Inverse overvoltage

This negative overvoltage in the anodic hole transfer reaction may better be called the undervoltage or the inverse overvoltage (the negative overvoltage in the anodic reaction) rather than the usual overvoltage which is positive in the... 

The energy equivalent to the inverse overvoltage corresponds to the gain of energy due to the absorption of photons in n-type semiconductor electrodes. 

Fig. 10-22. Overvoltages in an anodic hole transfer (a) at a photoexcited n-type electrode and (b) at a p-type electrode of the same semiconductor iih = overvoltage for hole transfer across an interface = inverse overvoltage due to generation and transport of photoexcited holes in an n>type electrode.

Figure 10-23 shows the electron levels and the polarization curves for the transfer of anodic redox holes both at a photoexcited n-fype electrode and at a dark p-type electrode of the same semiconductor. The range of potential where the anodic hole current occurs at the photoexcited n-type electrode is more cathodic (more negative) than the range of potential for the anodic hole current at the dark p-type electrode. The difference between the polarizatitm potential aE(i) (point N in the figure) of the photoexcited n-type electrode and the polarization potential pE(i) (point P in the figme) of the dark p-type electrode at a constant anodic current i is equivalent to the difference between the quasi-Fermi level pej of interfacial holes and the Fermi level bEf of interior holes (electrons) in the photoexcited n-type electrode this difference of polarization potential, in turn, equals the inverse overvoltage rip.sc(i) defined in Eqn. 10-46 ... 

For cathodic hole injection, the overvoltage tip.sc(i) includes both diffusion and recombination of holes in the electrode this overvoltage occurs in the same cathodic direction as the cathodic hole injection so that tip. sc is the usual overvoltage (a negative quantity in the cathodic reaction) rather than the inverse overvoltage. Then, we obtain Eqn. 10-50 ... 

Fig. 10-28. Polarization curves for cell reactions of photoelectrolytic decomposition of water at a photoezcited n-type anode and at a metal cathode solid curve M = cathodic polarization curve of hydrogen evolution at metal cathode solid curve n-SC = anodic polarization curve of oxygen evolution at photoezcited n-type anode (Fermi level versus current curve) dashed curve p-SC = quasi-Fermi level of interfadal holes as a ftmction of anodic reaction current at photoezcited n-type anode (anodic polarization curve r re-sented by interfacial hole level) = electrode potential of two operating electrodes in a photoelectrolytic cell p. sc = inverse overvoltage of generation and transport ofphotoezcited holes in an n-type anode.

As shown in Eqn. 10-46, the difference in the polarized potential at constant anodic current, between the photoexcited n-type and the dark p-type anodes of the same semiconductor, represents the inverse overvoltage iip sc for the generation and transport of photo-excited holes. 

The linear polarization technique estimates instantaneous corrosion rates under various process conditions. The corrosion current, according to the Stem-Geary equation, is inversely proportional to polarization resistance, which allows the measured polarization resistance to be normalized directly into corrosion rates. Because the current follows the appHed overvoltage, the polarization resistance curve is plotted automatically. Because this technique accurately measures corrosion rates <0.1 mpy, it is of a great importance in water distribution systems and food industries that face problems with traces of impurities and contamination. It can be used to measure the corrosion rates in civil engineering structures that cannot be subjected to weight loss measurements. Usually, Hnear polarization measurements are executed in 10 min. As shown in Fig. 5.3, the current as a... 

In exceptional cases it might be possible that the transition of ions from the surface to the solution or in the inverse direction needs an activation energy. That such a barrier at the interface of two phases may metimes l>e present is suggested by certain phenomena (overvoltage, etc.) observed in electrolytic processes. In that case adjustment of the charge would occur slowly, and the assumption that the double layer charge is a constant, independent of the particle distance, would then be a more suitable approximation h In a case like that of Agl, behaving as a perfectly reversible electrode, and in many other systems, the assumption -Pq — constant will be more correct. 

The inversion was performed in section 1.9, leading to activation overvoltages, when we can discount the influence of the variation in concentration of the species, i.e. the influence of diffusion. What about the expression which integrates this phenomenon of diffusion Let us return to the expressions [1.28] ... 

In order to reach these expressions, we remove an exponential term from the Butler-Volmer equations. The approximate expression for inversion of the equations is valid only if the current density is sufficiently high. This approximation is, of course, seen again after inversion of that expression equations [1.55] are not correct for overly low values of current density and are not defined in 0. In order to avoid numerical instabiUty, it is usual to add a term of internal current into the expression of the activation overvoltage ... 

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