Tafel lines electrodes

The polarization relations found in the region of high polarization are usually plotted semilogarithmically as AE vs. log i (Eig. 6.1). These plots are straight lines, called Tafel lines (curve 1 in Eig. 6.1), when relation (6.3) holds. More complicated polarization functions are found at many real electrodes in the region of high polarization. Sometimes several Tafel sections can be distinguished in an actual polarization curve (curve 2 of Eig. 6.1) each of these sections has its own characteristic values of parameters a and b). 

Potential Sweep Method, In the transient techniques described above, a set of measurements of the potential for a given current or the current for a given potential is measured in order to construct the current-potential function, i = f(E). For example, the Tafel lines shown in Figure 6.20 were constructed from a set of galvanostatic transients of the type shown in Figure 6.18. In the potential sweep technique, i = f(E), curves are recorded directly in a single experiment. This is achieved by sweeping the potential with time. In linear sweep voltammetry, the potential of the test electrode is varied linearly with time (Fig. 6.23a). If the sweep rate is... 

The current 7 is an extensive quantity, in that it depends on the size of the electrode. For this reason, the reaction rate is conveniently referred to the unit surface area (7/S=j, current density). Even so, the current density continues to be an extensive quantity if referred to the geometric (projected) surface area since electrodes are as a rule rough and the real surface does not coincide with the geometric surface [23]. Conversely, b is an intensive quantity, in that it depends only on the reaction mechanism and not on the size of the electtode. The term b is the most important kinetic parameter in electrochemistry also because of the easy and straightforward procedure for its experimental determination. Most electrode mechanisms can be resolved on the basis of Tafel lines only. 

Figure 15.5 shows the net current density i as a curve defined by the sum of if and ir, which goes to zero when if = ir = io- This curve merges asymptotically with the two Tafel lines when substantial currents axe drawn in either direction, so that the intersection point of these lines, which defines E° and io, is obtainable experimentally by extrapolation of the linear (i.e., Tafel) portions of EMF versus log i plots. We can now define the overpotential 77 quantitatively. It is the excess electrical potential of the electrode relative to the reversible value E°, for a particular value of the... 

Fig. 7.37. A typical Tafel line for a one electron-transfer electrode reaction, showing the exponential relationship at high overpotentials, which makes the relation between ii and log r linear.

The study of the reduction of 02 on well-defined crystal planes (Adzic, 1984) confirms that the character of an electrode depends sharply on the crystal plane exposed to the solution. Measurements made on polycrystals reflect a mixture of properties characteristic of each plane. The results are much clearer if one sticks to observations from one plane. For example, a study of 02 reduction on the three planes of Au gives quite different Tafel lines (Fig. 7.80). 

The steady-state Tafel lines for methanol oxidation in acid solution are 55-60 mV/decade over the potential range 0.4-0.5 (SHE). When the potential of the working electrode on this scale is made more positive, the Tafel slope changes and becomes 110 mV/decade. These two numerically stated Tafel slopes can readily be reexpressed in electrode kinetic terms to correspond, respectively, to ... 

Fig. 8.3. ATafel line. No special effort is made to reduce the limiting current density in case 1 and the Tafel line has a relatively small range, e.g., only 102 times in current density. In case 2, a rotating disk electrode is used to cause an increased limiting current density, and hence a larger range (say, 104 times) of current density.

An objection to consideration of vibrational states above the ground state (Levich, 1970) was that if such states were indeed involved in electron transfer, then there would be no smooth Tafel lines because as a change in overpotential altered the energy of the Fermi level (from which, e.g., cathodic electrons come), matching levels in the solution species would not be available until the next vibrational state, perhaps 1/2 eV away, was reached by the change in the electrode potential. Hence, in this picture, the... 

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). 

W. Schmickler, J. Electroanal. Theory 100 533 (1979). Theory of electrodic currents through coatings (and oxide films) in terms of resonance tunneling. Tafel lines curve. 

Fig. 19. Tafel lines for hydrogen evolution in 30 wt% KOH, 80 °C, on plasma-sprayed Ni cathode coatings reduced under H2 atmosphere for 30 min at different temperatures. (1) Electrode as prepared (2) Reduced at 200, (3) 300, (4) 400, (5) 500 °C. After ref. 386, by permission of Chapman Hall.

Fig. 12.21. The cathodic and anodic Tafel lines at two different electrode reactions. At l/corr there is a steady state. No net current passes, but there is a steady production of A (e.g., H2) and B+ (the metal, corroding) in a net electrochemical reaction that appears to be chemical (no net current flows to an outside circuit). Note the difference in these diagrams from the Evans-Hoar diagrams, which show corrosion is spontaneous and drives itself. The difference is similar to that between an electrochemical reaction and a fuel cell. (Reprinted from J. O M. Bockris and S. N. M. Kahn, Surface Electro Chemistry, Fig. 8.1, p. 747 Plenum, 1993).

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... 

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. 

The above analysis of a mixed electrode in terms of the current components is usually simplified under several common, and often very accurate, assumptions. With reference to Fig. 4.13, if the intersection of the I0X and the Ired lines occurs at a potential, Ecorr, that deviates by more than approximately 50 mV from both equilibrium potentials, E x and E m, the contributions of I0 x and Ired M become insignificant, and the analysis of the corrosion is based on the intersection of the Ired x and Iox M lines. These individual Tafel lines are plotted (dashed lines) in Fig. 4.15. Ecorr and Icorr are identified, again assuming that Rtotai is very small. 

The sign holds for anodic and cathodic overpotentials respectively. A plot of electrode potential versus the logarithm of current density is called the Tafel plot and the resulting straight line is the Tafel line" The linear part (5=2.3 RT/anF) is the Tafel slope that provides information about the mechanism of the reaction, and "a" provides information about the rate constant of the reaction. The intercept at r =0 gives the exchange current density... 

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