Tafel constants experimentally determined

Although the primary objective of Tafel analysis based on experimental measurements is the determination of the corrosion current density, icorr, the measurements also can give values for the cathodic and anodic Tafel constants, Pred x and Pox M, and estimates of the exchange current densities, i0 x and i0 M. The values of these parameters can provide information on the kinetic mechanisms of the electrochemical reactions,... 

This equation is used directly to determine icorr, providing that the experimentally measured potential, Eexp, is the actual potential at the WE/electrolyte interface, E (i.e., no IR correction is needed). Under these conditions, the analysis procedure involves evaluating the slope of the E versus iex curve at Ecorr, as shown in Fig. 6.12, to determine Rp. From Rp, and known or experimentally determined Tafel constants (P values), icorr is calculated. If an IR correction is necessary, then, because E = Eexp - iexRs (Eq 6.20) ... 

As previously stated, once Rp is determined, calculation of icorr requires knowledge of the Tafel constants. These constants can be determined from experimental anodic and cathodic polarization curves, or by Tafel-curve modeling, forthe material and solution of interest as discussed earlier. In the absence of these values, an approximation is sometimes used. 

Once Rp is determined by the EIS method, icorr is evaluated in the same way as with the polarization-resistance method (i.e., with Eq 6.28). Therefore, the Tafel constants still must be experimentally determined. The intrinsic value of the EIS method lies in the fact that extensive information is extracted (i.e., Rp, Rs, and C are all determined) and, ideally, interpreted to not only determine the corrosion rate but also the rate-controlling mechanisms at the material surface and within the electrolyte. 

In order to experimentally determine the reaction order of a given species i, two methods are used. The first is based on equations (5.58) and (5.59), which define, respectively, the anodic and cathodic reaction order of the species. They show that we can obtain p i and Pc.i by measuring the shift of the anodic and cathodic Tafel lines as a function of the concentration of species i, when the concentrations of the other species are maintained constant. 

Fig. 1.4 - Experimental determination of the kinetic constants, 4 and a, using the Tafel equations. Note the deviations from linearity at low 17 where the limiting form of the Butler-Volmer equation is no longer appropriate.

Figure 6.4 Dependence of the apparent rate constants and the apparent intrinsic rate constant on the potential ( Tafel plots ), determined by fitting the experimental transients with (6.5).

The above-described theory, which has been extended for the transfer of protons from an oxonium ion to the electrode (see page 353) and some more complicated reactions was applied in only a limited number of cases to interpretation of the experimental data nonetheless, it still represents a basic contribution to the understanding of electrode reactions. More frequently, the empirical values n, k° and a (Eq. 5.2.24) are the final result of the investigation, and still more often only fcconv and cm (cf. Eq. 5.2.49) or the corresponding constant of the Tafel equation (5.2.32) and the reaction order of the electrode reaction with respect to the electroactive substance (Eq. 5.2.4) are determined. 

It is thus seen that interpretation of Tafel slopes requires information on adsorption behavior as /(F), complementary to that as /(C,). The derivative dln6/d nC, required for interpretation of reaction order, R = dlni/dlnC, must also be taken at a controlled potential that is, d n6/d nC,)y/, the isotherm derivative in the reaction-order expression (Section X), must also be evaluated at constant overpotential, r , or electrode potential, V, in the case of electrocatalytic reactions, especially those involving small organic molecules or Cl. Unfortunately, in many experimental works on electrode kinetics, except those on pH effects, these important details involving the adsorption behavior of reactant and/or intermediate(s) have been neglected, with adverse consequences for mechanism determination. 

Surface concentrations of complex species and ligands can be determined by means described in Chapter 3 further, the normalized Tafel plots (NTPs) can be obtained. However, initially, we shall make use of isosurface concentration voltammetry presented in Section 5.3.1. Using experimental data obtained at constant surface concentrations, one can estimate the value of without any tentative assumptions as to the mechanism of the charge transfer step, that is, for unknown composition of the EAC. It follows from Eq. (4.3) that for t/r = const, the surface concentrations of the components do not depend on time. Selected in this way, data (Figure 8.7) are satisfactorily approximated by the lines with similar slopes, which yield = 0.37 0.03 (see Eq. (8.17)). This value canbe checked by the analysis of individual transients of the potential, but then the composition of the EAC must be established. 

The plot of U versus log / in Fig. 5 demonstrates that the data can be represented by Tafel lines between 0.03mA and 10mA. The slope of the Tafel lines is nearly the same (about 75 mV) for the four bulk concentrations. This result might be regarded as evidence that the same step is rate-determining. However, such an interpretation is in contradiction to the data in Fig. 4. The drastic change in the efficiency of CO2 production with the methanol bulk concentration at constant potential is not reflected by the Tafel slope. The results in Fig. 4 and Fig. 5 illustrate that the origin of an experimental Tafel relationship is not easily interpretable in the case of complex reactions. 

FIGURE 16.4 Determination of the Hj oxidation heterogeneous rate constant ( 5) from SECM approach curves, (a) SECM approach curves, (b) Magnification of (a). The solid lines a and b are theoretical approach curves at conducting and insulating substrates, respectively. Experimental approach curves are represented by circle symbols solid lines are theoretical curves at a Pt substrate with its potential held at, from top to bottom 0, 0.4, 0.45, 0.5, 0.55, 0.6, and 1V. (e) Heterogeneous reaction rate constant k of Hj oxidation at a Pt substrate with different potentials, k was obtained by fitting the experimental approach curves with the theoretical ones shown in (b). (d) Tafel plot of H2 oxidation. Approach speed 3 pm/s. 

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