Tafel curve

The slope of the Tafel curve drj/d log / is only one of the criteria that are required to determine the mechanism of the h.e.r., since different mechanisms, involving different r.d.s. often have the same Tafel slope. Parameters that are diagnostic of mechanism are the transfer coefficient, the reaction order, the stoichiometric number, the hydrogen coverage, the exchange current density, the heat adsorption, etc. 

Figure 4.14 is the Tafel curves of jamesonite under the conditions of different concentration of DDTC in natural pH solution. Obviously, the corrosive potential moves negatively and its corrosive current decreases with the DDTC concentration increasing. DDTC can obviously inhibit the anodic corrosion of jamesonite due to its chemisorption. 

Figure 4.14 Tafel curves of jamesonite electrode in 0.1 mol/L KNO3 solution under the conditions of different DDTC concentration (unit of/ A/cm )...

In 0.1 mol/L KNO3 solution, pH is adjusted to 10.0 by NaOH, Ca(OH)2 and Na2C03. The Tafel curves of marmatite electrode in the above solutions are determined as shown in Fig. 5.9. It follows from Fig. 5.9 that the electrochemical parameters of corrosive potential and current are almost not affected by the pH... 

The Tafel curves of jamesonite electrode in the above solutions are determined and shown in Fig. 5.12. It may be seen from Fig. 5.12 that ... 

The Tafel curves of the galena electrode in xanthate solution under the conditions of the mechanical power and non-mechanical powers are given in Fig. 8.20. It follows from Fig. 8.20 that Ig/o of the anode action on the surface of galena raises from -6.5 to -5.9 with the increase of Tafel slope from -40 mV to -28 mV under the mechanical action. It shows that the reaction is favored in dynamics due to the grinding. 

Tafel curve is overpotential of the electrode and the current density passing through the electrode r] = a + b log i, is an efficient measure to be applied in electrochemistry. The Tafel slope can be used to address the catalytic activity of the catalytic material and also provide information about the mechanism of the reaction. Here we also give an example to address this (Fig. 14.19). 

Tafel curves of Pt, Ti/Ru02, and Ti/Sn02-Sb were tested using polarization in 0.1 mol L 1H2S04 solution, as shown in Fig. 14.19. The logarithm of current density is in line with the potentials of the electrodes, which is corresponding to Tafel equation (14.1)... 

Fig. 14.24 Tafel curves of Dy, Nd, Eu, and Gd doped Ti/Tafel curves of Dy, Nd, Eu, and Gd doped Ti/Sn02-Sb electrodes in 0.5M H2S04 solution...

Ding, H.Y., Feng, Y.J. and Liu, J.F. (2007) Comparison of electrocatalytic performance of different anodes with cyclic voltammetry and Tafel curves. Chin. J. Catal. 28(7), 646-650 (in Chinese). 

At the transition between the two current density ranges, the polarization curve for Cu deposition starts diverging from the calculated Tafel curve. This divergence was attributed to the transition from charge transfer to concentration overvoltage control of the copper reduction. It was concluded from these results that the reduction at the cathode surface of metal ions adsorbed on the particles plays a fundamental role in the codeposition mechanism. 

The anodic and cathodic currents are given in a semilogarithmic plot vs. overvoltage in Fig. 7.14. It should be emphasized that the Tafel curves have a slope of 60 mV/decade which corresponds to a transition factor of a = 1, whereas with metal electrodes an a value of about 0.5 is usually found (see Section 7.1). Semiconductor and metal electrodes behave differently because any overvoltage occurs across the space charge region of the semiconductor, whereas it leads to change of the Helmholtz potential in the case of metal electrodes. 

With reference to Fig. 4.13, Eq 4.51 is the sum of the values of the currents of the oxidation Tafel curves minus the sum of the values of the currents of the reduction Tafel curves (i.e., Iex = XIox - XIrcd) at any value of E. Since Iex changes from a negative to a positive quantity on increasing E from E < Ecorr to E > Ecorr (a discussion follows Eq 4.48), the equation is plotted as log I ed versus E for E < Ecorr (the lower solid curve in Fig. 4.13, net reduction) and as log Iexox versus E for E > Ecorr (the upper solid curve, net oxidation). Both curves approach very low values of current as E —> Ecorr. The log Iex ox curve becomes asymptotic to the log XIox curve for E Ecorr, and the log Iex red curve becomes asymptotic to the log XIred curve for E Ecorr. 

All of the curves in Fig. 5.6 start in the active dissolution potential range and hence do not show the complete polarization curve for the iron extending to the equilibrium half-cell potential as was done in Fig. 5. 4. This extension was shown as dashed lines and the equilibrium potential was taken as -620 mV for Fe2+ = 10 6. Qualitatively, the basis for estimating how the active regions of the curves in Fig. 5.6 would be extrapolated to the equilibrium potential can be seen by reference to Fig. 4.16. There, the corrosion potential is represented as the intersection of the anodic Tafel curve and the cathodic polarization curve for hydrogen-ion reduction at several pH values. It is pointed out that careful measurements have shown that the anodic Tafel line shifts with pH (Ref 6), this shift being attributed to an effect of the hydrogen ion on the intermediate steps of the iron dissolution. 

When E > Ecorr, the first exponential term is greater than the second exponential term and Iex is positive. Plotted as E versus log Iex, Eq 6.5 plots as the upper solid curve in Fig. 6.2. For E < Ecorr, Iex is negative, and a plot of E versus log Iex plots as the lower solid curve in Fig. 6.2. These equations will be used in establishing relationships for the analysis of corrosion rates by the experimental techniques of Tafel-curve modeling and polarization resistance. 

Tafel Curve Modeling (Ref 4, 5). Equation 6.5 provides the form of the experimental polarization curve when the anodic and cathodic reactions follow Tafel behavior. The equation accounts for the curvature near Ecorr and Icorr, which is observed experimentally. Physically, the curvature is a consequence of both the anodic and cathodic reactions having measurable effects on Iex at potentials near Ecorr. Tafel-curve modeling uses experimental data taken within approximately 25 mV of Ecorr where the corrosion process is less disturbed by induced corro-... 

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. 

In contrast to the EIS method, the Tafel-extrapolation, Tafel-curve-modeling and polarization-resistance methods are conducted under essentially dc conditions. In these cases, in generating the appropriate Eexp versus log iex or iex curve, the potentiodynamic potential scan rate is very slow, or the time between potentiostatic potential steps is very long. The common practice is a potential scan rate of 600 mV/h or an equivalent step rate of 50 mV every 5 min. Underthese conditions, it is assumed that a steady-state, extemal-current-density results at every discrete potential. Consequently, every element in the electrical circuit is purely resistive in nature, and therefore, the applied potential and resultant extemal-current-density are exactly in phase. Since the impedance (normalized with respect to specimen area) is dEexp/diex, under these conditions, the impedance, Z, at Ecorr is given by (see Eq 6.29) ... 

If the potential-current (E-i) characteristics of the individual reactions were measured, the reactions could be readily modeled as electrochemical reactions with the battery at open circuit as indicated by the processes in Figure 10. If dynamic electrode potential-current relationships were determined, the electrode is expected to show the classic Tafel slope behaviors as the exchange current of the anodic-cathodic equilibrium is shifted into either direction. From the Tafel curves a value for the Eq and Iq of the electrode could be defined. 

The sharp point in the Tafel curve corresponds to the corrosion potential and the point where the extrapolated straight lines intersect correspond to the log of the corrosion current. In Figure 9-3 the Tafel plot of the Ag electrode exhibited a sharp point at approximately 0.1 V, at a current density of approximately 10 - A/cm. ... 

Fig. 13 Upper part Tafel curves for ETR on passive iron [24]. The /-values of different authors were normalized taking the ratio ijc. Lower part transfer coefficients taken from the Tafel plot in dependence on the band bending U — Ufb-...

The hydrogen over-voltage on lead at a given current density depends on the time of polarization and the nature of the anions in the solution [28]. Figure 2.14 shows the 77 vs Ig I c relationship at two different polarization rates. It can be seen that the Tafel curve displays hysteresis phenomena which depend on the speed with which the polarization is changed [28]. The observed hysteresis has been attributed (a) to adsorption of anions on the Pb surface which alter both the distribution of the surface charges and the surface H concentration [28,29] or (b) to dissolution of a certain amount of hydrogen in the Pb [30,31]. 

Once the corrosion (mixed) potential is known, the estimation of the cathodic protection current is relatively simple the cathodic Tafel line is extended until the ordinate reaches the anode equifibrium value. The current corresponding to that ordinate value is the minimum value of the external current that must be suppfied to stop the corrosion process. For processes in which there are multiple species undergoing cathodic or anodic reactions, the resultant cathodic and anodic Tafel curves are calculated by adding the individual polarization curves within the respective potential range. 

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