Impedance spectra

Introducing the complex notation enables the impedance relationships to be presented as Argand diagrams in both Cartesian and polar co-ordinates (r,rp). The fomier leads to the Nyquist impedance spectrum, where the real impedance is plotted against the imaginary and the latter to the Bode spectrum, where both the modulus of impedance, r, and the phase angle are plotted as a fiinction of the frequency. In AC impedance tire cell is essentially replaced by a suitable model system in which the properties of the interface and the electrolyte are represented by appropriate electrical analogues and the impedance of the cell is then measured over a wide... 

The interfacial phenomena in LiX/PE systems were studied extensively by Scro-sati and co-workers [3, 53, 130]. They found that the high-frequency semicircle in the impedance spectrum of LiC104/ P(EO)8 electrolyte (EO = ethylene oxide),... 

Electrochemical impedance spectroscopy techniques record impedance data as a function of the frequency of an applied signal at a fixed potential. A large frequency range (65 kHz-1 mHz) must be investigated to obtain a complete impedance spectrum. Dowling et al. and Franklin et al. demonstrated that the small signals required for EIS do not adversely affect the numbers, viability, and activity of microorganisms within a biofilm. EIS data may be used to determine the inverse of the corrosion... 

In an analysis of an electrode process, it is useful to obtain the impedance spectrum —the dependence of the impedance on the frequency in the complex plane, or the dependence of Z" on Z, and to analyse it by using suitable equivalent circuits for the given electrode system and electrode process. Figure 5.21 depicts four basic types of impedance spectra and the corresponding equivalent circuits for the capacity of the electrical double layer alone (A), for the capacity of the electrical double layer when the electrolytic cell has an ohmic resistance RB (B), for an electrode with a double-layer capacity CD and simultaneous electrode reaction with polarization resistance Rp(C) and for the same case as C where the ohmic resistance of the cell RB is also included (D). It is obvious from the diagram that the impedance for case A is... 

Figure 6.7 Complex impedance of a polycrystalline ceramic sample (a) representation of the equivalent circuit of a component (b) the impedance spectrum of the equivalent circuit in (a) (c) the impedance spectrum of a typical ceramic sample. Each semicircular arc represents one component with an equivalent circuit as in (a) that at the highest frequency corresponds to the repose of the bulk, that at middle frequencies to the grain boundary response, and that at lowest frequencies to the electrodes.

Typically, the frequency lu of the modulation is varied over a considerable range, and an impedance spectrum Z(lS) recorded. Various electrode processes make different contributions to the total impedance. In many cases it is useful to draw an equivalent circuit consisting of... 

There are several ways to plot the impedance spectrum Z(uj) or Z(u). A common procedure is to plot the absolute value Z of the... 

Figure 4. Impedance spectrum of gold in liquid (278K) and frozen (19 8K) HC104 5.5H20.

A constant phase element (CPE) rather than the ideal capacitance is normally observed in the impedance of electrodes. In the absence of Faradaic reactions, the impedance spectrum deviates from the purely capacitive behavior of the blocking electrode, whereas in the presence of Faradaic reactions, the shape of the impedance spectrum is a depressed arc. The CPE shows... 

Figure 4.16 is the electrochemistry impedance spectrum (EIS) of jamesonite electrode under the conditions of different DDTC concentration, and its EIS parameters are shown in Table 4.2. It follows that ... 

Abstract The flotation mechanism is discussed in the terms of corrosive electrochemistry in this chapter. In corrosion the disolution of minerals is called self-corrosion. And the reaction between reagents and minerals is treated as inhibition of corrosion. The stronger the ability of inhibiting the corrosion of minerals, the stronger the reagents react with minerals. The two major tools implied in the research of electrochemical corrosion are polarization curves and EIS (electrochemistry impedance spectrum). With these tools, pyrite, galena and sphalerite are discussed under different conditions respectively, including interactions between collector with them and the difference of oxidation of minerals in NaOH solution and in lime. And the results obtained from this research are in accordance with those from other conventional research. With this research some new information can be obtained while it is impossible for other methods. 

Keywords corrosive electrochemistry corrosive potential corrosion inhibition polarization curves Electrochemistry Impedance Spectrum... 

In general it will be necessary to measure via impedance measurements using a four electrode cell. A schematic diagram of the cell which would be used for such measurements is shown in Fig. 10.15. The expected behaviour will be as described in Eqn (10.3) except that Warburg impedances can arise from either or both phases. An example of an impedance spectrum of the H2O/PVC interface is shown in Fig. 10.16. The application of a constant overpotential will, in general, lead to a slowly decaying current with time due to the concentration changes which occur in both phases, so that steady state current potential measurements will be of limited use. 

In general, it is necessary to have a reference electrode to separate anode and cathode losses. In this case, the impedance spectrum between reference and either anode or cathode allows one to determine the electrode loss from the nonohmic part of the... 

S. Doerner, T. Schenieder and PR. Hauptmann, Wideband impedance spectrum analyzer for process automation... 

Figure 8 presents the Impedance behavior of polyurethane-painted specimen after 4 hours of Immersion and after 10 days of Immersion. The Impedance spectrum does not show any appreciable variation. Further Information on the behavior of the Tremclad and the Marlnox systems (specimens 25 and 27) for Immersion times upto 10 days Is given In Table IV. The variation In corrosion... 

Another practical matter is the frequency range to be used. One wants this range to be as large as possible so that the chance of discovering information-giving types of behavior (which may show up in various frequency ranges in the impedance spectrum) is increased. 

The relevance of a recorded impedance spectrum is not clear, as is the case for experiments done with instrumental methods. A number of potentially occurring errors can give rise to a distortion (small or large) of the impedance spectrum, with a certain impact on the interpretation of the data and the curves. A method to analyse the obtained impedance spectra makes use of so-called Kramers-Kronig transformations50,51, which are a set of coupled integral equations that describe the relationship between the real and imaginary part of the impedance. For impedance Z ... 

Figure 15. Impedance spectrum of 10 mol% Y2C>3-doped zirconia according to Ref.96 The rhs semicircle represents the grain boundary impedance. Reprinted from S.P.S. Badwal, Solid State Ionics 76 (1995), 67-80. Copyright 1995 with permission from Elsevier.

Figure 37. The impedance spectrum of the cell Pt Ag2Te Pt displays the stoichiometry polarization (200°C, fine composition set up by Coulometric titration). The transition from a straight 45° line to a semicircle, before the maximum frequency, corresponds to the theoretical treatment given in Section III.3.227 Reprinted from R. Andreaus and W. Sitte, J. Electrochem. Soc., 144 (1997) 1040-1044. Copyright 1997 with permission from The Electrochemical Society, Inc.

Figure 39. The complete impedance spectrum of a mixed conductor contacted by ion-blocking electrodes.3,15 Regarding signal 3 The dashed curve corresponds to the heuristic approach (Eq. (64)), the straight line to the solution of the diffusion law with respect to the detailed behavior around the maximum see Figure 37. Figure 39 is the translation of Figure 38 into the frequency domain. Reprinted from J. Maier, Z. Phys. Chem. NF, (1984) 191-215. Copyright 1984 with permission from Oldenbourg Verlagsgruppe.

From the quantitative coincidence of the impedance spectrum experimentally measured with that theoretically calculated with Eq. (38) as depicted in Figure 10, they suggested that such non-ideal... 

Figure 10. Nyquist plot of the impedance spectrum experimentally measured on the ACFCE at an applied potential of 0.1 V (vs. SCE) in a 30 wt % H2SO4 solution. Dotted and solid lines represent the impedance spectra theoretically calculated based upon the transmission line model (TLM) in consideration of pore size distribution (PSD) and pore length distribution (PLD), respectively. Reprinted with permission from G. -J. Lee, S. -I. Pyun, and C. -H. Kim, J. Solid State Electrochem., 8 (2004) 110. Copyright 2003, with kind permission of Springer Science and Business Media.

Impedance spectroscopy has been extensively used to characterize carbon, electrode, and capacitor properties [27,48,49], From the frequency impedance spectrum shape, it is possible to understand the physical origins of the observed characteristics, especially the different factors contributing to the series resistance. 

The capacitance and the series resistance have values which are not constant over the frequency spectrum. The performances may be determined with an impedance spectrum analyzer [70], To take into account the voltage, the temperature, and the frequency dependencies, a simple equivalent electrical circuit has been developed (Figure 11.10). It is a combination of de Levie frequency model and Zubieta voltage model with the addition of a function to consider the temperature dependency. 

Constable, P. D., Smith, G. W., Rottinghaus, G. E., Tumbleson, M. E., and Haschek, W. M. (2003). Fumonisin-induced blockade of ceramide synthase in sphingolipid biosynthetic pathway alters aortic input impedance spectrum of pigs. Am. J. Phusiol. Heart Circ. Physiol. 284(6), H2034 2044. 

Fig. 8. Impedance spectrum calculated for a cubic sample (size L = 1 cm) with a linear, one-dimensional conductivity gradient Ubuik = 10 6 S cm-1 + (1 — x/L) 2 1CT5 S cm-1. Ohmic/ reversible electrodes are assumed.

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