Conduction path Bulk capacitance

One limit of behavior considered in the models cited above is an entirely bulk path consisting of steps a—c—e in Figure 4. This asymptote corresponds to a situation where bulk oxygen absorption and solid-state diffusion is so facile that the bulk path dominates the overall electrode performance even when the surface path (b—d—f) is available due to existence of a TPB. Most of these models focus on steady-state behavior at moderate to high driving forces however, one exception is a model by Adler et al. which examines the consequences of the bulk-path assumption for the impedance and chemical capacitance of mixed-conducting electrodes. Because capacitance is such a strong measure of bulk involvement (see above), the results of this model are of particular interest to the present discussion. 

In moderately resistive samples with ionic conduction migration process controls the bulk-media conduction and the bulk resistance exceed the bulk capacitive impedance only at the highest frequencies. In practically all "real life" systems there is at least some "lossy path" through a bulk-media resistance RguLK in parallel with the Cg, resulting in predominant conduction through a resistive element at the frequencies where > Rg. The... 

Introduction of the complex conductivity into Eq. (5.262) (a instead of capacitive effects. This will be treated in more detail in Chapter 7. Here it will suffice to mention that the relevant, high-conductivity paths are parallel to the buLk. More complex distributions must be dealt with using percolation theory, effective medium theory or finite element calculations [265,266]. The result for the... 

On account of the nonzero conductivities of the homocontacts and the bulk phases the percolation problem is complex, even when the grains are randomly distributed and of the same size. Put in a very simplified manner, we expect and observe that the relevant conduction paths will not only consist of heterocontacts but will be made up of a sequence of homocontacts and heterocontacts. Hence the fraction of heterocontacts (Fig. 5.96 centre) and, thus, both the resistance ratio Rhetero/Rhomo and the capacitance ratio Chomo/Chetero will exhibit maxima roughly at the centre of... 

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