Eq. 4D has been dropped from Eq. 5D, since it is tacitly assumed that electrode reactions occur by the transfer of one electron at a time. Tlius, for any rate-determining step, the value of z is always taken as unity. Second, the parameter P, called the symmetry factor, has been introduced. By definition it can take values from zero to unity,... 

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. 

Here, a, the symmetry factor, is generally assigned a value of 0.5. As concentrations Cj(0) are measured at the electrode surface, the exchange current density is a function of applied potential. 

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