High-Overpotential Region

In the high-overpotential region the peak potential depends logarithmically on sweep rate, following the equation 

From a plot of Fp, jnev versus log v one can obtain the Tafel slope, b, and from the intercept at Fp, irrev = rev the specific rate constant can be calculated. Note that the value of fef obtained in this way is that corresponding to F = Frev only but since the Tafel slope is known, kf at any other potential can readily be calculated. 

The peak current density in the high-over potential region is given by 

In this equation a is the transfer coefficient, which is obtained directly from the Tafel slope. 

Since (a/n) is usually smaller than unity, the peak current in the high-overpotential region is, as a rule, smaller than that in the reversible region. The difference is not very large, however. For a = 0.5 and n = 1 the above ratio is equal to 0.78. For a=0.5 and n=2, it is reduced to 0.55. 

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In the CP-rich bath type, experimental transfer coefficients were ttc= a - 0.5 0.05, while in the H -rich baths the values were ttc= 0.3 0.05 and = 0.65 0.05. The stoichiometric number for the process was calculated by coupling the charge-transfer resistance with the extrapolated exchange current density from low and high overpotential regions, respectively, and by back-reaction correction. " It was determined to be 3 by both methods and for all bath compositions. It has been suggested that... 

ORR kinetic currents at a given potential than those on the individual components, namely, CoPc/C, CoPcFig/C, or Ag/C. The RDE and RRDE measurements indicate that the ORR on these new catalysts occurs almost entirely via a four-electron pathway and shows 50 mV lower overpotentials for CoPc Ag/C and 82 mV for CoPcFi6 Ag/C as compared to that found on Ag/C catalyst. The current densities are higher, and Tafel slopes are lower for ORR on CoPc Ag/C and CoPcFi6 Ag/C than on Ag/C catalysts in the high overpotential region. 

The method of extrapolation of a linear section of the Tafel line, which is realized over the high overpotential region, to zero overpotential is much simpler, but it introduces a degree of uncertainty as the method relies upon the assumption of a constant Tafel slope, independent of the overpotential. Experiments, however, often indicate some concave curvature in a linear ... 

The situation is different for large overpotentials. Namely, if the electrode potential is shifted into the high overpotential region (i.e. if r/ RT/F), the second term of the series becomes negligible. In this case, we obtain so called Tafel equation (Fig. 5.3) ... 

Potential Step, High Overpotential Region (Chrono-amperometry)... 

Figure 15.4 Variation of the peak potential Ep over a wide range of sweep rates, covering both the reversible and the high-overpotential regions. Ep,rev s arbitrarily taken as zero. The critical" sweep rate Vc is the one to be used in Eq. (15.11) to calculate kf.

This value of is applicable to the Langmuir isotherm, and should therefore be compared with Eq. (15.19) with /= 0. The peak in the high-overpotential region is thus somewhat lower than in the reversible region, as shown in Figure 15.8. 

In the high-overpotential region, j is an exponential function of the overpotential, hence the differential Faiadaic resistance also depends exponentially on potential. 

Combining the last two equations one has, for the high-overpotential region... 

Considering the high-overpotential region, the relevant rate equation is... 

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