Impedance Nyquist plot

Figure 13.35. Impedance (Nyquist) plot of the imaginary vs. the real part of the ac-impedance, measured between 0,1 and 10 Hz, of a (sidechain-substituted) tetra-dodecyl-al2T/In Schottky diode at 0.5 eV forward bias. The frequency is the implicit variable +, measured data points x, data fitted to the equivalent circuit as shown in the inset. The fitted data for the equivalent circuit elements are suiiiniarized in the table [260].

Impedance plots (Nyquist and Bode plots) for the PS/PA-PEG5 and PS/PA-PEG25 membranes are shown in Figure 2.5b and 2.5c, where the effect of the asymmetric structure on the impedance (Nyquist) plot is indicated, but the differences depending on the PEG concentration are also evident. The equivalent circuit for the total membrane system, (R C ) - (RmQmX is also indicated in Figure 2.5b the depressed semicircle, attributed to the nonconstant phase circuit element (Q, is due to the porous structure of these membranes and the mixture of the relaxation times associated with their electrical response (polymeric matrix and solution). 

Yang [14] reported that the specific surface area of steam-activated carbon nanofibers (steam-ACNFs) decreased with increasing activation temperature (from 700 to 850 °C) due to the unification of micropores at elevated temperatures, whereas the electrical conductivity of ACNF electrodes and the accessibility of ions were increased according to cyclic voltammetry curves and impedance Nyquist plots. 

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... 

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. 

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. 

Consider the impedance circuit of Fig. 13.6. Show that for Zw = 0 a Nyquist plot gives a semicircle. If Zw / 0 calculate the frequency region in which the semicircle merges into a straight line of unit slope. 

A mathematician would say that a plot of Z" (as y ) against Z (as jc ) forms an Argand diagram (or Argand plane ). As electroanalysts, we will call such a set of axes a Nyquist plot or simply an impedance plot (see Figure 8.9). 

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

At the heart of impedance analysis is the concept of an equivalent circuit. We assume that any cell (and its constituent phases, planes and layers) can be approximated to an array of electrical components. This array is termed the equivalent circuit , with a knowledge of its make-up being an extremely powetfitl simulation technique. Basically, we mentally dissect the cell or sample into resistors and capacitors, and then arrange them in such a way that the impedance behaviour in the Nyquist plot is reproduced exactly (see Section 10.2 below on electrochemical simulation). 

On a Nyquist plot of Z" against Z, the impedance of a capacitor is represented by a vertical line along the y-axis, with its value descending this axis as the... 

Figure 8.11 Nyquist plots for circuits comprising more than one electrical component (a) pure resistive impedances in series (b) pure resistive impedances in parallel (c) an RC element (d) an RC element in series with a resistance.

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 nearest impedance feature to a spike we have seen so far was shown in Figure 8.10(b), which represented the Nyquist plot for a capacitor. Why is the feature displayed in region (v) called a spike ... 

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.)...

Figure 66. Nyquist plots of the impedance spectra as measured for the fully charged lithium ion cells at —30 °C in which the inset shows the magnified view of the high-frequency part. Electrolytes are 1.0 m LiPFe (hollow) and L1BF4 (solid) in PC/EC/EMC (1 1 3). Note that the semicircles In the inset are almost invisible in the scale of the whole spectra. (Reproduced with permission from ref 134 (Figure 4). Copyright 2002 Elsevier.)...

Figure 68. Nyquist plots of a charged lithium ion cell, a lithiated graphite/graphite cell, and a delithiated cathode/ cathode symmetrical cell. The inset is an equivalent circuit used for the interpretation of the impedance spectra. (Reproduced with permission from ref 512 (Figure 3). Copyright 2003 Elsevier.)...

To better understand the diffusion-limited school of thought mentioned above, it is worth digressing momentarily on another noble -metal electrode system silver on YSZ. Kleitz and co-workers conducted a series of studies of silver point-contact microelectrodes, made by solidifying small (200—2000 //m) silver droplets onto polished YSZ surfaces. Following in-situ fabrication, the impedance of these silver microelectrodes was measured as a function of T (600-800 °C), P02 (0.01-1.0 atm), and droplet radius. As an example. Figure 9a shows a Nyquist plot of the impedance under one set of conditions, which the authors resolve into two primary components, the largest (most resistive) occurring at very low frequency (0.01—0.1 Hz) and the second smaller component at moderately low frequency ( 10 Hz). 

Flash Rusting (Bulk Paint and "Wet" Film Studies). The moderate conductivity (50-100 ohm-cm) of the water borne paint formulations allowed both dc potentiodynamic and ac impedance studies of mild steel in the bulk paints to be measured. (Table I). AC impedance measurements at the potentiostatically controlled corrosion potentials indicated depressed semi-circles with a Warburg diffusion low frequency tail in the Nyquist plots (Figure 2). These measurements at 10, 30 and 60 minute exposure times, showed the presence of a reaction involving both charge transfer and mass transfer controlling processes. The charge transfer impedance 0 was readily obtained from extrapolation of the semi-circle to the real axis at low frequencies. The transfer impedance increased with exposure time in all cases. 

Electrochemical impedance spectroscopy (EIS) profiles, measured as a function of the interrogating frequency, can be represented on both Bode and Nyquist plots. The two-component Bode plot presents a comprehensive and... 

We first follow the route leading to the Nyquist plot. In the BVD circuit the current passing from input to output encounters the following impedances. 

Fig. 5.6 Equivalent electrical circuit of electrochemical cell (top) and corresponding Nyquist plot containing Warburg impedance W (bottom)...

The same consideration applies to the impedance measurement according to Fig. 8.1b. It is a normal electrochemical interface to which the Warburg element (Zw) has been added. This element corresponds to resistance due to translational motion (i.e., diffusion) of mobile oxidized and reduced species in the depletion layer due to the periodically changing excitation signal. This refinement of the charge-transfer resistance (see (5.23), Chapter 5) is linked to the electrochemical reaction which adds a characteristic line at 45° to the Nyquist plot at low frequencies (Fig. 8.2)... 

Figure 2.7 shows a Nyquist plot corresponding to the electrical equivalent circuit of Fig. 2.6. The slope of the impedance can be explained by a circuit, consisting of different resistive and capacitive components37. The...

It is often experimentally observed that in the Nyquist plot, semi-circles are obtained with a centre point below the x-axis. Analysis of the situation tells us that the double-layer capacity is not a suitable description of the system occurring and should be replaced by an element with an impedance function given in Equation 2.51 ... 

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