Impedance data analysis

Digitizing the waveforms at 5 ns increments over nearly 6 decades yields in excess of 260,000 data points. This has two drawbacks. One is that it is simply inconvenient the excessive number of data points is cumbersome and impedes data analysis and display. The second drawback has a more important consequence. Digitizing a long time span in small intervals leads to unnecessary point density at longer times. For example, at t — 25 ns, the... 

Impedance Data Analysis 16.2.2.1 Evaluation of Data Quality... 

The author would like to thank Thomas Springer (Los Alamos) for many contributions to the mathematical modelling aspects mentioned here, Ruth Sherman (Los Alamos) who gathered much experimental data on RuOj, Judith Rishpon (University of Tel Aviv) who made the quartz crystal microbalance measurements of Fig. 14, and Bernard Boukamp (University of Twente) who has allowed the author to use his non-linear least-squared error fitting routines for impedance data analysis. 

Measurements of electrochemical noise and AC impedance of coated metal substrates are under development (indeed have been used for quite some time). These measurements relate to the corrosion protection afforded by the coating and can, in principle, be made continuously. The complexity of the electrochemical reactions require sophisticated data analysis for extraction of useful information and relationships. 

The impedance data were fitted to candidate electrical circuits using the non-linear weighted least-squares fitting program "EQIVCT" developed by Boukamp ( ). Graphical analysis was utilized to furnish reasonable first guesses of the circuit parameters for input to EQIVCT. 

The technique of constructing an equivalent circuit for impedance analysis represents the exception to the general rule that a chosen model can be almost certain to be correct. It is all too easy to compile an equivalent circuit which fits the impedance data, but is altogether wrong. In fact, many practitioners would say that impedance studies are so susceptible to this fitting to a bogus model that another technique should always be applied as a form of validation . It is much more unlikely for two techniques to fit a particular model, and the latter still be wrong ... 

Surface path at low overpotential. Qualitative and quantitative analysis of impedance data, tracer studies, as well as various studies of thin-film electrodes suggest that under low-overpotential LSM operates primarily via a surface-mediated mechanism (like Pt). This conclusion appears to be consistent with the properties of LSM, which is fully oxygen stoichiometric under ambient Pq. However, little is known about how far the active region of reduction extends beyond the solid/solid interface (via surface diffusion) or the relative importance of chemical steps (on the LSM surface) vs electrochemical kinetics at the solid/solid interface. 

It can be seen that for severely degraded specimens, both the harmonic analysis and Impedance techniques are capable of detecting the presence of gross corrosion. The harmonics method provides a reasonable estimation of the corrosion rate when the Impedance data exhibits Warburg type behaviour. For less severely degraded specimens, especially those exhibiting blister attack, the Impedance method Is not as successful as the harmonic analysis technique. 

The capacitance-potential dependences of Cd(OOOl) in dilute solutions of Cl04, N02, and NOs" were also studied [6]. A weak specific adsorption of anions increasing in the order Cl04 < N02 < N03 was observed. The adsorption of halides on the Cd(OOOl) single crystal electrode was studied [7], and was found to increase in the sequence Cl < Br < 1 [8]. Analysis of the impedance data does not point to the specific adsorption of Cl ions, and shows that the surface excess (T) of halide ions changes with potential and increases from Br to 1 (Fig. 1) [7]... 

DOPC) monolayer-coated mercury electrodes in contact with different electrolytes, using electrochemical impedance spectroscopy and a multivariate analysis of impedance data. Rueda et al. [181] have analyzed impedance spectra of DOPC-coated mercury electrodes. 

The quantitative analysis of conventionally obtained grain boundary impedance data is problematic if grain boundary properties strongly vary from boundary to bound-... 

The impedance spectroscopy is most promising for electrochemical in situ characterization. Many papers have been devoted to the AB5 type MH electrode impedance analysis [15-17]. Prepared pellets with different additives were used for electrochemical measurements and comparing. Experimental data are typically represented by one to three semicircles with a tail at low frequencies. These could be described to the complex structure of the MH electrode, both a chemical structure and porosity [18, 19] and it is also related to the contact between a binder and alloy particles [20]. The author thinks that it is independent from the used electrolyte, the mass of the electrode powder and the preparing procedure of electrode. However, in our case the data accuracy at high frequencies is lower in comparison with the medium frequency region. In the case, the dependence on investigated parameters is small. In Figures 3-5, the electrochemical impedance data are shown as a function of applied potential (1 = -0.35V, 2 = -0.50V and 3 = -0.75V). 

The most commonly used method for the electrochemical studies of Li electrodes was impedance spectroscopy (EIS). Table 5 provides a partial listing of papers published during the past two decades dealing with the EIS of Li electrodes. However, the following precautions must be taken into account in the application of EIS to Li electrochemistry and the data analysis ... 

The last comment relates to the data analysis and the choice of appropriate models for impedance spectra. As shown by Orazem et al. [241], each single impedance spectrum can be fitted by a number of equivalent circuit analogs. Hence, the choice of a model has to be based on... 

During deposition, poly(vinylferrocene) films are non-rigid. Analysis of crystal impedance data yields shear moduli that are typical of a rubbery material this contrasts with the rigid film characteristics observed in aqueous media. 

Figure 35 Bode magnitude plot for a leads unconnected measurement with a commercial electrochemical impedance system. Analysis of the data enable an estimate of the potentiostat input impedance (2 X 109 Q) and the stray capacitance (2 X 10 1° F).

The interpretation of measured data for Z(oi) is carried out by their comparison with predictions of a theoretical model based either on the (analytical or numerical) integration of coupled charge-transport equations in bulk phases, relations for the interfacial charging and the charge transfer across interfaces, balance equations, etc. Another way of interpretation is to use an -> equivalent circuit, whose choice is mostly heuristic. Then, its parameters are determined from the best fitting of theoretically calculated impedance plots to experimental ones and the results of this analysis are accepted if the deviation is sufficiently small. This analysis is performed for each set of impedance data, Z(co), measured for different values of external parameters of the system bias potentials, bulk concentrations, temperature... The equivalent circuit is considered as appropriate for this system if the parameters of the elements of the circuit show the expected dependencies on the external parameters. 

The traditional way is to measure the impedance curve, Z(co), point-after-point, i.e., by measuring the response to each individual sinusoidal perturbation with a frequency, to. Recently, nonconventional approaches to measure the impedance function, Z(a>), have been developed based on the simultaneous imposition of a set of various sinusoidal harmonics, or noise, or a small-amplitude potential step etc, with subsequent Fourier- and Laplace transform data analysis. The self-consistency of the measured spectra is tested with the use of the Kramers-Kronig transformations [iii, iv] whose violation testifies in favor of a non-steady state character of the studied system (e.g., in corrosion). An alternative development is in the area of impedance spectroscopy for nonstationary systems in which the properties of the system change with time. 

The selection of impedance or admittance for presentation of experimental results and data analysis is dependent on the type of equivalent electric circuit. For instance, for the analysis of -> charge-transfer processes and -> double-layer charging, the impedance may be preferred, while for the resonance circuits (e.g., in piezometric systems) the admittance may offer advantages. 

In order to understand electrochemical impedance spectroscopy (EIS), we first need to learn and understand the principles of electronics. In this chapter, we will introduce the basic electric circuit theories, including the behaviours of circuit elements in direct current (DC) and alternating current (AC) circuits, complex algebra, electrical impedance, as well as network analysis. These electric circuit theories lay a solid foundation for understanding and practising EIS measurements and data analysis. 

EIS data analysis is commonly carried out by fitting it to an equivalent electric circuit model. An equivalent circuit model is a combination of resistances, capacitances, and/or inductances, as well as a few specialized electrochemical elements (such as Warburg diffusion elements and constant phase elements), which produces the same response as the electrochemical system does when the same excitation signal is imposed. Equivalent circuit models can be partially or completely empirical. In the model, each circuit component comes from a physical process in the electrochemical cell and has a characteristic impedance behaviour. The shape of the model s impedance spectrum is controlled by the style of electrical elements in the model and the interconnections between them (series or parallel combinations). The size of each feature in the spectrum is controlled by the circuit elements parameters. 

However, although powerful numerical analysis software, e.g., Zview, is available to fit the spectra and give the best values for equivalent circuit parameters, analysis of the impedance data can still be troublesome, because specialized electrochemical processes such as Warburg diffusion or adsorption also contribute to the impedance, further complicating the situation. To set up a suitable model, one requires a basic knowledge of the cell being studied and a fundamental understanding of the behaviour of cell elements. 

Urquidi-Macdonald M, Real MS, Macdonald DD (1986) Application of Kramers-Kronig transforms in the analysis of electrochemical impedance data. J Electrochem Soc 133(10) 2018-24... 

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