Diffusion impedance Capacitance, limiting

Figure 10. Kleitz s reaction pathway model for solid-state gas-diffusion electrodes. Traditionally, losses in reversible work at an electrochemical interface can be described as a series of contiguous drops in electrical state along a current pathway, for example. A—E—B. However, if charge transfer at point E is limited by the availability of a neutral electroactive intermediate (in this case ad (b) sorbed oxygen at the interface), a thermodynamic (Nernstian) step in electrical state [d/j) develops, related to the displacement in concentration of that intermediate from equilibrium. In this way it is possible for irreversibilities along a current-independent pathway (in this case formation and transport of electroactive oxygen) to manifest themselves as electrical resistance. This type of chemical valve , as Kleitz calls it, may also involve a significant reservoir of intermediates that appears as a capacitance in transient measurements such as impedance. Portions of this image are adapted from ref 46. (Adapted with permission from ref 46. Copyright 1993 Rise National Laboratory, Denmark.)...

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. 

Finite-space diffusion takes place during the charging of insertion electrodes at moderate frequencies, transforming into mainly capacitive behavior within the limit of very low frequencies, in contrast to the semi-infinite diffusion for solution redox-species (except for thin-layer solution electrochemistry) electrochemical impedance spectroscopy becomes a very useful diagnostic tool for the characterization of insertion mechanisms ... 

Two impedance arcs, which correspond to two relaxation times (i.e., charge transfer plus mass transfer) often occur when the cell is operated at high current densities or overpotentials. The medium-frequency feature (kinetic arc) reflects the combination of an effective charge-transfer resistance associated with the ORR and a double-layer capacitance within the catalyst layer, and the low-fiequency arc (mass transfer arc), which mainly reflects the mass-transport limitations in the gas phase within the backing and the catalyst layer. Due to its appearance at low frequencies, it is often attributed to a hindrance by finite diffusion. However, other effects, such as constant dispersion due to inhomogeneities in the electrode surface and the adsorption, can also contribute to this second arc, complicating the analysis. Normally, the lower-frequency loop can be eliminated if the fuel cell cathode is operated on pure oxygen, as stated above [18],... 

In the presence of a redox reaction without diffusion limitations, the system impedance is described by the electrical equivalent circuit / s(Cdi ct) displayed in Fig. 2.34. Replacing the double-layer capacitance with the CPE produces complex plane and Bode plots (Fig. 8.4) corresponding to the equation for the impedance of such a system ... 

Figure 4.5.1 compares the impedance spectrum of reflective finite-length diffusion with the spectrum of its limiting equivalent circuit, a limiting resistance in series with a limiting capacitance. It can be seen that these responses approach each other as the frequency deaeases. 

Here, Z is the absolute magnitude of the impedance. What allows us to separate different electrochemical processes using EIS is the fact that capacitors have a frequency-dependent ability to be charged or discharged - a property called capacitive reactance. As a consequence, different capacitances within the system will respond at different frequencies, allowing us to separate temporally the electrochemical processes in EIS experiments on the basis of their capacitive reactance. Similarly, diffusion limitations usually also have a characteristic low frequency where they predominantly govern the system response and thus are easily distinguishable. 

Coulometric titration techniques were used to measure chemical diffusion at between 700 and lOOOC. The transient current response to a potentiostatic step was transformed from the time domain to the frequency domain. The equivalent circuit which was used to fit the resultant impedance data contained an element which described the finite-length diffusion of O into the sample. Other elements which were included were the gas-phase capacitance, and the sum of the gas-phase diffusion resistance and that which was associated with the limited surface exchange kinetics of the sample. The chemical diffusion coefficient of the perovskite, Laq gSrq 2C0O3,... 

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