Butler-Volmer equation-high field approximation

Special cases of Butler-Volmer equation-high field approximation... 

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... 

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... 

When Ip I >100 mV then the Butler-Volmer equation reduces to its high field approximation form ... 

These studies have shown that, quite often, over relatively wide (e.g., 0.3-0.5 V) ranges of potential, the catalytic rates depend on catalyst-electrode potential in an exponential manner, similar to the high field approximation of the Butler-Volmer equation, that is,... 

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.. 

---