Tafel line, curvature

A lively subsection in applications of quantum theory to transitions at electrodes concerns the tunneling of electrons through oxide films. This work has been led by Schmickler (1980, 1996), who has used a quantum mechanical approach known as resonance tunneling to explain the unexpected curvature of Tafel lines for electron transfer through oxide-covered electrodes (Fig. 9.21). 

The search for such curved Tafel plots has yielded some well-documented examples where essentially straight Tafel lines are observed, even when slight curvature is predicted from eqn. (37). In particular, this is the case for proton reduction [73] and the outer-sphere reduction of some Cr(III) aquo complexes [34] at mercury electrodes over wide overpotential ranges (> 600 mV). However, the former reaction is not an outer-sphere process with symmetrical reactant and product parabolae to which eqn. (37) should apply, but rather involves the formation of an adsorbed hydrogen atom intermediate. The influence of such a mechanistic feature upon the rate-potential behavior is unclear even now [74]. The Cr(III)/Cr(II) aquo couple at mercury has also been examined over wide ranges of anodic as well as cathodic over-potentials [75]. In contrast to the cathodic behavior, marked... 

For the electronic terms in the electrolyte, Schmickler did not use the usual harmonic approximation, since this always produces a curvature of Tafel plots at high overpotentials even for redox reactions at bare metal electrodes. There is little experimental evidence for such an effect. In this study, there is a particular interest in possible curvature of the theoretically deduced Tafel lines caused by the resonance nature of the electron transfer. The electronic term in the electrolyte, using the linear approximation, is expressed as... 

The method of extrapolation of a linear section of the Tafel line, which is realized over the high overpotential region, to zero overpotential is much simpler, but it introduces a degree of uncertainty as the method relies upon the assumption of a constant Tafel slope, independent of the overpotential. Experiments, however, often indicate some concave curvature in a linear ... 

Some examples of the distortion of the polarization curves by the double-layer effect are shown in Fig. 3. Two generalizations can be made. First, the overall appearance of the polarization curves remains normal even when the double-layer effect causes a change of several orders of magnitude in the current density. More noticeable distortion, such as strong curvature or a maximum, appears only in extreme cases, and even then it may be mistaken for other effects, such as insufficient solution resistance compensation, diffusional limitations, or passivation. Therefore, significant errors can exist in the corrosion measurements without any obvious indication in the experimental polarization curves. Second, the double-layer effect changes the slope of the Tafel lines more drastically than the corrosion current density determined from the intersection of the Tafel lines. 

In Figure 25 are shown corrected Tafel curves for reduction of S208 on a number of metals. As can be seen, after the if/i correction has been introduced, the curve with the minimum becomes the straight line. This is another proof that the theory adequately describes the experimental situation. In the case of a mercury cathode, though, slight curvature remains in the bottom portion, which may be attributed to the effect of weak specific adsorption of the anion. 

Fig. 3.8 — (a) Normalised Tafel plots, (logio(///o)), for different values of the standard rate constant k. The dashed line shows the limiting linear Tafel behaviour, whereas the solid curves predicted by Equation (3.33a) and (3.33b) exhibit curvature, (b) Potential dependence of a predicted by Equation (3.34) for different values of the standard rate constant k. ... 

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