Interfacial impedance Kinetics

Figure 26. Predictions of the Adler model shown in Figure 25 assuming interfacial electrochemical kinetics are fast, (a) Predicted steady-state profile of the oxygen vacancy concentration ( ) in the mixed conductor as a function of distance from the electrode/electrolyte interface, (b) Predicted impedance, (c) Measured impedance of Lao.6Cao.4Feo.8-Coo.203-(5 electrodes on SDC at 700 °C in air, fit to the model shown in b using nonlinear complex least squares. Data are from ref 171.

However, as we saw in section 3.3 for platinum on YSZ, the fact that i—rj data fits a Butler—Volmer expression does not necessarily indicate that the electrode is limited by interfacial electrochemical kinetics. Supporting this point is a series of papers published by Svensson et al., who modeled the current—overpotential i—rj) characteristics of porous mixed-conducting electrodes. As shown in Figure 28a, these models take a similar mechanistic approach as the Adler model but consider additional physics (surface adsorption and transport) and forego time dependence (required to predict impedance) in order to solve for the full nonlinear i—rj characteristics at steady state. 

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. 

While the calculations presented here were performed in terms of solution of Laplace s equation for a disk geometry, the nature of the electrode-electrolyte interface can be imderstood in the context of the schematic representation given in Figure 13.5. Under linear kinetics, both Co and Rt can be considered to be independent of radial position, whereas, for Tafel kinetics, 1/Rf varies with radial position in accordance with the current distribution presented in Figure 5.10. The calculated results for global impedance, local impedance, local interfacial impedance, and both local and global Ohmic impedances are presented in this section. 

For the linear kinetics calculation, where / is independent of radial position, the scaled real part of the local interfacial impedance follows... 

The global interfacial impedance for linear kinetics is independent of radial position and is given by... 

When the above conditions of effects of convection and migration are realized, the resulting current is limited only by the diffusion-driven transport of the electroactive species to the electrode-solution interface. At the interface charge transfer reactions take place that can be studied as a function of the electrochemical potential (Fig. 4). That experimental situation contains the fundamental premise of the traditional impedance analysis - make mass-transport effect on interfacial impedance exclusively diffusion limited (Ldiff) and investigate the interfacial kinetic phenomena composed of the diffusion and electrochemical reaction (discharge or electrolysis Rqi) impedances that can be combined in the so-caUed Faradaic impedance. 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

In this section, the principles outlined above will be applied to derive the expression for the interfacial admittance valid for a simple system as described before. In addition, this treatment will illustrate the use of impedances and admittances in the study of electrochemical kinetics. 

Thus, the fundamental difference between N-NDR and HN-NDR systems is that the former s stationary polarization curve exhibits a range of negative real impedance, whereas for the latter the zero-frequency impedance is strictly positive in the potential region of interest. From this observation one might get the impression that the mechanisms of electrode reactions are fundamentally different for systems in the two groups. But in fact it is only a small step, or more precisely, one additional potential-dependent process, that transforms an N-NDR system into an HN-NDR system. Formally, any HN-NDR system is composed of a subsystem with an N-shaped stationary polarization curve whose NDR is hidden by at least one further slow and potential-dependent step of the interfacial kinetics of the total system. This step dominates the faradaic impedance at low perturbation frequencies, whereas at higher... 

In many of the reported instances [157, 159, 200], the current calculated from Eq. 19 is much higher than that measured experimentally, signaling that interfacial charge-transfer kinetics are limiting the overall rate. On the other hand, in the n-GaAs-acetonitrile-Co(Cp)2 case [198], AC impedance spectroscopic data appear to support the assumption that thermionic emission is the current-limiting transport mechanism. 

Two features of the fuel cell cathode were, however, highlighted uniquely by impedance spectra the complex effect of cathode dehydration and the effect of backing tortuosity. Three different types of losses caused by insufficient cell hydration, related to cathode interfacial kinetics, proton conductivity in the catalyst... 

The local Ohmic impedance Zg accounts for the difference between the loccil interfacial and the local impedances. The calculated local Ohmic impedance for Tafel kinetics with 7 = 1.0 is presented in Figure 13.9 in Nyquist format with normalized radial position as a pcirameter. The results obtained here for the local Ohmic impedance are very similar to those reported for the ideally polarized electrode and for the blocking electrode with local CPE behavior. ° ° At the periphery of the electrode, two time constants (inductive and capacitive loops) are seen, whereais at the electrode center only an inductive loop is evident. These loops are distributed around the asymptotic real value of 1/4. 

During the last 30 years, the measurement of the impedance of an electrode has become a technique widely used for investigating numerous interfacial processes. The interpretation of this quantity is based on models obtained from the equations governing the coupled transport and kinetic processes, which may include heterogeneous and/or homogeneous reaction steps. Although these models are able to... 

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