Tafel slope factor

VII. Tafel Slope Factor in Electrocatalysis and Its Relation to Chemisorption of Intermediates... 

Because of the different potential distributions for different sets of conditions the apparent value of Tafel slope, about 60 mV, may have contributions from the various processes. The exact value may vary due to several factors which have different effects on the current-potential relationship 1) relative potential drops in the space charge layer and the Helmholtz layer 2) increase in surface area during the course of anodization due to formation of PS 3) change of the dissolution valence with potential 4) electron injection into the conduction band and 5) potential drops in the bulk semiconductor and electrolyte. 

The performance of oxide electrodes depends on both factors, electronic and geometric. The latter is especially important since the preparation of oxide layers as a rule produces very high surface areas. A way to disentangle the two factors is to scrutinize the behavior of an intensive property. In electrochemical kinetics, the Tafel slope is the most appropriate, since it depends closely on the reaction mechanism and not on the extension of the surface area. 

The Pt alloy monolayer nanoparticle catalysts (e.g., Pt-Re layer on Pd cores) showed a clearly improved specific (Pt surface normalized) ORR activity their Pt mass-based electrocatalytic activity, however, exceeded that of pure Pt catalysts by an impressive factor of 18 x— 20 x. Their noble metal (Pt, Re, and Pd) mass-based activity improvement was still about a factor 4x. The Tafel slope in the 800-950 mV/RHE range suggested that the surface accumulation of Pt-OH species is delayed on the Pt monolayer catalyst. The enormous increase in Pt mass-based activity is obviously due to the small amount of Pt metal inside the Pt monolayer. 

This cathode (called TWAC) exhibits a low Tafel slope up to a few kA m-2 so that the reduction in overpotential, compared to the traditional cathodes, reaches 0.2 V at 3 kA m 2 which is almost the same as that achieved with a Rh-activated cathode. The resistance to poisoning by Fe impurities is also improved this is probably related to its exceptionally high surface area, the roughness factor being of the order of 104. 

Since Ru02 and Ir02 are usually prepared by thermal decomposition of suitable precursors on an inert support, the morphology of the active layer is very like that of a compressed powder [486]. The surface area plays an important role since the roughness factor can be between 102 and 103. However, the low Tafel slope observed is a clear indication of electrocatalytic effects and the high surface area is the factor which extends the low Tafel slope to much higher current densities. Thus, the combination of these two factors renders these oxides very efficient electrocatalysts for H2 evolution. 

It should be pointed out that an exact knowledge of the Tafel slopes is often unnecessary, because in the normal range of values experienced in electrochemical systems, the effect on the corrosion rate of wide changes in Tafel constants is small as compared to equivalent changes in Rp. To prove this to yourself, range the Tafel slopes from 40 to 200 mV/decade to And out what combinations give more than a factor of 2 from the value of 100 mV/decade. 

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]. 

We can readily calculate the Tafel slope for this case, if we assign a numerical value to the symmetry factor p. This, as we have said before, is commonly taken to be 0.5. The Tafel slope can then be obtained either from Eq. 5F, namely... 

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. 

It is interesting to note that the symmetry factor P did not appear in any of these equations. This is because the rate-determining step assumed here does not involve charge transfer. The current depends indirectly on potential, through the potential dependence of the fractional coverage 0. The transfer coefficient is = 2, as can be seen in Eq. 43F, corresponding to a Tafel slope of b = - 30 mV at room temperature. 

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. 

While an ovapotential may be applied electrically, we are interested in the overpotential that is reached via chemical equilibrium with a second reaction. As mentioned previously, the oxidation of a metal requires a corresponding reduction reaction. As shown in Figure 4.34, both copper oxidation, and the corresponding reduction reaction may be plotted on the same scale to determine the chemical equilibrium between the two reactions. The intersection of the two curves in Figure 4.34 gives the mixed potential and the corrosion current. The intersection point depends upon several factors including (the reversible potential of the cathodic reaction), cu2+/cu> Tafel slopes and of each reaction, and whether the reactions are controlled by Tafel kinetics or concentration polarization. In addition, other reduction and oxidation reactions may occur simultaneously which will influence the mixed potential. 

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). 

High r factors are, however, not without some other complications since they imply porosity of materials. Porosity can lead to the following difficulties (a) impediment to disengagement of evolved gases or of diffusion of elec-trochemically consumable gases (as in fuel-cell electrodes 7i2) (b) expulsion of electrolyte from pores on gas evolution and (c) internal current distribution effects associated with pore resistance or interparticle resistance effects that can lead to anomalously high Tafel slopes (132, 477) and (d) difficulties in the use of impedance measurements for characterizing adsorption and the double-layer capacitance behavior of such materials. On the other hand, it is possible that finely porous materials, such as Raney nickels, can develop special catalytic properties associated with small atomic metal cluster structures, as known from the unusual catalytic activities of such synthetically produced polyatomic metal clusters (133). 

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