Tafel control cathodic reaction under

A very low frequency or scan rate may be required to obtain Rp defined by Eq 34 under circumstances where reactions are mass transport limited, as indicated by Eq 32. Here, a 1 of 0.1 cm and D = 10" cm /sec requires that a frequency below 0.1 mHz be implemented to obtain Rp from IZ( )I at the zero frequency limit. Hence, a common experimental problem in the case of diffusion controlled electrochemical reactions is that extremely low frequency (or scan rates) are required to complete the measurement of Rp. In the case where Rp is dominated by contributions from mass transport such that Eq 33 applies, the Stem approximation of Eqs 25 and 26 must be modified to account for a Tafel slope for either the anodic or cathodic reaction under diffusion controlled conditions (i.e., Pa or Pa = oo). In fact, Eq 19 becomes invalid. 

It is useful now to describe the origins of the shape of the anodic and cathodic E-log i behaviors shown in Fig. 2. Note that the anodic reaction is linear on the E-log i plot because it is charge transfer controlled and follows Tafel behavior discussed in Chapter 2. The cathodic reaction is under mixed mass transport control (charge transfer control at low overpotential and mass transport control at high overpotential) and can be described by Eq. (1), which... 

The use of Tafel plots for the analysis of metal corrosion systems indicates how dissolved O2 in solution and the subsequent O2 reduction (which is under kinetic control) accelerates metal corrosion. Due to the high value of E for O2 reduction (+1.23 V vs. SHE), the intersection of the oxygen reduction and metal dissolution Tafel lines occurs at high values of E and When the reduction of both H+ and O2 drives metal corrosion (with the reduction reactions under kinetic control), one simply adds together the current-voltage Tafel lines for the two reduction reactions. A new line is then drawn for the sum of the cathodic currents on the corroding metal. The intersection of this new line with the metal oxidation Tafel line gives E and... 

The earlier sections of this chapter discuss the mixed electrode as the interaction of anodic and cathodic reactions at respective anodic and cathodic sites on a metal surface. The mixed electrode is described in terms of the effects of the sizes and distributions of the anodic and cathodic sites on the potential measured as a function of the position of a reference electrode in the adjacent electrolyte and on the distribution of corrosion rates over the surface. For a metal with fine dispersions of anodic and cathodic reactions occurring under Tafel polarization behavior, it is shown (Fig. 4.8) that a single mixed electrode potential, Ecorr, would be measured by a reference electrode at any position in the electrolyte. The counterpart of this mixed electrode potential is the equilibrium potential, E M (or E x), associated with a single half-cell reaction such as Cu in contact with Cu2+ ions under deaerated conditions. The forms of the anodic and cathodic branches of the experimental polarization curves for a single half-cell reaction under charge-transfer control are shown in Fig. 3.11. It is emphasized that the observed experimental curves are curved near i0 and become asymptotic to E M at very low values of the external current. In this section, the experimental polarization of mixed electrodes is interpreted in terms of the polarization parameters of the individual anodic and cathodic reactions establishing the mixed electrode. The interpretation then leads to determination of the corrosion potential, Ecorr, and to determination of the corrosion current density, icorr, from which the corrosion rate can be calculated. 

Fig. 4.26 Schematic polarization curves used in the analysis of cathodic protection by an impressed external current. Cathodic reaction is under Tafel control.

As tapp approaches the concentration overpotential, ti ,> becomes very large. The cathodic reaction may be under mixed charged transfer-mass transport or mass transpK>rt control for many corrosion situations, particularly if the cathodic reaction is O2 reduction [5]. The cathodic polarization behavior associated with mixed charge transfer— mass transfer control can be described mathematically by the algebraic combirration of Eqs 20 and 22. Tafel extrapolation of cathodic data becomes difficult under these conditions because the Tafel region may not be extensive. 

Tafel s original work in 1905 was concerned with organic reactions and H2 evolution at electrodes, and Eq. (1) was written as an empirical representation of the behavior he first observed. A particular value o b = RT/2F has come to be associated specifically with Tafel s name for the behavior of the cathodic H2 evolution reaction (h.e.r.) when under kinetic control by the recombination of two (adsorbed) H atoms following their discharge from or H2O in a prior step. Such kinetic behavior of the h.e.r. is observed under certain conditions at active Pt electrodes and in anodic CI2 evolution at Pt. (We note here, in parentheses, that an alternative origin for a Tafel slope of RT/2F for the h.e.r. at Pt has been discussed by Breiter and by Schuldiner in terms of a quasiequilibrium diffusion potential for H2 diffusing away from a very active Pt electrode at which H2 supersaturation arises). 

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