Tafel slope factor reaction order

The numerical values of the Tafel slope and reaction order will depend on the value of p (just as they both depend on the value of P), but the form of the rate equations is not changed. The same is true for any mechanism, and the use of the same symmetry factor in Eq. 5D and Eq. 171 does not restrict the validity or generality of the rate equations derived under Temkin conditions. 

When the electroactive species or an intermediate adsorbs on the electrode surface, the adsorption process usually becomes an integral part of the charge transfer process and therefore cannot be studied without the interference of a faradaic current. In this situation, surface coverages cannot be measured directly and the role of an adsorbate must be inferred from a kinetic investigation. Tafel slopes and reaction orders will deviate substantially from those for a simple electron transfer process when an adsorbed intermediate is involved. Moreover the kinetic parameters, exchange current or standard rate constant, are likely to become functions of the electrode material and even the final products may change. These factors will be discussed further in the section on electrocatalysis (Section 1.4). 

There are also some questionable explanations for the inconsistency between a low Tafel slope and the inductive behavior that characterizes the consecutive charge transfer. One of them is to accept that the symmetry factor has a totally asymmetric value, such as the limiting values 0 or 1, and that it is strongly potential dependent the other is to deny the mechanistic significance of steady-state characteristics, that is, of the Tafel slope and reaction orders, because they are influenced by the sweep rate and waiting time arbitrarily chosen by the experimentalists. ... 

This mechanism is in agreement with the experimentally observed Tafel slope of 40 mV decade 1 [assuming a symmetry factor / = 1/2 for reaction (47)] and a reaction order of 1 with respect to OH. The species M was suggested to be a hydrated surface Ru complex [227]. 

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. 

This leads to a Tafel slope of b = 2.3RT/PF = - 0.12 V for P = 0.5, and a reaction order (at constant potential) of unity. The transfer coefficient is equal to the symmetry factor P as in the case of mercury, but we recall that the Tafel slope is calculated here assuming essenti illy full coverage, whereas that on mercury was obtained assuming a very low value of the coverage. The Tafel plot observed on platinum in acid solutions is shown in Fig. 5F. 

The involvement of chemisorbed intermediates in electrocatalytic reactions is manifested in various and complementary ways which may be summarized as follows (i) in the value of the Tafel slope dK/d In i related to the mechanism of the reaction and the rate-determining step (ii) in the value of reaction order of the process (iii) in the pseudocapacitance behavior of the electrode interface (see below), for a given reaction (iv) in the frequency-response behavior in ac impedance spectroscopy (see below) (v) in the response of the reaction to pulse and linear perturbations or in its spontaneous relaxation after polarization (see below) (vi) in certain suitable cases, also to the optical reflectivity behavior, for example, in reflection IR spectroscopy or ellipso-metry (applicable only for processes or conditions where bubble formation is avoided). It should be emphasized that, for any full mechanistic understanding of an electrode process, a number of the above factors should be evaluated complementarily, especially (i), (ii), and (iii) with determination, from (iii), whether the steady-state coverage by the kinetically involved intermediate is small or large. Unfortunately, in many mechanistic works in the literature, the required complementary information has not usually been evaluated, especially (iii) with 6(V) information, so conclusions remained ambiguous. 

From the above it is seen how the same coverage functions, involving the lateral interaction factor g, determine both R and the Tafel slope values. In particular, for the electrochemical desorption mechanism, the Tafel slope b is found to be (RT/F)(—1 + whereas for the recombination-controlled mechanism it is simply (RT/F) , in terms of the reaction order, R. 

Extensive work on reaction orders in electrode kinetics, and their interpretation, have been made by Vetter (140), Yokoyama and Enyo for the Clj evolution and other reactions (141, 142, 144), and by Conway and Salomon for the HER (143). In the extensive treatment of the kinetics of O2 evolution by Bockris (145), reaction orders were derived for various possible reaction mechanisms and provide, among other factors, diagnostic criteria for the mechanisms in relation to the experimentally determined behavior, for example, pH effects in the kinetics and Tafel slope values (145). 

Of special interest for the topic of the present chapter is the observation of Weaver that while the double-layer-corrected AS quantities are ligand sensitive, they are found to be independent of potential. This is not the case for the atom and electron transfer process involved in the hydrogen evolution reaction at Hg studied by Conway, et where an appreciable potential dependence of AS is observed, corresponding to conventionally anomalous variation of the Tafel slope with temperature. Unfortunately, in the work with the ionic redox reactions, as studied by Weaver, it is only possible to evaluate the variation of the transfer coefficient or symmetry factor with temperature with a limited variety of redox pairs since Tafel slopes, corresponding to any appreciable logarithmic range of current densities, are not always easily measurable. Alternatively, evaluation of a or /3 from reaction-order determination requires detailed double-layer studies over a range of temperatures. 

From the above discussion, it is clear that various kinetic criteria (reaction orders, Tafel slopes, and log/-AGads plots on different electrode materials, where appropriate) can be used to determine the reaction mechanism and the coverage conditions. For reactions involving protons, the separation factors (H-T or H-D) can also be used as another criterion, since the barrier heights vary characteristically with mechanism because of the relatively large zero point energy difference between the isotopes and their different quantum mechanical tunneling properties. This is evaluated in Refs. 50 and 51, and may be used to confirm other evidence. 

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