The Tafel Slope

The most intensively studied experimental parameter has naturally been the Tafel slope, i.e., the dependence of rj upon log /. The Tafel constants, a+ and a, for the anodic and cathodic Tafel lines, respectively, are defined by the relation 

These have the significance of a reaction order with respect to the electron. The kinetic expression which covers the whole overpotential region is 

Since we have a unique rds in the present case, we obtain from Eq. (24) 

Equation (30) is, in principle, applicable for determining However, in practice, it has rather a limited application since, strictly speaking, it is valid only if a+ and a- are observed under the same experimental conditions, particularly the same electrode potential. In, e.g., the cathodic region, a is directly observable, but a+ could be obtained only if a special technique is devised, such as the use of an isotope tracer.  

A general expression for a+ and a to cover various mechanisms has been repeatedly presented in the literature.A simple derivation of these expressions will be given below. An approximation will be made throughout that the reaction conditions are such that the double-layer correction term is always negligible. 

Electrochemical kinetic measurements show that many reactions have a rather constant Tafel slope over a wide overpotential range. This is true for both redox79 and combined electron- and atom-transfer reactions, particularly proton transfer.3,80 None of the approaches discussed above account for the experimental facts. References 41-50, 55-59, and 67 all 

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The two dashed lines in the upper left hand corner of the Evans diagram represent the electrochemical potential vs electrochemical reaction rate (expressed as current density) for the oxidation and the reduction form of the hydrogen reaction. At point A the two are equal, ie, at equiUbrium, and the potential is therefore the equiUbrium potential, for the specific conditions involved. Note that the reaction kinetics are linear on these axes. The change in potential for each decade of log current density is referred to as the Tafel slope (12). Electrochemical reactions often exhibit this behavior and a common Tafel slope for the analysis of corrosion problems is 100 millivolts per decade of log current (1). A more detailed treatment of Tafel slopes can be found elsewhere (4,13,14). 

As with all elec trochemical studies, the environment must be electrically conduc tive. The corrosion rate is direc tly dependent on the Tafel slope. The Tafel slope varies quite widely with the particular corroding system and generally with the metal under test. As with the Tafel extrapolation technique, the Tafel slope generally used is an assumed, more or less average value. Again, as with the Tafel technique, the method is not sensitive to local corrosion. 

The effects of adsorbed inhibitors on the individual electrode reactions of corrosion may be determined from the effects on the anodic and cathodic polarisation curves of the corroding metaP . A displacement of the polarisation curve without a change in the Tafel slope in the presence of the inhibitor indicates that the adsorbed inhibitor acts by blocking active sites so that reaction cannot occur, rather than by affecting the mechanism of the reaction. An increase in the Tafel slope of the polarisation curve due to the inhibitor indicates that the inhibitor acts by affecting the mechanism of the reaction. However, the determination of the Tafel slope will often require the metal to be polarised under conditions of current density and potential which are far removed from those of normal corrosion. This may result in differences in the adsorption and mechanistic effects of inhibitors at polarised metals compared to naturally corroding metals . Thus the interpretation of the effects of inhibitors at the corrosion potential from applied current-potential polarisation curves, as usually measured, may not be conclusive. This difficulty can be overcome in part by the use of rapid polarisation methods . A better procedure is the determination of true polarisation curves near the corrosion potential by simultaneous measurements of applied current, corrosion rate (equivalent to the true anodic current) and potential. However, this method is rather laborious and has been little used. 

Blocking of reaction sites The interaction of adsorbed inhibitors with surface metal atoms may prevent these metal atoms from participating in either the anodic or cathodic reactions of corrosion. This simple blocking effect decreases the number of surface metal atoms at which these reactions can occur, and hence the rates of these reactions, in proportion to the extent of adsorption. The mechanisms of the reactions are not affected and the Tafel slopes of the polarisation curves remain unchanged. Behaviour of this type has been observed for iron in sulphuric acid solutions containing 2,6-dimethyl quinoline, /3-naphthoquinoline , or aliphatic sulphides . 

Participation in the electrode reactions The electrode reactions of corrosion involve the formation of adsorbed intermediate species with surface metal atoms, e.g. adsorbed hydrogen atoms in the hydrogen evolution reaction adsorbed (FeOH) in the anodic dissolution of iron . The presence of adsorbed inhibitors will interfere with the formation of these adsorbed intermediates, but the electrode processes may then proceed by alternative paths through intermediates containing the inhibitor. In these processes the inhibitor species act in a catalytic manner and remain unchanged. Such participation by the inhibitor is generally characterised by a change in the Tafel slope observed for the process. Studies of the anodic dissolution of iron in the presence of some inhibitors, e.g. halide ions , aniline and its derivatives , the benzoate ion and the furoate ion , have indicated that the adsorbed inhibitor I participates in the reaction, probably in the form of a complex of the type (Fe-/), or (Fe-OH-/), . The dissolution reaction proceeds less readily via the adsorbed inhibitor complexes than via (Fe-OH),js, and so anodic dissolution is inhibited and an increase in Tafel slope is observed for the reaction. 

Adsorbed species may also accelerate the rate of anodic dissolution of metals, as indicated by a decrease in Tafel slope for the reaction. Thus the presence of hydrogen sulphide in acid solutions stimulates the corrosion of iron, and decreases the Tafel slope The reaction path through... 

In Fig. 19.106 it has been assumed that the Tafel slopes are equal, i.e. 6a = = b and the modified expression for the right-hand side of equa-... 

Determine from this plot the Tafel slopes 6, and 6 by curve fitting using the theoretical curves calculated for various values of 6 and 6,.. Calculate from equation 19.14 using the Rp, value evaluated in Step 1 and the Tafel slopes determined in Step 3. 

Attention should be drawn to the signs in equations 20.66 and 20.67 and it should be noted that the Tafel slope b is always positive for an anodic process and negative for a cathodic process and that the constant a is of opposite sign to the slope. 

These are the coefficients that determine the Tafel slope of the log / against q curve of a multistep reaction, and they are of fundamental importance in providing information on the mechanism of the reaction. Equations 20.86 and 20.87 are of the same form as equations 20.59 and 20.58 that were derived for a simple one-step reaction involving a symmetrical energy barrier, and under these circumstances equations 20.90 and 20.91 simplify to... 

The ability to use the Tafel slope as a diagnostic criterion can be exemplified by considering a discharge-chemical desorption mechanism for the h.e.r. in which either discharge or chemical desorption may be rate determining. ... 

From the magnitude of the Tafel slope 3tj/3 log / ( 0-12V), the magnitude of dr)/d In ( 0-24 V) and the linearity of the J vs. /i curves for pure iron in H2SO4 and NaOH at various temperatures in the range 18-80°C, Bockris, et al. concluded that the mechanism conformed to the reaction sequence shown in equation 20.107. 

The Tafel slopes obtained under concentrations of the chemical components that we suspect act on the initiation reaction (monomer, electrolyte, water contaminant, temperature, etc.) and that correspond to the direct discharge of the monomer on the clean electrode, allow us to obtain knowledge of the empirical kinetics of initiation and nucleation.22-36 These empirical kinetics of initiation were usually interpreted as polymerization kinetics. Monomeric oxidation generates radical cations, which by a polycondensation mechanism give the ideal linear chains ... 

If we want to use the Tafel slopes to obtain the empirical kinetics of polymerization, we have to use a metallic electrode coated with a previously electrogenerated thin and uniform film of the polymer in a fresh solution of the monomer. In some cases experimental Tafel plots present the two components (Fig. 4) before and after coating. 

The break in the plot log I vs coincides with the observed inflection in rH2 and r0, and corresponds to the onset of Pt oxide formation.6 As shown in Fig. 10.3 the, predominantly catalytic, rates rH2 and r0 depend exponentially on catalyst potential Uriie, as in studies with solid electrolytes with slopes comparable with the Tafel slopes seen here. This explains why the observed magnitude of the faradaic efficiency A (-2-20) is in good agreement with 2F rc° /I0 (rc° is the open-circuit catalytic rate and I0 is the exchange current) which is known to predict the expected magnitude of A in solid-electrolyte studies. 

Because of the logarithmic relation, polarization depends more strongly on parameter a than on parameter b. The parameter a, which is the value of polarization at the unit current density (1 mA/cm ), assumes values which for different electrodes and reactions range from 0.03 to 2-3 V. Parameter b, which is called the Tafel slope, changes within much narrower limits in many cases, at room temperature b 0.05 V and 0.115 V (or roughly 0.12 V). 

Tafel extrapolation technique, the Tafel slope generally used is an assumed, more or less average value. Again, as with the Tafel technique, the method is not sensitive to local corrosion. 

The relevance of Pt-OH formation to the change in the Tafel slope has been demonstrated by varying the content of water in the electrolyte [Murthi et al., 2004]. The experiments were performed in H20/trifluoromethanesulfonic acid (TFMSA) mixtures with several water/acid molar ratios. Whereas at high water contents the usual change in the Tafel slope from —112 to —59 mV/dec observed in aqueous solutions of H2SO4 and HCIO4 took place, at low water contents no change in the Tafel slope was observed. This corroborates the involvement of water in the formation... 

Finally, we briefly discuss the mechanism of enhanced specific ORR activities (ki p) at the Pt skin layer on the alloys. The Tafel slope in the high current density region at the Pt skin layer was found to be 120mV/decade [Toda et al., 1999 Wakabayashi et al., 2005b], indicating that the enhancement of ORR activities at... 

Gnanamuthu DS, Petrcelli JV. 1967. A generalized expression for the Tafel slopes and the kinetics of oxygen reduction on nohle metal and alloys. J Electrochem Soc 114 1036-1041. 

Admixtures of Ir to Ru or Ru02 resulted in an increased Tafel slope for the 02 evolution reaction. The Tafel slope for the pure Ir compound was achieved for an Ir concentration below 50%. This observation can be taken as an indication that the... 

The position of the 4-derived t2g band in the mixed oxides shifts from 0.8 eV for Ru02 to 1.5 eV for Ir02 proportional to the composition of the oxide. As a consequence of common 4-band formation the delocalized electrons are shared between Ir and Ru sites. In chemical terms, Ir sites are oxidized and Ru sites are reduced and electrochemical oxidation potentials are shifted. Oxidation of Ru sites to the VIII valence state is now prohibited. Thus corrosion as well as 02 evolution on Ru sites is reduced which explains the Tafel slope and overpotential behaviour. Most probably Ru sites function as Ir activators [83]. 

The method permits the simultaneous determination of reaction order, m, and reaction rate constant, k, from the slope and the intercept of the straight line. The procedure can be repeated for various potential values below the limiting current plateau to yield k as a function of electrode potential. The exchange current density and the Tafel slope of the electrode reaction can be then evaluated from the k vs. potential curves. 

As described above, the mechanism for C02 reduction in aqueous solutions proposed by Eyring and co-workers45 has been widely accepted. However, there remains a rather large difference between theoretical and observed values for the Tafel slope,45 and... 

The first step [Eq. (5)] was postulated to be rate determining because of the Tafel slope of 107 mV/ decade and the first-order dependence of the reduction current on the C02 concentration. The second-order rate constant of Eq. (6) was estimated to be 7.5 x 103 M-1 s-1. 

The overpotential A( A< 0/s) could not be experimentally determined. However, taking only the first term in Eq. (24) (which is a reasonable assumption at any real anodic dissolution current density), one could derive the ratio of the Tafel slopes of the two currents as... 

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