Differential Impedance Analysis

Stoynov and coworkers [28, 390-398] proposed another method for the determination of the distribution of parameters called differential impedance analysis (DIA). It is based on the application of a simple three parameter / i(/ 2C) model [a so-called local operating model (LOM)] to the impedance spectra. At each frequency three parameters Z, Z , and co are known but they are not sufficient to determine the parameters / i, / 2 and C. Therefore, two more parameters are added dZ /d logta and dZ /d logto. This LOM is swept across the experimental impedance data producing series of the parameters at each frequency. The impedance of the LOM is 

An example of the application of DIA to the impedance analysis of SOFCs is shown in Fig. 8.23. 

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Z. Stoynov and D. Vladikova, Differential Impedance Analysis, Akademicno Izdatelstvo, Sofia, Bulgaria, 2005. 

Stoynov Z, Vladikova D (2005) Differential impedance analysis. Marin Drinov Academic Publishing House, Bulgaria... 

Z. Sto5mov, "Differential Impedance Analysis - An Insight into the Experimental Data," Polish Journal of Chemistry, 71 (1997) 1204-1210. 

Vladikova, D. et al., Differential impedance analysis of single crystal and polycrystalline yttria stabilized zirconia, Electroch. Acta 51 (2006) 1611-1621. 

Electrochemical impedance spectroscopy is usually presented in electrochemistry handbooks [12-22], although such presentations are usually quite brief. There are few books on impedance in English [3, 23-26], one in Russian [27], one on differential impedance analysis [28], and many chapters on specific topics [29-72]. The first book [23] on the topic was edited by Macdonald and centered on solid materials the second edition [24] by Macdonald and Barsoukov was enlarged by including other applications. Recently, three new books, by Orazem and Tribollet [3], by Yuan et al. [26] on proton exchange membrane fuel cells (PEM EC), and by Lvovich [25], have been published, while that by Stoynov et al. [27] was never translated into English. A third edition of the book by Macdonald and Barsoukov is in preparation. However, not all aspects of EIS are presented, and these books are not complete in the presentation of their applications. Plenty of review articles on different aspects of impedance and its applications have been published however, they are very specific and can usually be used only by readers who aheady know the basics of this technique. A Scopus search for electrochemical impedance spectroscopy to the end of 2012 comes up with 18,000 papers, most of them since 1996. 

Polar Cell Systems for Membrane Transport Studies Direct current electrical measurement in epithelia steady-state and transient analysis, 171, 607 impedance analysis in tight epithelia, 171, 628 electrical impedance analysis of leaky epithelia theory, techniques, and leak artifact problems, 171, 642 patch-clamp experiments in epithelia activation by hormones or neurotransmitters, 171, 663 ionic permeation mechanisms in epithelia biionic potentials, dilution potentials, conductances, and streaming potentials, 171, 678 use of ionophores in epithelia characterizing membrane properties, 171, 715 cultures as epithelial models porous-bottom culture dishes for studying transport and differentiation, 171, 736 volume regulation in epithelia experimental approaches, 171, 744 scanning electrode localization of transport pathways in epithelial tissues, 171, 792. 

Enhanced sensitivity in detection of events can be obtained by using the differential plot dZJdv against log k To demonstrate the kind of results obtained from impedance analysis, Fig. 14.35 shows the impedance variation in the hippocampus of a cat s brain when the stimulus is changed. 

Figure 3 Differential thermal analysis (DTA) and impedance (1000 Hz - Z sin (p) of a 2 p. 100 solution of Cl Na in water during controlled freezing.

Figure 7 Differential thermal analysis and impedance (1000 Hz) of pure glycerol.

Figure 15 Differential thermal analysis/1000 hz impedance/thermoluminescence after gamma irradiation at -196°C (30 kGy) of a 50/50 mixture of glycerol/H O plus 10 p. 1000 ClNa. A more complex system containing an electrolyte (Cl Na) displays a quite analogous behavior to the one of pure glycerol Z sin (p starts to drop while the vitreous transformation is taking place (-114°C) and quite abruptly again after the devitrification peak (-100°C). This second fall is concomitant with the thermoluminescence peak (-95°C).

An alternate mechanism has recently been considered for carbohydrates and polyalcohols (129,130). These additives might alter the state of liquid water so as to impede ice-crystal formation. This view finds some support from data obtained by differential thermal analysis at low temperatures (130). 

Important plasma diagnostics include Langmuir probes, optical emission spectroscopy, laser induced fluorescence, absorption spectroscopy, mass spectrometry, ion flux and energy analysis, and plasma impedance analysis. A plasma reactor equipped with several of these diagnostics is shown in Fig. 51 [35, 160]. A capacitively coupled plasma is sustained between the parallel plates of the upper (etching) chamber. The lower (analysis) chamber is differentially pumped and communicates with the etching chamber through a pinhole on the lower electrode. 

Depending upon the products, there might be very narrow margins to that exercise and the endpoint temperatures, velocities of cooling, and rewarming need to be known very accurately by previous laboratory determinations such as differential thermal analysis (DTA) or differential scanning calorimetry (DSC), low temperature electric impedance measurements, velocity of crystallization in the supercooled state, etc. 

The resulting dependence of Z" on Z (Nyquist diagram) is involved but for values of Rp that are not too small it has the form of a semicircle with diameter Rp which continues as a straight line with a slope of unity at lower frequencies (higher values of Z and Z"). Analysis of the impedance diagram then yields the polarization resistance (and thus also the exchange current), the differential capacity of the electrode and the resistance of the electrolyte. 

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