Gerischer impedance

Figure 26b shows the impedance predicted by eqs 8 and 9. As previously discussed, this function is known as the Gerischer impedance, derived earlier in section 3.4 for a situation involving co-limited adsorption and surface diffusion (in the context of Pt). As with the surface-mediated case, the present result corresponds to a co-limited reaction regime where both kinetics and transport determine the electrode characteristics (as reflected in the dependency of 7 chem and Qs on both fq and T eff)- The essential difference between this and the Pt case is that here the kinetics and diffusion parameters refer to a bulk-mediated rather than surface-mediated process. 

So, the term [A0a0 + AR aR ] co-1/2 (1 — i) resembles the Warburg impedance corresponding to diffusional mass transport of A, O and R, with a mobile equilibrium between A and 0, i.e. kQ -> °°, whereupon the term in g = kQ /co would vanish. If, however, kQ has a finite value, the faradaic impedance is enlarged by the Gerischer impedance expressed by the term containing g. 

More quantitatively, it can be deduced that the Gerischer impedance, ZG o takes a reduced form in the cases... 

Gerischer impedance — The Gerischer impedance is a transport-related interfacial impedance element which differs from the Warburg impedance in that the electroactive species taking part in the electrode process is chemically generated in a spatially homogeneous way prior to diffusing to the interface. It has the form ... 

This term was first obtained by Gerischer [1%] and is called the Gerischer impedance. Such a behavior was observed in solid oxide fuel cells [197-199] and interpreted as a competition between surface [200] and bulk diffusion coupled... 

A distributed element which shares some features with Zw, Eq. (14), is the Gerischer impedance,... 

IfRw Rj, (Ryy / Rf, 1), the Gerischer impedance with boimdary conditions becomes irrelevant and impedance becomes ... 

At very low frequencies the Gerischer impedance reaches a constant real value inversely proportional to a value of kinetic rate constant k. 

In recent years, the potential relaxation method has been extensively developed and analyzed by Kobussen et al. (102) and by Conway and co-workers (75, 100-105) for the study of the behavior of chemisorbed intermediates, whereas the ac method was first applied to this problem by Gerischer and Mehl (106) with later developments by Armstrong and Henderson (108), Brossard et al. (110), and Bai, Harrington, and Conway (113) for sequential processes involving more than one adsorbed intermediate. These approaches had their origins in the work of the Sluyters and of Randles (111), as well as in the important works of Keddam et al. (112) on the impedance behavior of iron and corrosion processes thereat. 

Early work by Gerischer and Mehl (106) employed impedance analysis at Ag and Cu electrodes. However, these metals are not of major interest as H adsorption is weak, and these materials are not attractive as water electrolyzer cathodes. Bockris et al. (121) and Selvaratnam and Devanathan (122) employed the double-pulse method (see Section VI,B,1) for Ag and Ni, but the results did not seem to be very meaningful. 

Process models Nemst dielectrics (1894) Warburg diffusion (1901) Finkelstein Solid film (1902) Randles double layer and diffusion impedance (1947) Gerischer two heterogeneous steps with adsorbed intermediate (1955) De Levie porous electrodes (1967) Schuhmann homogeneous reactions and diffusion (1964) Gabrielli generalized impedance (1977) Isaacs LEIS (1992)... 

Based on the extensive DRT analysis shown above, the ECM depicted in Figure 16.13 is proposed. The equivalent circuit consists of six serial impedance elements the processes Pic, Pia, and P3A are modeled by an RQ element, whereas Pia and Pic are modeled by a G-FLW element and a Gerischer element, respectively. The ohmic losses are accounted by an ohmic resistor Rq-... 

An ECM is proposed that consists of six serial impedance elements three RQ elements, a G-FLW element, a Gerischer element, and an ohmic resistor. 

Many phenomena can lead to such behavior. Over the years, many possible causes have been suggested and analyzed, all of them based on the general principle advanced in 1955 by Gerischer and Mehl The origin of a capacitive or inductive electrode impedance would be the relaxation of the surface coverage by adsorbed intermediate. These may be classified as follows ... 

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