Impedance imaginary

Figure 2.18 Impedance imaginary part (Z") of the spectra versus frequency for (a) wet PVA and (b) wet and dry PVA. Note a-Relaxation shifts to lower frequencies in dry films. Window inset Relaxation time (t) versus lOOO/r the same behavior has conductivity plot is displayed. Source Reproduced with permission from Gonzilez-Campos JB, Garcia-Carvajal ZY, Prokhorov E, Luna-Barcenas JG, Mendoza-Duarte ME, Lara-Romero J, Del Rio RE, Sanchez IC. J Appl Polym Sci 2012 125 4082 [7]. Copyright 2012 John Wiley and Sons, Inc.

Upper limits of the pore fractality Lower limits of the pore fractality Electrochemical impedance Real impedance Imaginary impedance Impedance of the pore Total impedance of the pores... 

The comparison between measured data and simulated data are good for the imaginary part, but differences appear for the real part. The ratio between simulated data and measured data is about 0.75 for TRIFOU calculation, and 1.33 for the specialised code. Those differences for the real part of the impedance signal can be explained because of the low magnitude of real part compared to imaginary part signal. 

Interpretation of the impedance signal for set 2 (imaginary part function of the probe position along the slot)... 

The variation response of the real and imaginary parts of the impedance in function of the frequency, with or without the sample presence. 

Measurement of real- and imaginary part of a coil complex impedance... 

A common known method to get eddy-current informations about material flaws is the measurement of real- and imaginary part of the complex impedance of a coil in absolute circuit. The measurement, shown in this paper, are done with an impedance analyzer (HP4192A). The device measures the serial inductance L, and the serial resistance Rs of the complex impedance with an auto-balance bridge measurement circuit [5]. 

Two difierent components contribute to impedance the resistive or real component due to resistors and the reactive or imaginary component from AC circuitry elements, such as capacitors, inductors, etc. Unlike the resistive component, the reactive impedance affects not only the magnitude of the AC wave but also its time-... 

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... 

In a transient or an AC circuit we term the sum of resistance, inductance, and capacitance as impedance. Using complex notation, the energy storage properties of inductance and capacitance are represented as purely imaginary quantities, while the resistance is represented as a (+) real quantity. Capacitance is represented as the negative imaginary axis, and current through a pure capacitance is said to lead... 

Nyquist Plot a graph of the frequency response of an electrode in which the imaginary component of the impedance is plotted as a function of the real component for a range of frequencies. 

The technique of AC Impedance Spectroscopy is one of the most commonly used techniques in electrochemistry, both aqueous and solid.49 A small amplitude AC voltage of frequency f is applied between the working and reference electrode, superimposed to the catalyst potential Uwr, and both the real (ZRe) and imaginary (Zim) part of the impedance Z (=dUwR/dI=ZRc+iZim)9 10 are obtained as a function of f (Bode plot, Fig. 5.29a). Upon crossplotting Z m vs ZRe, a Nyquist plot is obtained (Fig. 5.29b). One can also obtain Nyquist plots for various imposed Uwr values as shown in subsequent figures. 

In particular, the coupling between the ion transfer and ion adsorption process has serious consequences for the evaluation of the differential capacity or the kinetic parameters from the impedance data [55]. This is the case, e.g., of the interface between two immiscible electrolyte solutions each containing a transferable ion, which adsorbs specifically on both sides of the interface. In general, the separation of the real and the imaginary terms in the complex impedance of such an ITIES is not straightforward, and the interpretation of the impedance in terms of the Randles-type equivalent circuit is not appropriate [54]. More transparent expressions are obtained when the effect of either the potential difference or the ion concentration on the specific ion adsorption is negli-... 

Since the ion transfer is a rather fast process, the faradaic impedance Zj can be replaced by the Warburg impedance Zfy corresponding to the diffusion-controlled process. Provided that the Randles equivalent circuit represents the plausible model, the real Z and the imaginary Z" components of the complex impedance Z = Z —jZ " [/ = (—1) ] are given by [60]... 

Equivalent Circuit Analysis. IS measurements yield values of V and Z the real and imaginary components of the impedance, as a function of f, the AC frequency. The data are usually displayed as Nvauist plots (Z, vs. Z ) or Bode plots (impedance modulus,... 

This circuit is usually referred to as the Randles circuit and its analysis has been a major feature of AC impedance studies in the last fifty years. In principle, we can measure the impedance of our cell as a function of frequency and then obtain the best values of the parameters Rct,<7,C4i and Rso by a least squares algorithm. The advent of fast micro-computers makes this the normal method nowadays but it is often extremely helpful to represent the AC data graphically since the suitability of a simple model, such as the Randles model, can usually be immediately assessed. The most common graphical representation is the impedance plot in which the real part of the measured impedance (i.e. that in phase with the impressed cell voltage) is plotted against the 90° out-of-phase quadrature or imaginary part of the impedance. 

Figure 2.84 A plot of the real part of the measured impedance. Ztm, vs. the imaginary part of...

If the real part of the impedance is written Z and the imaginary part as Z", where... 

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... 

We will give the symbol Z to the overall (or complete ) impedance. In fact, Z comprises two components, which we will term real and imaginary (Z and Z", respectively). Z, Z and Z" are related as follows ... 

Figure 8.9 A Nyquist plot of the imaginary impedance Z" against the real impedance Z, showing how Z and 6 are defined.

From our definition of a pure capacitor (i.e. one having no resistive component), we can say that the real impedance Z is zero. We see straightaway from equation (8.8) that the impedance is a function of frequency. The impedance of a capacitor is infinite when a DC voltage is applied (just put ru = 0 into equation (8.8)), while the imaginary impedance Z" decreases as the frequency co is increased. 

Notice that if we are strict with ourselves, we should really include the term, although we should note that most workers don t do this. If we had written Z", then the f term would not have been needed since an imaginary impedance presupposes the inclusion of this term. 

As a rule, when thinking in terms of genuine electrical components, rather than pure ones, we can still say that the real impedances Z behave largely like resistors while the imaginary impedances Z" behave largely like capacitors. 

To summarize the impedance discussion so far an electrochemical cell is constructed, and its impedance Z determined as a function of frequency. From these impedance values, the real and imaginary impedances, Z and Z", respectively, are computed and hence a Nyquist plot is drawn. 

The electrical components within the impedance plot are listed in Table 8.1. In summary, we see that a Nyquist plot of imaginary against real impedances can be dissected piece by piece, with each component representing a physical part of the cell or a kinetic phenomenon. We see that impedance analysis is a powerful and versatile tool which is capable of discerning the individual processes... 

Having introduced the concept of impedance, Z (and its nomenclature), the methodology involved in obtaining impedance data was outlined. It was seen that the most powerful way to interpret impedance data of an electroanalytical nature was to plot the imaginary impedance Z" (as y ) against the real impedance Z (as jc ), thus constructing a so-called Nyquist plot. 

Figure 10. Impedance complex plane (Nyquist plots) of lithium electrode in (A) 1.0 M LiPFe/EC/PC and (B) 1.0 M LiC104/EC/PC at initial time (0.0 h) and after 24 h. Re and Im stand for the real and imaginary parts of the impedance measured, respectively. Frequency was indicated in the figure for selected data points. Note that the first semicircle corresponds to SEI impedance. (Reproduced with permission from ref 86 (Figure 2). Copyright 1992 The Electrochemical Society.)...

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