Impedance response electrode

The CPE appears to arise solely from roughening of the surface by the corrosion process. This was verified with IS experiments on iron and several steels in 15% HC1 at 25°C. The electrodes were polished with alumina and maintained at 150 mV cathodic of the rest potential. Complex plane plots of the impedance responses were nearperfect semi-circles centered on the V axis. Analyses via EQIVCT using the Rq+P/R circuit, gave rise to n-values of the CPE in excess of 0.93 in all cases and remained constant throughout the tests. 

Figure 3.5 [36], For the 02 reduction reaction on freshly prepared LSM electrodes, the initial polarization losses are very high and decrease significantly with the cathodic polarization/current passage (see Figure 3.5b). Consistent with the polarization potential, the impedance responses at open circuit decrease rapidly with the application of the cathodic current passage. For example, the initial electrode polarization resistance, RE, is 6.2 Qcm2 and after cathodic current treatment for 15 min RK is reduced to 0.7 Qcm2 see Figure 3.5 (a). The reduction in the electrode polarization resistance is substantial. The analysis of the impedance responses as a function of the cathodic current passage indicates that the effect of the cathodic polarization is primarily on the reduction in the low-frequency impedance [10]. Such activation effect of cathodic polarization/current on the electrochemical activity of the cathodes was also reported on LSM/YSZ composite electrodes [56-58], Nevertheless, the magnitude of the activation effect on the composite electrodes is relatively small.

Here j is the imaginary unit, co is the angular frequency, and C is the capacitance. For solid electrodes, however, the impedance response deviates from a purely capacitive one and the empirical equation should be used... 

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. 

As expected, the impedance responses obtained in practice do not fully match that of the model of Fig. 9.13. However, as shown by the typical case of Fig. 9.14 which illustrates the response obtained for a 5 mol% ClO -doped polypyrrole electrode in contact with a LiC104-propylene carbonate solution (Panero et al, 1989), the trend is still reasonably close enough to the idealised one to allow (possibly with the help of fitting programmes) the determination of the relevant kinetics parameters, such as the charge transfer resistance, the double-layer capacitance and the diffusion coefficient. 

Fig. 9.14 The ac impedance response of a Q04-doped polypyrrole electrode over a frequency range extending from 0.006 Hz to 6.5 kHz.

Figure 25. Adler s ID macrohomogeneous model for the impedance response of a porous mixed conducting electrode. Oxygen reduction is viewed as a homogeneous conversion of electronic to ionic current within the porous electrode matrix, occurring primarily within a distance A from the electrode/electrolyte interface (utilization region). (Adapted with permission from ref 28. Copyright 1998 Elsevier.)...

A result of significant interest in this discussion is that of Jiang and Love, who examined the effects of acid treatment (as well as polarization) on the performance of A-site-deficient porous LSM on YSZ at 900 °C in air (Figure 43). Consistent with prior studies, they showed that cathodic polarization substantially reduces the low-frequency portion of the impedance response at zero bias. They then studied an identical electrode that had been etched in 1 M HCl for 15 min at room temperature prior to testing. The acid-etched cell had a much smaller impedance to start with, nearly identical to that of an unetched cell that had been polarized for several hours. Cathodic polarization of the etched cell yielded little additional benefit. Again, it was only the low-frequency portion of the impedance that was reduced by acid etching. 

Figure 53. Idealized half-cell response of a thin solid electrolyte cell, (a) Cell geometry including working electrodes A and B and reference electrode (s). (b) Equivalent circuit model for the cell in a, where the electrolyte and two electrodes have area-specific resistances and capacitances as indicated, (c) Total cell and half-cell impedance responses, calculated assuming the reference electrode remains equipotential with a planar surface located somewhere in the middle of the active region, halfway between the two working electrodes, as shown in a.

Rogozhnikov [95] has analyzed the impedance response of an Ag electrode in cyanide solutions. The impedance spectra have shown time evolution of the surface blocking. Time evolution of the active Ag electrode area after immersion in CN containing solutions has been analyzed by Baltrunas et al. [96]. A time of20-60 s was required for settling down the blocking (dependent also on CN concentration). 

At the present time, the theory of electrochemical impedance of electrodes with distributed potentials is not yet completed, and algorithms of parametrical and structural identification procedures are not available. In addition, the interpretation of the results is very complicated. For this reason, in this work we analyzed only the frequency characteristics of impedance s components in the modified electrode system. As a result, we obtained a set of response peculiarities in the frequency range under investigation. Rather low frequency dispersion was observed in a solution containing a ferri-ferrocyanide system for both active (Fig.3, curve 2) and reactive (Fig.4, curve 3) components. In our opinion, this fact confirms that the independent on frequency resistance of charge transfer determines the main contribution to the impedance. 

Figure 57. In the case of current constriction induced by a partially contacted metal electrode (shown by electrical potential lines in the inset, contact in the center, separation by an air gap otherwise) the impedance response ideally consists of two semicircles. At high frequencies the air gap (cf. distance between curved electrode and plane surface) becomes dielectrically permeable.286 Reprinted from J. Fleig and J. Maier, Electrochim. Acta, 41 (1996), 1003-1009. Copyright 1996 with permission from Elsevier.

That is, in the specific case of electrochemical impedance spectroscopy (EIS), the steady, periodic linear response of a cell to a sinusoidal current or voltage perturbation is measured and analyzed in terms of gain and phase shift as a function of frequency, to, where the results are expressed in terms of the impedance, Z. In this regard, the impedance response of an electrode or a battery is given by... 

Figure 6.1. Impedance spectra at several electrode potentials for H2/02 PEFCs with 30 wt% Pt/C, 0.4 mg Pt/cm2 and 0.7 mg Nafion /cm2 electrodes, Nafion 117 membrane at T = 25°C and atmospheric gas pressure a full range of frequency (0.05 Hz to 10 kHz) b details of the high-frequency region (o) 0.925 V, (A) 0.9 V, (V) 0.875 V, and (+) 0.65 V [4], (Reprinted from Electrochimica Acta, 43(24), Paganin VA, Oliveira CLF, Ticianelli EA, Springer TE, Gonzalez ER. Modelistic interpretation of the impedance response of a polymer electrolyte fuel cell, 3761-6, 1998, with permission from Elsevier and the authors.)...

To increase fundamental knowledge about ionic resistance, it is important to develop a methodology to experimentally isolate the contributions of the various cell components. Electrochemical impedance spectroscopy has been widely used by Pickup s research group to study the capacitance and ion conductivity of fuel cell catalyst layers [24-27] they performed impedance experiments under a nitrogen atmosphere, which simplified the impedance response of the electrode. Saab et al. [28] also presented a method to extract ohmic resistance, CL electrolyte resistance, and double-layer capacitance from impedance spectra using both the H2/02 and H2/N2 feed gases. In this section, we will focus on the work by Pickup et al. on using EIS to obtain ionic conductivity information from operational catalyst layers. 

Fig. 16. Nyquist plot of the impedance response of an electrode. The equivalent electrical circuit is shown above the plot. Ra is the solution resistance, Cp the electrode/solution interface capacitance, and Rp the electrode/solution interface polarization resistance.

Access to powerful computers and to commercial partial-differential-equation (PDE) solvers has facilitated modeling of the impedance response of electrodes exhibiting distributions of reactivity. Use of these tools, coupled with development of localized impedance measurements, has introduced a renewed emphasis on the study of heterogenous surfaces. This coupling provides a nice example for the integration of experiment, modeling, and error analysis described in Chapter 23. 

The impedance response of electrochemical systems is often normalized to the effective area of the electrode. Such a normalization applies only if the effective area can be well defined, and is not used in this chapter on the impedance response of electrical circuits. The capacitance used in this chapter, therefore, has units of F rather than F/cm, the resistance has units of O rather than fl cm, and the inductance has units of H rather than H cm. ... 

The impedance response can be strongly influenced by the distribution of current and potential at the electrode under study. Some general guidelines can be established to help determine conditions under which a nonuniform distribution can arise. 

A schematic representation of the electrode-electrolyte interface is given as Figure 7.10, where the block used to represent the local Ohmic impedance reflects the complex character of the Ohmic contribution to the local impedance response. The impedance definitions presented in Table 7.2 were proposed by Huang et al. ° for local impedance variables. These differ in the potential and current used to calculate the impedance. To avoid confusion with local impedance values, the symbol y is used to designate the axial position in cylindrical coordinates. 

Figure 8.1 Schematic illustration of cell configurations employing reference electrodes to isolate the impedance response of working electrodes and membranes, a) 2-electrode b) 3-electrode and c) 4-electrode cell design.

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... 

Example 8.3 Influence of Capacitance on Linearity While the capacitance for a coated surface may be independent of applied potential, as shown in Figure 5.12, the capacitance for a bare electrode may be a function cf potential. Explore the influence of a potential dependent capacitance on the linearity of the impedance response. 

Surface films commonly form in electrochemical studies, and these films can influence the impedance response. The electrode coated with an inert porous layer may be considered to be an extension of the case described in Section 9.2.2 in which the film is thicker and the fractional surface coverage approaches unity. 

Many electrochemical reactions are influenced by the rate of transport of reactants to the electrode surface. Formal treatment of the impedance response for such a system requires both the kinetic analysis presented in this chapter and consideration of mass transfer as presented in Chapter 11. 

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