Tafel lines

For large overpotential Tafel lines can be observed. For large anodic overpotential (E Eq) one obtains from Eq. (6.8). 

Similar Tafel lines can be derived for large cathodic overpotential E Eq)  

One can determine the charge transfer coefficient from the slope of the Tafel lines and the exchange current density from an extrapolation to the Nemst potential E = Eq. 

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The time dependence of the changes in the measured values is important in determining J(U) curves. In the region of the Tafel lines, stationary states are reached... 

Fig, 1.24 Tafel lines for a single exchange process. The following should be noted (a) linear f-log I curves are obtained only at overpotentials greater than 0-052 V (at less than 0-052 V E vs. i is linear) b) the extrapolated anodic and cathodic -log / curves intersect at tg the equilibrium exchange current density and (c) /, and the anodic and cathodic current densities... 

Average from cathodic and anodic Tafel lines. 

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). 

If one of the concentrations Cj is varied, the Tafel lines are shifted, and the electrochemical reaction orders xai and x b can be determined from ... 

Fig. 5. Comparison of anodic Tafel lines during oxygen evolution in 1 N H2S04 on (1) Pt, (2) Pb02 and (3) Sb (4 mol%) doped Sn02 [82, 84]...

Tafel constant) obtained from the slope b of Tafel line (Eqns. 7—19 and 7-32) and is defined in Eqn. 7-36 ... 

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... 

Figure 8.4. Current-potential curves for the reduction of Cu ions and the oxidation of reducing agent Red, formaldehyde, combined into one graph (an Evans diagram). Solution for the Tafel line for the reduction of Cu ions O.IM CUSO4, 0.175M EDTA, pH 12.50, Egq (Cu/Cu ) = -0.47 V versus SCE for the oxidation of formaldehyde 0.05 M HCHO and 0.075 M EDTA, pH 12.50, (HCHO) = -1.0 V versus SCE temperature 25 0.5°C. (From Ref. 10, with permission from the American Electroplaters and Surface Finishers Society.)...

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 7.4 Sketch of Tafel lines for two different materials.

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... 

Tafel equation, 1054,1066,1106,1115,1133, 1249,1404,1440, 1456,1507,1528 applications, 1508 and distribution of electronic states, importance, 1466 importance, 1508 in quantum calculations, 1495 in semiconductors, 1085 tunneling, 1495 Tafel, Julius, 1106 Tafel lines, oxygen reduction, 1207 Tamm states, 1082 Tarasevich, 1495 Taylor, electrodeposition, 1303 Temkin isotherm, 927, 938, 1195... 

When T) values are obtained at various currents, it is possible to obtain t) vs. log i plots. Sucht) vs. log i plots are known as Tafel lines, in recognition of Julius Tafel,33 who first (1903) published measurements that showed the behavior of Eq. (7.83). An... 

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 ... 

Thus, the value of the limiting currents determines the range of current densities over which a Tafel line can be measured, independent of the interference of diffusion (see Fig. 8.3). One needs to take steps to make iL as large as possible. 

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. 

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