Tafel control

The curves in Fig. 3.21 apply to a platinum substrate in an environment of pH = 7, aNo2 = 0.01 and aNH+ = 10 5. The equilibrium potential calculated from the Nemst equation is 250 mV (SHE). The reduction branch of the curve shows a transition from Tafel control to diffusion control with a limiting diffusion current density of 103 mA/m2, followed at lower potentials by the reduction of water. An anodic branch... 

Fig. 4.26 Schematic polarization curves used in the analysis of cathodic protection by an impressed external current. Cathodic reaction is under Tafel control.

Schalt-jahr. n. leap year, -plan, m., -skizze, /. (Elec.) wiring diagram, -stiick, n. insert piece, insert (Elec.) contact part, contact, -tafel, /. switchboard instriiment board. Schaltung, /. disposal (Elec.) connection, hookup, wiring, also switching gear shift control. 

This is commonly known as the high field equation. It is of similar form to the Tafel equation for activation controlled electrochemical reactions with... 

The controversy that arises owing to the uncertainty of the exact values of and b and their variation with environmental conditions, partial control of the anodic reaction by transport, etc. may be avoided by substituting an empirical constant for (b + b /b b ) in equation 19.1, which is evaluated by the conventional mass-loss method. This approach has been used by Makrides who monitors the polarisation resistance continuously, and then uses a single mass-loss determination at the end of the test to obtain the constant. Once the constant has been determined it can be used throughout the tests, providing that there is no significant change in the nature of the solution that would lead to markedly different values of the Tafel constants. 

Figure 4. Log intensity vs. potential plots (Tafel plots) obtained from the voltammograms of a platinum electrode submitted to a 2 mV s l potential sweep polarized in a 0.1 M LiC104 acetonitrile solution having different thiophene concentrations. (Reprinted from T. F. Otero and J. Rodriguez, Parallel kinetic studies of the electrogeneration of conducting polymers mixed materials, composition, and kinetic control. Electrochim, Acta 39, 245, 1994, Figs. 2, 7. Copyright 1997. Reprinted with permission from Elsevier Science.)...

It has been seen from the above simple examples that the concentration of the substrate has a profound effect on the rate of the electrode process. It must be remembered, however, that the process may show different reaction orders in the different potential regions of the i-E curve. Thus, electron transfer is commonly the slow step in the Tafel region and diffusion control in the plateau region and these processes may have different reaction orders. Even at one potential the reaction order may vary with the substrate concentration as, for example, in the case discussed above where the electrode reaction requires adsorption of the starting material. 

A qualitative measure of the corrosion rate can be obtained from the slope of the curves in Fig. 2. Z INT is given in units of s ohm" . Owing to the presence of the uncompensated ohmic resistance and lack of values for Tafel slopes [Eq. (2)], data in Fig. 2 should be viewed as indicative of significant changes in corrosion rates. Corrosion loss remained low during the first 2 months, followed by a large increase for both flushed samples and controls. The corrosion rate increased when the surface pH reached values of 1 or less. Total corrosion loss as determined from integrated Rp data was less for the control than for the flushed sample. 

This is the Tafel equation (5.2.32) or (5.2.36) for the rate of an irreversible electrode reaction in the absence of transport processes. Clearly, transport to and from the electrode has no effect on the rate of the overall process and on the current density. Under these conditions, the current density is termed the kinetic current density as it is controlled by the kinetics of the electrode process alone. 

The anodic evolution of oxygen takes place at platinum and other noble metal electrodes at high overpotentials. The polarization curve obeys the Tafel equation in the potential range from 1.2 to 2.0 V with a b value between 0.10 and 0.13. Under these conditions, the rate-controlling process is probably the oxidation of hydroxide ions or water molecules on the surface of the electrode covered with surface oxide ... 

Spiro [27] has derived quantitative expressions for the catalytic effect of electron conducting catalysts on oxidation-reduction reactions in solution in which the catalyst assumes the Emp imposed on it by the interacting redox couples. When both partial reaction polarization curves in the region of Emp exhibit Tafel type kinetics, he determined that the catalytic rate of reaction will be proportional to the concentrations of the two reactants raised to fractional powers in many simple cases, the power is one. On the other hand, if the polarization curve of one of the reactants shows diffusion-controlled kinetics, the catalytic rate of reaction will be proportional to the concentration of that reactant alone. Electroless metal deposition systems, at least those that appear to obey the MPT model, may be considered to be a special case of the general class of heterogeneously catalyzed reactions treated by Spiro. 

When the cathodic reaction is the reduction of oi n molecules for which the equilibrium potential is relatively high (much more anodic than the corrosion potential), the corrosion current is frequently controlled by the diffusion of hydrated o Q en molecules towards the corroding metal electrode thus, the corrosion ciurent equals the diffusion current of o en molecules as shown in Fig. 11-8. For this mode of diffusion-controlled corrosion of metals the cathodic Tafel constant is... 

Activation Polarization Activation polarization is present when the rate of an electrochemical reaction at an electrode surface is controlled by sluggish electrode kinetics. In other words, activation polarization is directly related to the rates of electrochemical reactions. There is a close similarity between electrochemical and chemical reactions in that both involve an activation barrier that must be overcome by the reacting species. In the case of an electrochemical reaction with riact> 50-100 mV, rjact is described by the general form of the Tafel equation (see Section 2.2.4) ... 

The central Tafel portions of Figure 7.12 haven t been discussed in much detail yet. We sometimes call these linear Tafel regions the potentials under kinetic control , since the magnitude ofl g, is a function of the rate constant of electron transfer (itself a Junction of the overpotential r)). 

Figure 7.13 Tafel plot constructed with the data from worked example 7.4. These data refer to a solution containing [Fe"(CN)6] ] = [Fe" (CN)6]2 ] = 20 mmol dm and [KCl] = 0.1 mol dm" . Only those data (both anodic and cathodic) corresponding to kinetic control are included. The logarithmic current where the two lines intercept is log I /(). ...

With both approaches, it is key to establish the current regions where samples are under kinetic control to allow the correct comparison. Many reported comparisons of catalysfs in MEA sfrucfures point to differences in performance, which are attributed to intrinsic catalyst differences when it is clear that differences are due to mass fransport effects because of catalyst layer structure. To help overcome these difficulties, it is recommended that, for catalyst evaluation, pure reactants be used (e.g., O2 instead of air) and at relatively high stoichiometries. Use of current-voltage curves should be corrected for elecfrolyte or membrane resistances and Tafel analysis used to identify fhe kinefically confrolled current regions. 

At 60 minutes only, dc potentiodynamic curves were determined from which the corrosion current was obtained by extrapolation of the anodic Tafel slope to the corrosion potential. The anodic Tafel slope b was generally between 70 to 80 mV whereas the cathodic curve continuously increased to a limiting diffusion current. The curves supported impedance data in indicating the presence of charge transfer and mass transfer control processes. The measurements at 60 minutes indicated a linear relationship between and 0 of slope 21mV. This confirmed that charge transfer impedance could be used to provide a measure of the corrosion rate at intermediate exposure times and these values are summarised in Table 1. 

The interpretation of the anodic branch of LSV for p-Si is apparently more simple because the current increases following an exponential variation with a Tafel slope of 60-80 mV/decade. In this case, an accumulation layer is generated, and then the current is only controlled by the kinetics of the electrochemical reaction, which involves several successive steps. It is not necessary to account for the various reaction paths proposed by many authors. 

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