High-frequency electrochemical impedance spectroscopy

Dispersion — Frequency dispersion results from different frequencies propagating at different speeds through a material. For example, in the electrochemical impedance spectroscopy (EIS) of a crevice (or porous) electrode, the solution resistance, the charge transfer resistance, and the capacitance of the electric double layer often vary with position in the crevice (or pore). The impedance displays frequency dispersion in the high frequency range due to variations in the current distribution within the crevice (pore). Additionally, EIS measurements in thin layer cells (such as electro chromic... 

The above formulas may become inapplicable for systems with adsorption processes or/and coupled chemical steps in solution whose characteristic times are comparable with the inverse frequency within the impedance measurement interval. In this case the charge-transfer resistance, Rct, must be replaced by a complex charge-transfer impedance, Zct. Another restriction of this treatment is its assumption of the uniform polarization of the m s interface which requires to ensure a highly symmetrical configuration of the system. Refs. [i] Sluyters-Rehbach M, Sluyters JH (1970) Sine wave methods in the study of electrode processes. In Bard A/ (ed) Electroanalytical chemistry, vol. 4. Marcel Dekker, New York, p 1 [ii] Bard A], Faulkner LR (2001) Electrochemical methods, 2nd edn. Wiley, New York [iii] Retter U, Lohse H (2005) Electrochemical impedance spectroscopy. In Scholz F (ed) Electroanalytical methods. Springer, Berlin, pp 149-166 [iv] Bar-soukov E, Macdonald JR (ed) (2005) Impedance spectroscopy. Wiley, Hoboken... 

Figure 6.24. Expansion of the high-frequency region of Figure 5.4 [24]. (Reprinted from Electrochimica Acta, 50(12), Easton EB, Pickup PG. An electrochemical impedance spectroscopy study of fuel cell electrodes. Electrochim Acta, 2469-74, 2005, with permission from Elsevier and the authors.)...

Figure 6.39. Progression of the high-frequency resistances over time [38], (Reprinted from Journal of Power Sources, 154(2), Hakenjos A, Zobel M, Clausnitzer J, Hebling C. Simultaneous electrochemical impedance spectroscopy of single cells in a PEM fuel cell stack, 360-3, 2006, with permission from Elsevier and the authors.)...

If the series resistance is high and the parallel resistance is low, one faces an adverse experimental situation. In this case, measurements should be conducted over a range of frequencies, with the highest possible accuracy, and the optimum conditions for the experiment should be carefully chosen. Under such conditions, electrochemical impedance spectroscopy apparatus may be indispensable. 

Electrochemical impedance spectroscopy (EIS) analysis of such electrodes is shown in Figure 7.2. At high frequencies, the imaginary part of the impedance tends to zero, whereas at low frequencies it increases sharply, thus approaching the variation of impedance with the frequency expected for a pure capacitor (see Chapter 1). In the intermediate frequencies, a semicircle can be observed, the amplitude of the loop varying with the nature of the activated material. This semicircle can be... 

This operation determines the values of R and C that, in series, behave as the cell does at the measurement frequency. The impedance is measured as a function of the frequency of the ac source. The technique where the cell or electrode impedance is plotted V5. frequency is called electrochemical impedance spectroscopy (EIS). In modem practice, the impedance is usually measured with lock-in amplifiers or frequency-response analyzers, which are faster and more convenient than impedance bridges. Such approaches are introduced in Section 10.8. The job of theory is to interpret the equivalent resistance and capacitance values in terms of interfacial phenomena. The mean potential of the working electrode (the dc potential ) is simply the equilibrium potential determined by the ratio of oxidized and reduced forms of the couple. Measurements can be made at other potentials by preparing additional solutions with different concentration ratios. The faradaic impedance method, including EIS, is capable of high precision and is frequently used for the evaluation of heterogeneous charge-transfer parameters and for studies of double-layer structure. 

To determine numerical values for the different elements of the equivalent circuit they have to be separated, for example, by electrochemical impedance spectroscopy (EIS). Similar to the above-described lock-in measurement a small ac signal of a few mV is superimposed to the electrode potential. The resulting current and its phase shift are then measured as a function of the frequency. Typical impedance spectra of thin oxide films on aluminum are shown in Fig. 17. At high frequencies (10 — lO Hz) the capacitors act as shorts and only the electrolyte resistor determines the impedance, which is typically 10 Ohm for concentrated electrolytes and independent of the electrode. At the lowest frequencies, for example, 10 Hz or below, current flow through the capacitors is impossible and the impedance of the system is given by the sum of the 3 resistors in the current path. The... 

Electrochemical impedance spectroscopy (EIS) provides indirect information about the surface phenomena of all kinds of electrodes [32]. The high-frequency part of impedance spectra of electrodes is usually attributed to surface phenomena such as Li-ion migration through surface films, surface film capacitance, and interfacial charge transfer [33]. However, it should be noted that EES provides very ambiguous information. A special skill, as well as experience, is needed for a reliable assignment of spectral features to the time constants of a complicated electrochentical system such as that of composite electrodes [34]. 

Electrochemical methods are well adapted for characterizing the corrosion behavior of coated metals in solution. Because of the high resistance of organic coatings, ac methods are generally more suited than dc polarization methods. In electrochemical impedance spectroscopy (EIC) one measures the response of the coated electrode to a small amplitude ac perturbation as a function of frequency (Chapter 5). The interpretation of the measured frequency response, in principle, requires a physical model. However, for coated metals useful information is more easily obtained by representing the metal-coating-electrolyte interface by an electrical circuit (equivalent circuit). 

Figure 4.23 High-frequency reference electrode impedance problems in electrochemical impedance spectroscopy. EIS with (A) single reference electrode and (B) double reference electrode (high-frequency shunt).

As discussed in piAL 11], using electrochemical impedance spectroscopy (EIS) to analyze a PEM electrolyzer very clearly reveals slow diffusion dynamics (very low frequencies), and less clearly, fast diffusion dynamics (low/medium frequencies) and very fast diffusion dynamics (high/very high frequencies). As, for our purposes, the truth of this observation is veiy comprehensive, we shall consider it to be general hereafter. 

Electrochemical impedance spectroscopy of a bare zinc specimen and of specimens coated with fluoro-organic compounds F-COOH(C5) and F-COF(C12) at a concentration of 1000 ppm in solution are shown as a Nyquist plot in Fig. 16.1. The plots for the specimens were almost semicireular or slightly semi-oval. The difference in impedance value at high and low frequency, that is, the diameter of this depressed semicircle, corresponds to the resistanee of the coating to corrosion. All specimens... 

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