Tafel

I begin my chapter by reminding the reader about the beginning of electrode kinetics. This was in a paper presenting an empirical law (the first law of electrode kinetics) that is the basis for our discussion. Of course, there is much else to say apart from this equation, but it plays the same part in electrochemistry as the famous Arrhenius equation, r = At E,RT, plays in physical chemistry. Julius Tafel made a very direct contribution to the subject of kinetics at electrodes. In fact, he founded it as a science with equations. Insofar as electrocatalysis concerns the acceleration of electrode reactions by means of the change of substrate, Tafel s equation is relevant, indeed [ 1], and, written in the original form, was 

At sufficiently high j values, the availability of material for the reaction at the desired rate becomes deficient to meet the demands of the electrode at this relatively high value of Try One comes 

FIGURE 1.1 (a) The typical Tafel line for a single electron-transfer process. The exponential relationship 

R and T are symbols, the meanings of which are well known in physical chemistry 

It turns out that a is also dependent on the mechanism of the reaction. Electrode materials on which a given electrode reaction takes place at a relatively high j, for a minimum T, are good electrocatalysts. 

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The first law of electrode kinetics, observed by Tafel in 1905 [197], is that overvoltage i) varies with current density i according to the equation... 

The measurement of a from the experimental slope of the Tafel equation may help to decide between rate-determining steps in an electrode process. Thus in the reduction water to evolve H2 gas, if the slow step is the reaction of with the metal M to form surface hydrogen atoms, M—H, a is expected to be about If, on the other hand, the slow step is the surface combination of two hydrogen atoms to form H2, a second-order process, then a should be 2 (see Ref. 150). 

Figure Bl.28.1. Schematic Tafel plot for the experimental detennination of and a.

Hi) Surface blockers. Type 1 tlie inliibiting molecules set up a geometrical barrier on tlie surface (mostly by adsorjDtion) such as a variety of ionic organic molecules. The effectiveness is directly related to tlie surface coverage. The effect is a lowering of tlie anodic part of tlie polarization curve witliout changing tlie Tafel slope. 

Type 2 tlie inliibiting species takes part in tlie redox reaction, i.e. it is able to react at eitlier catliodic or anodic surface sites to electroplate, precipitate or electropolymerize. Depending on its activation potential, tlie inliibitor affects tlie polarization curve by lowering tlie anodic or catliodic Tafel slope. 

Tafel equation Tafel kinetics Tafel slope Taffy process Taft s SV function Tagamet [51481-61-9] d-Tagatose... 

Overvoltage. Overvoltage (ti. ) arises from kinetic limitations or from the inherent rate (be it slow or fast) of the electrode reaction on a given substrate. The magnitude of this value can be generally expressed in the form of the Tafel equation... 

Fig. 5. Currrent—potential behavior of an electrode reaction based on equation 37. Tafel behavior is noted at high currents for two different values of d.

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). 

The sohd line in Figure 3 represents the potential vs the measured (or the appHed) current density. Measured or appHed current is the current actually measured in an external circuit ie, the amount of external current that must be appHed to the electrode in order to move the potential to each desired point. The corrosion potential and corrosion current density can also be deterrnined from the potential vs measured current behavior, which is referred to as polarization curve rather than an Evans diagram, by extrapolation of either or both the anodic or cathodic portion of the curve. This latter procedure does not require specific knowledge of the equiHbrium potentials, exchange current densities, and Tafel slope values of the specific reactions involved. Thus Evans diagrams, constmcted from information contained in the Hterature, and polarization curves, generated by experimentation, can be used to predict and analyze uniform and other forms of corrosion. Further treatment of these subjects can be found elsewhere (1—3,6,18). 

Fig. 2. Tafel plot, where and are both chosen to be 0.5 the temperature is 298.15 K. A iadicates the linear region (eq. 23) and B the Tafel (eq. 24).

This limit is called linear kinetics. On the other hand, if the surface overpotential is large, one of the exponential terms is negligible. This limit is called Tafel kinetics. The relationship was found empirically. In the anodic Tafel region... 

Tafel, J., 3, 246 (1893CB1501) 5, 541 (01CB258, OICBI165, OlCBl 170, 07CB3752, 1899CB68)... 

Tafel Extrapolation Corrosion is an elec trochemical reac tion of a metal and its environment. When corrosion occurs, the current that flows between individual small anodes and cathodes on the metal surface causes the electrode potential for the system to change. While this current cannot be measured, it can be evaluated indirectly on a metal specimen with an inert electrode and an external electrical circuit. Pmarization is described as the extent of the change in potential of an electrode from its equilibrium potential caused by a net current flow to or from the electrode, galvanic or impressed (Fig. 28-7). 

While the specific corrosion rate number determined by Tafel extrapolation is seldom accurate, the method remains a good confirmation tool. 

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. 

Corrosion Rate by CBD Somewhat similarly to the Tafel extrapolation method, the corrosion rate is found by intersecting the extrapolation of the linear poi tion of the second cathodic curve with the equihbrium stable corrosion potential. The intersection corrosion current is converted to a corrosion rate (mils penetration per year [mpy], 0.001 in/y) by use of a conversion factor (based upon Faraday s law, the electrochemical equivalent of the metal, its valence and gram atomic weight). For 13 alloys, this conversion factor ranges from 0.42 for nickel to 0.67 for Hastelloy B or C. For a qmck determination, 0.5 is used for most Fe, Cr, Ni, Mo, and Co alloy studies. Generally, the accuracy of the corrosion rate calculation is dependent upon the degree of linearity of the second cathodic curve when it is less than... 

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... 

In oxygen-free seawater, the J(U) curves, together with the Tafel straight lines for hydrogen evolution, correspond to Eq. (2-19) (see Fig. 2-2lb). A limiting current density occurs with COj flushing for which the reaction ... 

The Tafel potential is given by a bend in the U ff (log I) curve. According to criterion No. 4 in Table 3-3, under the conditions given in Section 3.3.3.1, it corresponds to the protection potential. 

The average protection current requirement can be conveniently determined for individual wells in an oilfield by measuring the Tafel potential. In contrast to profile measurements, internal measurements on the casing are not necessary. These measurements cannot be used to predict polarization behavior at greater depths. 

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