Bulk path

However, as discussed more fully in section 5, it is not entirely clear how significant the bulk path is in the case of LSM, which is almost a pure electronic conductor under typical cathode conditions. In the Mizusaki study cited above, the authors went on to show that following anodic polarization (or strong cathodic polarization), the LSM film becomes severely damaged and cracked and reverts to behavior more... 

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. 

There are several possible explanations for this behavior, all of which speak to various deficiencies of current models. First, even if the bulk path... 

Inconsistency of performance with a bulk path at low vacancy concentration. A quantitative comparison between predictions of the Adler model and impedance data for LSC shows the poorest agreement (underprediction of performance) at low temperatures, high F02. and/or low Sr content. These are the conditions under which the bulk vacancy concentration (and thus also the ionic conductivity and surface exchange rate of oxygen with the bulk) are the lowest. These are exactly the conditions under which we would expect a parallel surface path (if it existed) to manifest itself, raising performance above that predicted for the bulk path alone. Indeed, as discussed more fully in section 5, the Adler model breaks down completely for LSM (a poor ionic conductor at open-circuit conditions), predicting an... 

More recent studies of dense LSM films appear to confirm these original conclusions as well as fill in some of the details.In particular, loroi and co-workers ° were able to produce very high quality films with clean, well-resolved impedances at 800—1000 °C in air, as shown in Figure 36. Consistent with bulk transport limitations, the impedance of these films was Warburg-like in shape and scaled properly with electrode area and electrode thickness, assuming an entirely bulk path. By extrapolating their results to zero film thickness, the authors also... 

What this calculation shows is that the rate of bulk transport observed in a thin film of LSM is at least 3 orders of magnitude too low to explain the performance of porous LSM at low overpotential, assuming an entirely bulk transport path. This calculation echoes prior estimates of Adler and co-workers, who showed that the zero-bias impedance of porous LSM cannot be explained in terms of a bulk path. In addition, estimates of the chemical capacitance based on loroi s impedance for porous LSM yield values of 10 —10 F/cm , which as mentioned previously in section 5.2 are more consistent with a surface process... 

The results of this analysis are summarized in Figure 37. Like prior workers studying thin films, the authors conclude that dense films without a TPB under small or cathodic polarizations operate primarily by a bulk path since the surface path is blocked. (Interestingly, they found that dense films under anodic polarization appear to operate under a mixed regime, although it is not clear how much nucleation and transport of O2 along the solid—solid interface contributes to the apparent surface path current.) In contrast, as the porosity is increased (microelectrode diameter is decreased), the surface path be-... 

Figure 37. Qualitative summary of current contributions from the surface path (Is) and the bulk path (7b) for LSM disk microelectrodes on YSZ based on i— measurements in air at 800 °C. (Reprinted with permission from ref 228. Copyright 2002 Elsevier.)...

Figure 39 shows isotope tracer maps for LSM both at the surface and near the interface as a function of polarization. These results indicate that under increasing polarization, isotope tracer is incorporated more deeply into the LSM bulk and that this incorporation occurs everywhere with the LSM near the interface not just at the TPB. This result would seem to corroborate the increased significance of the bulk path with increased overpotential. Consistent with this result, when the LSM is removed and the YSZ underneath is analyzed (Figure 40a), it is found that... 

Bulk path at moderate to high overpotential. Studies of impedance time scales, tracer diffusion profiles, and electrode microstructure suggest that at moderate to high cathodic over potential, LSM becomes sufficiently reduced to open up a parallel bulk transport path near the three-phase boundary (like the perovskite mixed conductors). This effect may explain the complex dependence of electrode performance on electrode geometry and length scale. To date, no quantitative measurements or models have provided a means to determine the degree to which surface and bulk paths contribute under an arbitrary set of conditions. 

Workers have shown theoretically that this effect can be caused both at the microstructural level (due to tunneling of the current near the TPB) as well as on a macroscopic level when the electrode is not perfectly electronically conductive and the current collector makes only intermittent contact. ° Fleig and Maier further showed that current constriction can have a distortional effect on the frequency response (impedance), which is sensitive to the relative importance of the surface vs bulk path. In particular, they showed that unlike the bulk electrolyte resistance, the constriction resistance can appear at frequencies overlapping the interfacial impedance. Thus, the effect can be hard to separate experimentally from interfacial electrochemical-kinetic resistances, particularly when one considers that many of the same microstructural parameters influencing the electrochemical kinetics (TPB area, contact area) also influence the current constriction. 

From this observation it can be concluded that the rate-determining process directly involves the electrode area, i.e. occurs i) at the surface of the LSM ii) in the bulk of the thin LSM electrodes or iii) at the LSM/YSZ interface. From thickness-dependent measurements further information with respect to the rate-determining step could be expected, since a predominant bulk path with transport of oxide ions through LSM being rate-limiting should yield Rei oc tme (tme = microelectrode thickness). Hence, a sample with 60 pm microelectrodes of two different thicknesses... 

Figure 3.11. Scheme of multiple reflections of the incident beam (amplitude I) on a surface-bulk system. The amplitude of the surface (bulk) reflection is r (r ). The transmission amplitude of the surface is t. (Dephasing due to the surface-to-bulk path is negligible.)... 

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