Conduction path Bulk resistance

In accordance with this model, the current path is made through the contact resistance external collector - volume collectors (Rki), then goes through many other resistances, such as bulk resistance of the conductive particles (Rvi) and the contact resistance between the conductive particles in the volume of the electrode (Rci) at the end, there is contact resistance between the conductive particles and active mass particles (Rmi). 

There is, of course, a limit on the amount of solution resistance that can be overcome even with microelectrodes. Attempts have been made to perform electrochemistry in the gas phase [79] or in supercritical C02 180] with microelectrodes. In each case, however, the conduction path was shown to be not through the bulk phase, but rather across the insulating surface between the microelectrode and the counter electrode. This mechanism enables electrochemical detection in highly unusual media for voltammetry and illustrates that only very small conduction pathways are required to obtain well-defined electrochemical behavior. 

Given a certain cell design and operating temperature, the bulk material contributions to R (and hence the ASR) can also be calculated. Based on the detailed cell geometry, the length of both the ionic and electronic current paths and cross-sectional area for current conduction can be measured. Together with the resistivities of the materials used, they yield the bulk ASR. The contact resistance cannot be calculated from fundamental data, and is usually determined by difference between the measured total resistance and the computed bulk resistance. 

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... 

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... 

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. 

It is clear from Equation 11.3 that resistivity should approach within 10% of the bulk value when the film thickness exceeds about four times the mean free path. The better the conductor, the smaller the mean free path. Thus, the resistivity approaches the bulk value as the film thickness reaches typical values of 100-200 nm for metallic conductors, or perhaps as much as several micrometers for semiconductors, depending on the intrinsic or doped carrier density. For sufficiently thick metallic films with K 1, the temperature coefficient of resistivity becomes positive, as bulk electron-phonon scattering becomes the primary contribution to resistivity [5]. Conduction in semiconductor films remains activation-limited, and retains a negative temperature coefficient. Figure 11.1 illustrates the dependence of resistivity on film thickness for sputtered... 

Despite the rather low ionic conductivity and, hence, the poor utilization of the bulk path, porous LSM cathodes show acceptable polarization resistances in zirconia-based SOFCs at 1000°C. However, the activation energy of the polarization resistance is rather high (ca. 1.8-2.1 eV [94, 95, 119, 120, 131, 132]) and the trend to lower the operation temperature of fuel cells requires... 

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