Reduction Tafel curves

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. 

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. 

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. 

Fig. 6.2 Schematic experimental polarization curves (solid curves) assuming Tafel behavior for the individual oxidation and cathodic-reactant reduction polarization curves (dashed curves)...

The above relationship is equally applicable if either the metal oxidation-rate curve or the reduction-rate curve for the cathodic reactant does not obey Tafel behavior. To illustrate this point, three additional schematic pairs of individual anodic and cathodic polarization curves are examined. In Fig. 6.3, the metal undergoes active-passive oxidation behavior and Ecorr is in the passive region. In Fig. 6.4, where the total re-... 

In Figure 25 are shown corrected Tafel curves for reduction of S208 on a number of metals. As can be seen, after the if/i correction has been introduced, the curve with the minimum becomes the straight line. This is another proof that the theory adequately describes the experimental situation. In the case of a mercury cathode, though, slight curvature remains in the bottom portion, which may be attributed to the effect of weak specific adsorption of the anion. 

The value of is 1.0, which has been widely reported in the literature [135-137]. For the value of, the literature presents two Tafel slopes for the oxygen reduction polarization curve [138-141]. The first case, where the slope is approximately 60 mV/decade at 25 °C, corresponds to a value of 2.0 for a ... 

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. 

The polarization curve (polarization current i, versus polarization potential E) of a corroding metallic electrode can be measured by polarizing the electrode in the anodic and cathodic directions. In the range of electrode potential a short distance away from the corrosion potential, the polarization curve follows the Tafel relation as shown in Fig. 11-6. Here, the polarization current, ip, in the anodic direction equals the dissolution current of the metal i and the polarization current, ip, in the cathodic direction equals the reduction current of the oxidant i. In the range of potential near the corrosion potential, however, the polarization current, ip, is the difference between the anodic dissolution current of the metal... 

Figure 11-7 shows the polarization curve of an iron electrode in an acidic solution in which the anodic reaction is the anodic transfer of iron ions for metal dissolution (Tafel slope 40 mV/decade) the cathodic reaction is the cathodic transfer of electrons for reduction of hydrogen ions (Tafel slope 120 mV /decade) across the interface of iron electrode. 

Figure 8.4. Current-potential curves for the reduction of Cu ions and the oxidation of reducing agent Red, formaldehyde, combined into one graph (an Evans diagram). Solution for the Tafel line for the reduction of Cu ions O.IM CUSO4, 0.175M EDTA, pH 12.50, Egq (Cu/Cu ) = -0.47 V versus SCE for the oxidation of formaldehyde 0.05 M HCHO and 0.075 M EDTA, pH 12.50, (HCHO) = -1.0 V versus SCE temperature 25 0.5°C. (From Ref. 10, with permission from the American Electroplaters and Surface Finishers Society.)...

Equation 1.7 for the reduction of protons at a mercury surface in dilute sulphuric add is followed with a high degree of accuracy over the range -9 Tafel plot i.s shown in Figure 1.5. At large values of the overpotential, one reaction dominates and the polarization curve shows linear behaviour. At low values of the overpotential, both the forward and back reactions are important in determining the overall current density and the polarization curve is no longer linear. 

The current/voltage characteristic curves for the reduction of 2 on chelate catalysts mostly show a Tafel region with a slope of about 60 mV. This could... 

This is the steady-state current which is theoretically predicted if stage 1 is the rate-determining step in the sub-stages sequence represented in Equations 4.8 1.12. An important parameter to compare both in theory and experimentally is the Tafel slope or the transfer coefficient which results from it. Therefore, Equation 4.30 has to be written in a form that contains only one exponential term. Since the considered I-E curve is an oxidation wave, the effect of the reduction (second term in the right-hand part of Equation 4.30) will be negligible with potentials that are situated sufficiently far away from the equilibrium potential, and for the anodic current the following applies ... 

In the presence of oxidizing species (such as dissolved oxygen), some metals and alloys spontaneously passivate and thus exhibit no active region in the polarization curve, as shown in Fig. 6. The oxidizer adds an additional cathodic reaction to the Evans diagram and causes the intersection of the total anodic and total cathodic lines to occur in the passive region (i.e., Ecmi is above Ew). The polarization curve shows none of the characteristics of an active-passive transition. The open circuit dissolution rate under these conditions is the passive current density, which is often on the order of 0.1 j.A/cm2 or less. The increased costs involved in using CRAs can be justified by their low dissolution rate under such oxidizing conditions. A comparison of dissolution rates for a material with the same anodic Tafel slope, E0, and i0 demonstrates a reduction in corrosion rate... 

In analyzing the polarization data, it can be seen that the cathodic reaction on the copper (oxygen reduction) quickly becomes diffusion controlled. However, at potentials below -0.4 V, hydrogen evolution begins to become the dominant reaction, as seen by the Tafel behavior at those potentials. At the higher anodic potentials applied to the steel specimen, the effect of uncompensated ohmic resistance (IRohmk) can be seen as a curving up of the anodic portion of the curve. 

The search for such curved Tafel plots has yielded some well-documented examples where essentially straight Tafel lines are observed, even when slight curvature is predicted from eqn. (37). In particular, this is the case for proton reduction [73] and the outer-sphere reduction of some Cr(III) aquo complexes [34] at mercury electrodes over wide overpotential ranges (> 600 mV). However, the former reaction is not an outer-sphere process with symmetrical reactant and product parabolae to which eqn. (37) should apply, but rather involves the formation of an adsorbed hydrogen atom intermediate. The influence of such a mechanistic feature upon the rate-potential behavior is unclear even now [74]. The Cr(III)/Cr(II) aquo couple at mercury has also been examined over wide ranges of anodic as well as cathodic over-potentials [75]. In contrast to the cathodic behavior, marked... 

While an ovapotential may be applied electrically, we are interested in the overpotential that is reached via chemical equilibrium with a second reaction. As mentioned previously, the oxidation of a metal requires a corresponding reduction reaction. As shown in Figure 4.34, both copper oxidation, and the corresponding reduction reaction may be plotted on the same scale to determine the chemical equilibrium between the two reactions. The intersection of the two curves in Figure 4.34 gives the mixed potential and the corrosion current. The intersection point depends upon several factors including (the reversible potential of the cathodic reaction), cu2+/cu> Tafel slopes and of each reaction, and whether the reactions are controlled by Tafel kinetics or concentration polarization. In addition, other reduction and oxidation reactions may occur simultaneously which will influence the mixed potential. 

Kinetic data extracted from the foot of RDE dynamic polarization curves for 02 reduction yielded for pH < 11 linear log[i/(ilim — i)] versus E, or Tafel plots, with a slope of around 120 mV per decade, and thus consistent with the first electron transfer as being rate determining for the reduction of the CoPI-02 adduct. As expected for a reversible (Nerstian) two-electron redox couple, the Tafel slope at pH = 14, decreased to 30 mV per decade. It is interesting to note that an oxidized form of the closely related CoOEP displays extraordinary reversibility for the 02—H202 couple in solutions of pH < 1 [63]. 

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