Tafel behavior curves

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. 

Fig. 29. Polarization data for the OER on a C03O4 film thermochemically formed on a Ni metal substrate. behavior is shown as a function of potential in relation to the logi versus Tafel polarization curve. (From Ref 302.)...

Fig. 3.1 Polarization curves illustrating charge-transfer polarization (Tafel ° behavior) for a single half-cell reaction, (a) Anodic polarization,...

In Chapter 4, analysis of the kinetics of coupled half-cell reactions shows how the corrosion potential and corrosion current density depend on the positions of the anodic and cathodic polarization curves. The anodic polarization curves are generally represented as showing linear or Tafel behavior, and the cathodic curves are shown with both Tafel and... 

Fig. 5.20 Representative anodic polarization curves for indicated pure metals ini N H2S04, pH = 0.56. Linear sections at lower potentials are representative of Tafel behavior. Redrawn from Ref 5,10-14...

Interpretation of an experimentally determined polarization curve, including an understanding of the information derivable therefrom, is based on the form of the polarization curve, which results from the polarization curves for the individual anodic and cathodic half-cell reactions occurring on the metal surface. These individual polarization curves, assuming Tafel behavior in all cases, are shown in Fig. 6.2 (dashed curves) with Ecorr and the corrosion current, Icorr, identified. It is assumed that over the potential range of concern, the Iox x and Ired M contributions to the sum-anodic and sum-cathodic curves are negligible consequently, Uox = Iox M and Ured = Ired x. At any potential of the... 

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-... 

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-... 

This simple model of the inhibitor action which is based essentially on the potential independence of the inhibitor adsorption is, however, often not applicable. Kaesche (15) indicates that the corrosion inhibition of pure iron in sulfuric or perchloric acid by phenyl-thiourea strongly affects the slopes of the polarization curves, leaving the corrosion potentials almost unchanged Fig.7. In fact, the polarization curves for the inhibited situation do not exhibit real Tafel behavior. This behavior finds a partial explanation in the fact that the mechanism of the hydrogen evolution appears to be changed in the presence of... 

Equation (41) is identical in form to Eqs. (18 and 24). The curve is centered around Ecorr rather than and the current density at zero overpotential is icorr instead of io- This expression, along with the theory for mixed potentials, was derived by Wagner and Traud, and therefore will be referred to as the Wagner-Traud equation. As described in the Chapter 7.3.1.2 on experimental techniques, the Wagner-Traud equation is used in software analysis packages that accompany modem computer-controlled potentiostats. A nonlinear least squares fit of this equation to the experimental data provides values of corr. corr. ha. and he vvith the assumption that perfect Tafel behavior is observed for both the anodic and cathodic reactions, and that the extrapolations of the Tafel portions of the curves both intersect at the corrosion potential. 

The analysis in Eq. (24) does not take into account the transport limitations. Therefore these predictions of the diffuse-layer effects are only valid for the interval of the potentials in which the rate of the process is determined by the electron-transfer step. If this kinetic regime corresponds to high negative electrode charges, the Kfi factor in Eq. (25) varies slowly and the deviations from the Tafel behavior are rather weak. On the contrary, the anion electroreduction wave that starts at positive electrode charges may demonstrate a complicated curve a usual behavior within this potential range, with approach to the limiting current at less positive potentials. 

Hence, for a reversible system, the well-known linear relation is obtained between the potential E and log (/iim -///). Other equations have been derived for those reversible systems that involve semiquinone formation, dimerization, or the formation of complex compounds with mercury. Logarithmic analysis of the polarographic wave is often the only proof of reversibility which is considered but recently several authors, in particular Zuman and Delahay, " have pointed out that it is inadequate to assume that an electrode process is reversible on this evidence alone. For a reversible reaction, plots of E vs. In (/lim - ///) give the electron number z from the slope of the plot, RT/zF, A clearer indication of irreversibility is the evaluation of slopes of log i-E curves for higher concentrations (for i < /lim). Irreversible processes will give Tafel behavior. 

E-log(i) curve The decrease in corrosion rate due to the application of CP current can be determined provided the relationship between rebar potential (E) and current (i) can be measured and modeled. A simple model is Tafel behavior with a linear relationship between E and log(i). This methodology is structure specific and the measurements involved are relatively complex and require specialist interpretation. Ideal Tafel behavior is rarely observed for steel in concrete. 

The sohd line in Figure 3 represents the potential vs the measured (or the appHed) current density. Measured or appHed current is the current actually measured in an external circuit ie, the amount of external current that must be appHed to the electrode in order to move the potential to each desired point. The corrosion potential and corrosion current density can also be deterrnined from the potential vs measured current behavior, which is referred to as polarization curve rather than an Evans diagram, by extrapolation of either or both the anodic or cathodic portion of the curve. This latter procedure does not require specific knowledge of the equiHbrium potentials, exchange current densities, and Tafel slope values of the specific reactions involved. Thus Evans diagrams, constmcted from information contained in the Hterature, and polarization curves, generated by experimentation, can be used to predict and analyze uniform and other forms of corrosion. Further treatment of these subjects can be found elsewhere (1—3,6,18). 

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