Impedance response

IZI=J(Z )2+(Z ), and phase angle shift,, vs. f). The electrochemical system is then simulated with an electrical circuit that gives the same impedance response. Ideally this electrical circuit is composed of linear passive elements, e.g. resistors and capacitors, each of which represents individual physicochemical steps in the electrochemical reaction. ... 

This impedance response, in general, is similar to that elicited from an Armstrong electrical circuit, shown in Figure 3, which we represent by Rfl+Cd/(Rt+Ca/Ra). Rfl is identified with the ohmic resistance of the solution, leads, etc. Cj with the double-layer capacitance of the solution/metal interface Rfc with its resistance to charge transfer and Ca and Ra with the capacitance and resistance... 

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. 

Equivalent Electrical Circuit, In spite of the complex nature of the inhibition process, the inhibited systems actually display simple impedance responses. 

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... 

With this extension, the complex impedance response of the CCL could be calculated. The model of impedance amplifies diagnostic capabilities— for example, providing the proton conductance of the CCL from the linear branch of impedance spectra (in Cole-Cole representation) in the high-frequency limit. 

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.

The impedance response with frequency can be closely simulated by the equivalent circuit shown in Figure 27a, where Re, Ra, Cdi, Rad, and Cad represent the resistance or capacitance for the electrolyte solution, charge-transfer, double layer, and adsorbed layer, respectively. An interesting correlation was found between the passivating ability of various anions and the resistances of the two impedance components R and Rad, which are high for LiPFe-and LiBF4-based electrolytes and low for LiTf- or Lilm-based electrolytes. Using the rationale proposed by the authors, the former component (Ret) is... 

Figure 23. Impedance response of a thin film of LSC (x = 0.4) on GDC at 800 °C and Pq = 10 gxm as a function of polarization. (Reprinted with permission from ref 124. Copyright 2002 Electrochemical Society Inc.)...

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). 

Figure 3. Impedance response curves for n-CdSe single crystal in polysulfide (CdSe in NaOH/S=/S/1 1 1 potential +0.5 V, area = 0.15 cm2)...

It must be expected that a polymer material having a much lower conductivity than polyaniline will give impedance responses revealing the effect of the three time constants obtained in the model. The system investigated was chosen for this reason since pECBZ conductivity and redox capacity [94] correspond to DE = 10 7cm2,s 1 and therefore, for the same layer thickness (500nm), the diffusion time constant would be 0.025 s. Electron diffusion should therefore be detectable in the a.c. and even in the EHD frequency domain. 

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... 

The mathematical expressions which describe the impedance of some passive circuits are shown below, where a passive circuit is one that does not generate current or potential [129], In this regard, the impedance response of simple passive circuit elements, such as a pure resistor with resistance R, a pure capacitor with capacitance C, and a pure inductor with inductance L, are given, respectively ... 

Fig. 13.1. Schematic crystal impedance responses, plotted as admittance vs. frequency, for (a) purely gravimetric, (b) purely viscoelastic and (c) simultaneous gravimetric and viscoelastic changes in resonator loading. Curves 1 represent the bare crystal and curves 2 the coated...

Fig. 13.8. Equivalent circuit models for crystal impedance responses (a) transmission line model (b) lumped clement (modified Butterworth van Dyke) model.

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