High-frequency electrochemical impedance

Fig. 8 High-frequency electrochemical impedance spectrum, obtained at an illuminated n-CaAs electrode in a 0.1 M H2SO4 aqueous solution. Bias potential - 600 mV versus SCE (i.e. potential region A) limiting photocurrent density 380 pA cm . The resistance R- equals 71 2 cm, that is, 1.06 x kT/ejpu.

For electrochemical systems, however, the Bode representation has drawbacks. The influence of electroljde resistance confoimds the use of phase angle plots such as shown in Figure 16.2(b) to estimate characteristic frequencies. In addition. Figure 16.2(b) shows that the current and potential are in phase at high frequencies wherecis, at high frequencies, the current and surface potential are exactly out of phase. This result is seen because, at high frequencies, the impedance of the surface tends toward zero, and the Ohmic resistance dominates the impedance response. The electrolyte resistance, then, obscures the behavior of the electrode surface in the phase angle plots. 

An EG G PARC 273 Potentiostat/Galvanostat was used in both the electrolysis and the CV experiments, coupled with an HP 7044B X/Y recorder. A Solartron 1255 HF Frequency Response Analyzer and a Solartron 1286 Electrochemical Interface were employed for the a.c. impedance measurements, using frequencies from 0.1 to 65 kHz and a 10 mV a.c. amplitude (effective) at either the open circuit potential (OCP) or at various applied potentials. As the RE can introduce a time delay at high frequencies, observed as a phase shift owing to its resistance and capacitance characteristics, an additional Pt wire electrode was placed in the cell and was connected via a 6.8 pF capacitor to the RE lead [32-34]. 

Results are similar for films deposited on YSZ however, there appears to be a difference between films deposited on ceria vs YSZ in terms of interfacial electrochemical resistance. As shown previously in Figure 6c, LSC films on YSZ often exhibit a second high-frequency impedance associated with oxygen-ion exchange across the electrode/electrolyte interface.That this difference is associated with the solid—solid interface has been confirmed by Mims and co-workers using isotope-exchange methods. As discussed in greater detail in sections 6.1—6.3, this interfacial resistance appears to result from a reaction between the electrode and electrolyte, sometimes detected as a secondary phase at the interface. 

In studying a system by a nonlinear impedance method, use is made of the system s nonlinear characteristics. A variant of the nonlinear impedance method called the amplitude demodulation method was first applied in the electrochemistry of semiconductors, in particular to diamond electrodes, in [83] (see the quoted paper for the theory of the method and the experimental set-up). A perturbing current signal of a high frequency oo, modulated in amplitude at a low frequency 2, is applied to electrochemical cell the demodulated low-frequency voltage signal is to be measured at the frequency 2. In accordance with the theory of the method [83], under the condition of formation of a depletion layer in a semiconductor electrode, the in-phase component of the cell response Re h is inversely proportional to d(C 2)/dE. Hence, for the acceptor concentration in the semiconductor we have [compare Eq. (1)] ... 

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). 

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... 

Any electrochemical interface (or cell) can be described in terms of an electric circuit, which is a combination of resistances, capacitances, and complex impedances (and inductances, in the case of very high frequencies). If such an electric circuit produces the same response as the electrochemical interface (or cell) does when the same excitation signal is imposed, it is called the equivalent electric circuit of the electrochemical interface (or cell). The equivalent circuit should be as simple as possible to represent the system targeted. 

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.)...

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