High-overpotential approximation

BUTLER-VOLMER EQUATION HIGH-OVERPOTENTIAL APPROXIMATION... 

For small overpotentials the linear approximations of Eqs. (5.4) and (5.5) should be sufficient, but at high overpotentials higher-order terms are expected to contribute. 

Thus, the polarisation data, cyclic voltammetric results and the a.c. impedance measurements all suggest that, when an Ru02/TiC>2 anode exhibits a high overpotential, this is a direct consequence of the surface depletion of Ru. This is also consistent with the estimated Re values of approximately 20 Q for the failed electrodes, in contrast to the known, much higher specific resistivity of Ti02 of... 

Shown in Fig. 12 is an example of the nonadiabatic rate calculated using the full simulation method [ ]S. (27) and (28)] and the approximate formula [Eqs. (29)-(31)] for the + e Fe " reaction at the water/Pt( 100) interface with r= 10cm". For the reason discussed earlier, the full simulation method can only be used for the high overpotential case. In this region, the agreement between the two methods is quite good. 

More complex reductions of CO2 by enzyme cascades have also been achieved. A combination of an electron mediator and two enzymes, formate dehydrogenase and methanol dehydrogenase, was used to reduce CO2 to methanol. This system operates with current efficiencies as high as 90% and low overpotentials (approximately —0.8 V vs. SCE at pH 7) [125]. The high selectivity and energy efficiency of this system indicate the potential of enzyme cascades. There are also drawbacks to these systems. In general, enzymes are... 

In the high-overpotential case (cf. Section 7.2.3b.2), the first exponential term can be neglected for n 0, i.e., for net electronation, and the second exponential term for T) 0, i.e., for net deelectronation. In the low-field approximation, where both exponential terms in the Butler-Volmer equation can be linearized, Eq. (7.136) becomes... 

Fig. 7.185. In a self-driving cell, the plot of cell overpotential vs. log cell current density should be a straight line if the charge transfers at both electrodes are both rate controlling and valid under the high-field approximation. An apparent /0 for the cell as a whole can be deduced.

As another example of solving the nonlinear model by ADM, we assume that at high overpotentials the electrochemical kinetics can be represented by the following high field Butler-Volmer approximation, the current density in Eq. (227) is rewritten as ... 

The expression (12.27) for the corrosion potential can be introduced into Eq. (12.22) and thus, an explicit result for the corrosion current can be obtained. But the resulting equation is quite cumbersome and therefore a simpler equation will be derived by assuming that overpotentials are sufficiently large that the high-field approximation of the Butler-Volmer equation can be used for the electronation- and deelectronation-current densities. Thus, Eqs. (12.22) and (12.23) become... 

The usual procedure for extracting the exchange current Iq is then to measure q as a function of I and to plot Inl vs q (Tafel plot). Such plots are shown in Figures 3 and 4 for Pt and Ag catalyst electrodes deposited on YSZ and acting as catalyst for C2H4 oxidation. Throughout the rest of this discussion, we omit the subscript "W" from q and simply write q, since the only overpotential of interest is that of the catalyst film. When Iql >100 mV, then the Butler-Volmer equation (16) reduces to its "high field approximation" form, i.e.. 

Note that, in contrast to the low-field approximation, the Tafel equation is sometimes referred to as the high-field approximation since it is only valid for large values of overpotential. 

For the electronic terms in the electrolyte, Schmickler did not use the usual harmonic approximation, since this always produces a curvature of Tafel plots at high overpotentials even for redox reactions at bare metal electrodes. There is little experimental evidence for such an effect. In this study, there is a particular interest in possible curvature of the theoretically deduced Tafel lines caused by the resonance nature of the electron transfer. The electronic term in the electrolyte, using the linear approximation, is expressed as... 

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