Tafel slope estimation

Tafel-Slope Estimates (i) Polarization-Resistance Technique... 

The error due to Tafel-slope estimates is only a concern for the polarization-resistance technique. This error, which can be calculated from Eq. (35), is shown in Fig. 17 for the idealized polarization-resistance technique as a function of 1/6 and... 

Figure 17. Error in corrosion current density due to errors in Tafel-slope estimates for idealized polarization-resistance technique. ...

In contrast, the errors of the polarization-resistance technique have been very thoroughly and quantitatively evaluated, and the reported errors are the smallest among the four techniques for all error categories. On the other hand, this technique has two more error possibilities (in linearization and Tafel-slope estimate) than the other techniques. Consequently, the overall error may be comparable to those of the three-point and curve-fitting techniques, and it has to be evaluated for each experimental situation. The systematic errors can be avoided by using the appropriately corrected polarization equations in the data evaluation however, that requires numerical values for the appropriate parameters, such as mass transport, double layer, solution resistance, equi-... 

Ito et a/.18 supported the above reaction pathways for various cathode materials, such as In, Sn, Cd, and Pb, from the similarity in Tafel slopes. Hori and Suzuki46 verified the above mechanism in various aqueous solutions on Hg. Russell et al.19 also agreed with the above mechanism. Adsorbed CO J anion radical was found as an intermediate at a Pb electrode using modulated specular reflectance spectroscopy.47 This intermediate underwent rapid chemical reaction in an aqueous solution the rate constant for protonation was found to be 5.5 M-1 s-1, and the coverage of the intermediate was estimated to be very low (0.02). 

The first step [Eq. (5)] was postulated to be rate determining because of the Tafel slope of 107 mV/ decade and the first-order dependence of the reduction current on the C02 concentration. The second-order rate constant of Eq. (6) was estimated to be 7.5 x 103 M-1 s-1. 

Estimate the corrosion potential corr and the corrosion current density icorr of Zn in a deaerated HC1 solution of pH 1 at 298 K. In this solution Zn corrosion is accompanied by the hydrogen evolution reaction (h.c.r.). The parameters (standard electrode potential E°, exchange current density i0, Tafel slope b of Zn dissolution and the h.e.r. on Zn are... 

On the other hand, as was shown recently,75 the value of jo can be estimated using yfi value extracted from the polarization curve and known value of the cathodic Tafel slope bc by (71)... 

Fluorine is produced by electrolysis of molten salts on carbon anodes including KF-21TF at about 100°C, potassium bifluoride at about 250°C, and fluoride salts at about 1000°C. The decomposition potential of molten potassium bifluoride is 1.75 V at 250°C, a value close to that estimated thermodynamically [80]. The kinetics of the anodic process is characterized by a Tafel slope of 0.56 V per decade, j), = 1 x 10 A/cm [81], and by a complex reaction mechanism involving the formation of fluorine atoms on carbon. During the electrolysis, C-F surface compounds on the carbon anode are formed via side reactions. Intercalation compounds such as (CF) contribute to the anodic effect in the electrochemical cell, which can be made less harmful by addition of LiF. 

Reliable evaluation of A would also then lead to an estimate of absolute entropies of activation for those electrode processes that are characterized by temperature-independent Tafel slopes, e.g., for anodic Br2 evolution at C, O2 reduction at and N2 evolution from the NJ at... 

For reasons stated previously, it is considerably more difficult to construct illustrative polarization curves for the reduction of dissolved oxygen. Reasonable estimates of the exchange current densities, Tafel slopes, and diffusion rates have been used to construct the curves of Fig. 3.17 (Ref 3, 6). These curves, identified by letters, are described as follows ... 

The experimental plots of iR-free voltage vs. current density obtained for O2 or air and hydrogen as a fuel have been used for the estimation of the factors, which determine the cell polarization losses, namely activation potential, Tafel slope, and mass transport limitations. 

Data for Activation Controlled Reactions. Estimate the exchange current density and Tafel slopes for an electrode reaction from the data given below. 

For the data in Fig. 6, the ohmic and polarization resistances can be determined to be about 0.3 and just under 100 cm, respectively. The value of Rp is slightly higher than that determined by linear polarization (Fig. 4) in a measurement that just preceded the EIS experiment on the same electrode. The double layer capacitance is seen to be 1/3000 SI cm = 333 pF cm . The polarization resistance determined by EIS can be used to determine the corrosion rate with the Stern-Geary equation, just as was described above for polarization resistance determined by linear polarization. EIS data provide no estimation of the Tafel slopes, which are required in the Stem-Geary equation. 

EIS is the response of corrosion systems to ac excitations. It has been used in corrosion research to estimate corrosion rates or study the metal passivation, corrosion protection using inhibitors, sacrificial barrier properties, and polymer coating performance on metals. EIS only estimates polarization resistance. As with Hnear polarization, the corrosion current is calculated using the Stem-Geary equation for known values of the anodic and cathodic Tafel slopes. 

Calculate the corrosion currents for the metals in Example 5.1, using the Stearn-Geary equation for cathodic and anodic Tafel slopes of h — 0.1 V and h — 0.1 V. Estimate the corrosion rates in mpy. 

Macdonald summarized the hmitations of EIS technique when used to measure the corrosion current (corrosion rates) of metals [79]. A high level of mathematics is required to analyze data and interpret properties of the corrosion system. Analysis of impedance data results in determination of the polarization resistance. However, it requires obtaining a large number of low-frequency data for an accurate estimate. It is necessary to extract the noise from the data obtained at low frequency ranges to obtain meaningful mechanistic information. To calculate the corrosion rate using the Stem-Geary equation, the Tafel method should be used to estimate the Tafel slopes as a function of time. Due to the variation of porosity of corrosion products on metals, the corrosion products (oxides and hydroxides) contributions to the overall impedance spectra are difficult to evaluate. 

The anode and cathode corrosion currents, fcorr.A and fcorr,B. respectively, are estimated at the intersection of the cathode and anode polarization of uncoupled metals A and B. Conventional electrochemical cells as well as the polarization systems described in Chapter 5 are used to measure electrochemical kinetic parameters in galvanic couples. Galvanic corrosion rates are determined from galvanic currents at the anode. The rates are controlled by electrochemical kinetic parameters like hydrogen evolution exchange current density on the noble and active metal, exchange current density of the corroding metal, Tafel slopes, relative electroactive area, electrolyte composition, and temperature. 

An estimation of the effect of different parameters on the current density distribution can be made from Fig. 3.2, which shows the dependencies of the current densities at the closer, / > and further, if, part of the cathode from the anode on the cell voltage, (/, for different solution resistivity. As can be seen, the increase of the conductivity of the electrolyte leads to the more uniform current density distribution of deposits at the electrode surface. A similar but less pronounced effect of the increase of the cathodic Tafel slope can be seen, while the change of /q does not affect the current density distribution. It is necessary to note that a soluble anode is considered in this case and, hence, the anodic and cathodic exchange current densities are the same. 

Thus, the overvoltages, both anodic and cathodic, are linear with the logarithm of current density, as shown in Fig. 4.3.11 [45]. From this plot, the exchange current density can be estimated by extrapolation to 7 = 0, and flie slope of the rj vs log i curve provides the value of the Tafel slope, b = 2.303RT/aF, from which the transfer coefficient can also be evaluated. 

So, the Tafel slope is 93 mV per decade. At AE = 0, logj p = -4.344 then, = 0.045 mA cm. This value is within the range of the ORR jap° estimated using the Ft particle sizes shown in the last column in Table 2.3. Using 2.3RT/(an,F) = 0.404, a is estimated to be 0.7. It must be noted that since only three data points were collected in the activation region during this test, errors must... 

Other methods for calculating the activation energies of the ORR have been reported in the literature. Based on the linear Bronsted-Evans-Polanyi relationship, Norskov et al. [85] proposed a method to estimate the least activation energy by calculating the stability of the reaction intermediate. With this simple model, the study reported a Tafel slope of 60 mV at 300 K (71 mV at 357 K). The value was consistent with experimental results. 

A semiempirical model that considered only the effect of toluene on kinetics was constructed to describe cell voltage as a fimction of contamination time and current density. The parameters independent of the contamination process, i.e., open circuit voltage (E°), cell resistance (RJ, and Tafel slope (fc), were first estimated based on experimental data in the absence of toluene (giving a baseline). Then these parameters were used to empirically obtain the expressions of two other parameters, and Kcbc/ which accoimted for the effect of toluene contamination on transient and steady-state cell performance, using experimental data at various levels of toluene concentration imder four current densities. The model was validated by comparing the contamination testing results with model-predicted results. Several other definitions were also presented, based on the model, such as the threshold toluene concentration and the degradation rate. 

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