Complex impedance spectrum

F/gwre 5 JO, (a) Complex impedance spectra (Nyquist plots) of the CH4,02) Pd YSZ system at different Pd catalyst potentials. Open circuit potential U R =-0.13 V. Dependence on catalyst potential of the individual capacitances, C4i (b) and of the corresponding frequencies, fmii, at maximum absolute negative part of impedance (c).54 Reprinted with permission from Elsevier Science. 

Transmission line — This term is related to a more general concept of electric -> equivalent circuits used frequently for interpretation of experimental data for complex impedance spectra (-> electrochemical impedance spectroscopy). While the complex -> impedance, Z, at a fixed frequency can always by obtained as a series or parallel combinations of two basic elements, a resistance and a capacitance, it is a much more compli-... 

Figure 20 Complex impedance spectra (Nyquist plots) of the CH4, O2, PdjYSZ system at different Pd catalyst potentials. Open-circuit potential = 0.13 V.

The complex impedance spectra revealed that the resistance or real part ofthe impedance decreased as the SiC whisker content increased. A SiC whisker orientation effect was also found, with lower impedance being observed for samples measured perpendicular versus parallel to the hot-pressing direction. 

The relaxation time constant, Xq, represents the minimum time required to discharge all the energy from an ES with an efficiency of greater than 50% [60], which can be determined from the complex impedance spectra by [96]... 

Figure 3.5 Complex impedance spectra of MEEP-(LiAlCl4)n at room temperature. Frequency range=6 Hz-100 kHz.

Figure 3.7 Complex impedance spectra of MEEP/PEO-(LiC104)o.i3 at several temperatures. Frequency range = 6 Hz-100 kHz.

The use of a frequency domain transformation first described by Kramers [1929] and Kronig [1926] offers a relatively simple method of obtaining complex impedance spectra using one or two ac multimeters. More important, retrospective use of Kramers-Kronig (KK) transforms allows a check to be made on the validity of an impedance data set obtained for linear system over a wide range of frequencies. Macdonald and Urquidi-Macdonald [1985] have applied this technique to electrochemical and corrosion impedance systems. 

Fig. 8 Complex impedance spectra at 400°C of the various 8YSZ specimens sintered at (a), (b), (c) 1500 and (d), (e), (f) 1600 C. (8Y 8YSZ, BM Ball Milling, UD-Ultrasonic Dispersion, IA03 the addition of 1 mol% of AI2O3 sized 0.3 pm, IAiq the addition of 1 mol% of AI2O3 sized 10 pm, 1 AsoP the addition of 1 mol% of AI2O3 sol, 1200(40)-1500 heat treatment at 1200°C for 40 h prior to sintering at 1500°C for 4h) The semicircles indicated by arrows mean the grain-boundary contributions, according to [22].

Fig. 15 The complex impedance spectra of l-mol%-Al2O3(size=0.3pm)-doped 15CSZ specimens sintered at 1600°C for 4h. 1/20 of original sample thickness (t) was removed successively from both outer regions and the corresponding impedance was measured at 450"C in air, according to [66].

Figure 2. Complex impedance spectra of siloxane 30) LiS03CF3 15% with a) Pt and b) Li electrodes.

M. Itagaki, Y Hatada, I. Shitanda, K. Watanabe, Complex impedance spectra of porous electrode with fractal structure, Electrochim. Acta, 2010,55, pp. 6255-6262. 

Figure 13 shows typical complex impedance spectra of the three types of polymer electrolytes sandwiched between lithium electrodes at an oscillation level of 0.5 V. The profiles of the spectra were two neighboring arcs. The low-frequency arcs (right-hand side arcs) and the high-frequency arcs (left-hand side arcs) corresponded to the loci of the charge transfer impedance and the bulk electrolyte impedance, respectively. The bulk resistance (/ .0 and the charge transfer resistance (R ) are shown in Fig. 13. The ionic conductivities at 50°C for the polymer electrolytes (1), (2), and (3) were approximately 10 to 10 S cm (depending on the LiC104 concentration (see Table 1), 10 S cm, and 10 S cm , respectively. The values, corresponding to the electrode reaction, were about lO" Cl, irrespective of the kinds of polymer electrolytes. These values were similar to those found in the poly(propylene oxide) networks with dissolved lithium salts [93] and to those found in the poly(ethylene succinate) with dissolved lithium salts [88,94], but were considerably higher than those found in poly(p-propiolactone)-LiC104 complexes [95].

Figures 14-16 show the time dependence of the polarization current at different potentials for the polymer electrolytes (1), (2), and (3), respectively. The decrease in the polarization current with time became pronounced with increasing potential. However, the decrease in the current of (2), which has the fixed anion sites, was considerably lower than those of the others [(1) and (3)]. The stability of the polarization current has been observed in other polyelectrolyte-type polymers [96]. Because the lithium electrode is a non-blocking electrode for Li ions, but is a blocking electrode for the anions, the decrease seemed to be mainly due to the polarization of the anions. The stability of the polarization current in (2) may be concerned with its structure. Quasi-steady-state current was observed within 1 h when the applied potentials were lower than 0.1 V for (1) and (3), and 0.5 V for (2). The steady-state current values were lower than the current values calculated from / h + Re found in the complex impedance spectra for (1) and (3), whereas these current values were consistent with the calculated values from R, + / , for (2).

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