Impedance interpretation kinetics

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 particular, the coupling between the ion transfer and ion adsorption process has serious consequences for the evaluation of the differential capacity or the kinetic parameters from the impedance data [55]. This is the case, e.g., of the interface between two immiscible electrolyte solutions each containing a transferable ion, which adsorbs specifically on both sides of the interface. In general, the separation of the real and the imaginary terms in the complex impedance of such an ITIES is not straightforward, and the interpretation of the impedance in terms of the Randles-type equivalent circuit is not appropriate [54]. More transparent expressions are obtained when the effect of either the potential difference or the ion concentration on the specific ion adsorption is negli-... 

Even though the effect of moisture on the anode kinetics is well known, interpretation of experimental results on the effect of moisture can be tricky. As Nakagawa et al. [52] pointed out, the measurement of the total cell impedance under the OCV condition is not convincing since the reduction of polarization could as well be due to the availability of H20 for the cathodic reaction. In addition, the measurement of cell performance under the constant voltage or constant current conditions may also lead to wrong conclusions about the effect of water, because the addition of H20 will... 

Further information on this subject can be obtained by frequency response analysis and this technique has proved to be very valuable for studying the kinetics of polymer electrodes. Initially, it has been shown that the overall impedance response of polymer electrodes generally resembles that of intercalation electrodes, such as TiS2 and WO3 (Ho, Raistrick and Huggins, 1980 Naoi, Ueyama, Osaka and Smyrl, 1990). On the other hand this was to be expected since polymer and intercalation electrodes both undergo somewhat similar electrochemical redox reactions, which include the diffusion of ions in the bulk of the host structures. One aspect of this conclusion is that the impedance response of polymer electrodes may be interpreted on the basis of electrical circuits which are representative of the intercalation electrodes, such as the Randles circuit illustrated in Fig. 9.13. The figure also illustrates the idealised response of this circuit in the complex impedance jZ"-Z ) plane. 

Very early, Miller and Bruckenstein [6] had felt that for an electrochemical system under mixed kinetic control, HMRDE was able to derive information about the kinetic parameters and give more valuable interpretation than by conventional RDE technique. At that time, they developed a theoretical analysis, restricted to quasi steady state, and which is now presented in a more quantitative way and over a large frequency domain with the formalism of EHD impedance (see Chapter 4). 

The uncertainty associated with the interpretation of the impedance response can be reduced by using an electrode for which the current and potential distribution is uniform. There are two types of distributions that can be used to guide electrode design. As described in Section 5.6.1, the primary distribution accounts for the influence of Ohmic resistance and mass-transfer-limited distributions account for the role of convective diffusion. The secondary distributions account for the role of kinetic resistance which tends to reduce the nonuniformity seen for a primary distribution. Thus, if the primary distribution is uniform, the secondary... 

Experimental systems used for electrochemical measurements should be selected to take maximum advantage of well-imderstood phenomena such as mass transfer so as to focus attention on the less-understood phenomena such as electrode kinetics. For example, the study of electrochemical reactions in stagnant environments should be avoided because concentration and temperature gradients give rise to natural convection, which has an effect on mass transfer that is difficult to characterize. It is better to engage in such experimental investigations in systems for which mass transfer is well defined. To simplify interpretation of the impedance data, the electrode should be uniformly accessible to mass transfer. 

Numerical solutions have been presented for the impedance response of semiconducting systems that accoimt for the coupled influence of transport and kinetic phenomena, see, e.g., Bonham and Orazem. Simplified electrical-circuit analogues have been developed to account for deep-level electronic states, and a graphical method has been used to facilitate interpretation of high-frequency measurements of capacitance. The simplified approaches are described in the following sections. 

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... 

It should be mentioned, however, that surface inhomogeneities of different dimensionality (cf. Section 2.1) significantly influence the kinetics of metal electrodeposition and the time-dependent surface morphology. Therefore, an exact analysis of corresponding EIS spectra is rather difficult. The necessary presumptions of stationarity and linearity for EIS measurements and quantitative interpretation of EIS data are often violated. The lack of direct local information on surface dynamics strongly hinders a quantitative analysis of the impedance behavior of time-dependent systems. Such considerations have been mainly disregarded in previous EIS data interpretations. In future, a combination of EIS measurements with in situ local probe... 

The kinetics of dehydration [128] of Na2S203.5H20 were difficult to interpret because the course of the reaction was markedly influenced by the perfection of the initial reactant surface and the reaction conditions. No reliable Arrhenius parameters could be obtained. The mechanism proposed to account for behaviour was the initial formation of a thin superficial layer of the anhydrous salt which later reorganized to form dihydrate. The first step in the reaction pentahydrate - dihydrate was satisfactorily represented by the contracting area (0.08 < or, < 0.80) expression. The second reaction, giving the anhydrous salt, fitted the Avrami-Erofeev equation (n = 2) between 0.05 < 2< 0.8. The product layer offers no impedance to product water vapoiu escape and no evidence of diffusion control was obtained. The mechanistic discussions are supported by microscopic observations of the distributions and development of nuclei as reaction proceeds. 

They have extended the kinetic study of lithium intercalation to such transition metal oxides as Lii.gNi02," " " Lii.8Mn204," " Li +s[Ti5/3Li,/3]04," 205, and carbonaceous materials. In these works, they have reported that the theoretical CTs, based upon the cell-impedance control concept, matched quantitatively those experimentally measured all the anomalous features of the experimental transients were readily interpreted in the cell-impedance controlled transients with such simplified parameters as electrochemical active area, dimensionality of the diffusion path, cell impedance, etc. 

The frequency-response behavior is interpreted in an analytical, mathematical manner, based on electrochemical kinetic reaction mechanisms, together with a double layer capacitance. It must be emphasized that a given reaction mechanism dictates the equivalent circuit expected of it However, fitting the experimental data to the theoretical impedance behavior is generally difficult and hence, great... 

Choice of appropriate model IS is not a technique that can or should be apphed without prior knowledge of the system. Impedance spectra must be interpreted in the context of a model, be this a simple brick-layer model for a ceramic, or an advanced one based on electrode kinetics. When used in conjunction with electron microscopy, IS provides information about structure, and especially grain boundary structure. The microstructural information and the models derived from this are what make the conclusions of IS unequivocal. 

D. R. Franceschetti, J. R. Macdonald, and R. P. Buck [1991] Interpretation of Finite-Length-Warburg-Type Impedances in Supported and Unsupported Electrochemical Cells with Kinetically Reversible Electrodes,... 

However, the relaxation times of the physical processes themselves cannot be observed directly from the measurement data if their impedance contributions overlap in the spectrum. Therefore, the impedance data have to be analyzed with respect to the underlying dynamic processes. The physical interpretation of this kinetic information is the key to predicting fuel-cell properties under different operating conditions and different material configurations and thus to permitting a well-directed improvement of fuel-cell performance. 

Any electrode/solution interface may be characterised by an impedance which is frequently determined by imposing an a.c. current and measuring the potential response, or alternatively applying an a.c. voltage and measuring the current response. The interpretation of this impedance in terms of kinetic parameters requires the assumption of an equivalent circuit whose components will model the mechanism of the electrode reaction (see Chapter 8). The simple electrode reaction, (A.78), may be characterised by a two component, series... 

However, there are still unresolved issues regarding the explanation of the impedance spectra. For example, it is difficult to distinguish the individual contributions from the anode and cathode sides, although it is generally considered that the rapid kinetics and mass transport of the HOR result in a negligible impedance contribution from the anode catalyst layer. In addition, the interpretation of the low-frequency feature can be very sophisticated. 

The second difficulty results from the non-uniform state of the rubbed surface. Behind the slider the sample surface can be laid bare for some time before some new surface layers are rebuilt. The restored surface increases gradually with the distance behind the slider along the sliding track. Even if the first difficulty was already solved and the overall impedance of the rubbed surface is obtained, it can not be used as such to characterize the non-uniform distribution of the electrochemical states behind the slider. However, it is expected that impedance measurement procedures already developed for analyzing non-uniform distributions of surface states and the electrochemical models developed for the interpretation of such measurements (Zhang et al., 1987) could be transferred to tribocorrrosion test conditions. Such a study could allow a localized characterization of dissolution and pessivation kinetics. 

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