Complex-plane impedance plots

Figure 15 shows a set of complex plane impedance plots for polypyr-rolein NaC104(aq).170 These data sets are all relatively simple because the electronic resistance of the film and the charge-transfer resistance are both negligible relative to the uncompensated solution resistance (Rs) and the film s ionic resistance (Rj). They can be approximated quite well by the transmission line circuit shown in Fig. 16, which can represent a variety of physical/chemical/morphological cases from redox polymers171 to porous electrodes.172... 

Figure 15. Complex plane impedance plots for polypyrrole at (A) 0.1, (B) -0.1, (C) -0.2, (D) -0.3, and (E) -0.4 V vs. Ag/AgCl in NaCl04(aq). The circled points are for a bare Pt electrode. Frequencies of selected points are marked in hertz. (Reprinted from X. Ren and P. O. Pickup, Impedance measurements of ionic conductivity as a probe of structure in electrochemi-cally deposited polypyrrole films, / Electmanal Chem. 396, 359-364, 1995, with kind permission from Elsevier Sciences S.A.)...

Fig. 7 Complex plane impedance plot for p-type Si in 1% HF solution, in the dark, at bias potential 0 V vs. SCE (after Vanmaekelberg et al. [9]).

FIGURE 1.19 Complex-plane impedance plot (Nyquist plane) for an electrochemical reaction under kinetic control. 

FIGURE 1.20 Complex-plane impedance plot (Nyquist plane) for an electrochemical system, with the mass transfer and kinetics (charge transfer) control regions, for an infinite diffusion layer thickness. 

FIGURE 1.21 An example of a complex-plane impedance plot (Nyquist plane) for an electrochemical system under mixed kinetic/diffusion control, with the mass transfer and kinetics (charge transfer) control regions, for a finite thickness 8N of the diffusion layer. Assumption was made that Kf Kh at the bias potential of the measurement, and D0I = Dmd = D, leading to RB = RCT (krb8N/ >). 

FIGURE 1.22 (a) Capacitor C with a series resistance, (b) Complex-plane impedance plot for the equiva-... 

FIGURE 1.23 Complex-plane impedance plot for a 2.3V/10F supercapacitor laboratory cell using acetonitrile-based electrolyte. Bias voltage = 0 V room temperature. 

Fig. A2.2. Resistance and capacitance in series (a) Electrical circuit (b) Complex plane impedance plot.

This is a vertical line in the complex plane impedance plot, since Z is constant but Z" varies with frequency, as shown in Fig. A2.2b. 

Figure 5.48. Complex plane impedance plots for a 5 cm2 hydrogen fuel cell at a current density of 0.2 A cm2. The cell was run at ambient temperature with humidified H2 and dry air [64], (Reprinted from Electrochimica Acta, 49, Li G, Pickup PG. Measurement of single electrode potentials and impedances in hydrogen and direct methanol PEM fuel cells, 4119— 26, 2004, with permission from Elsevier and the authors.)...

Adding a solution resistance to the circuit shown in Fig. 12L, one obtains the complex-plane impedance plot shown in Fig. 13L(a), which is similar to Fig. 12L, except that the semicircle is displaced to the right on the ReZ axis. 

It would seem then that the complex-plane impedance plot is the better way of pre.senling the data, if one is mainly interested in the... 

In Fig. 15L(a-d) we show four complex-plane-impedance plots calculated for the concentrations of 100, 10, 1 and 0.1 mM, respective-... 

Fig. 17L Complex-plane impedance plots for the corrosion of iron at two different potentials, (a) two well-separated time constants are shown, (h) An inductive loop is observed. Data from Epelboin, Gabrielli, Keddam and Takenoiiti, Electrochini. Acta, 20, 9J3, 1975).

We shall refer to it as the complex-plane impedance plot, recognizing that the same data can also he represented in the complex-plane capacitance or the complex-plane admittance plots. The terms Cole-Cole plot, Nyqidst plot and Argand plot are also found in the literature. 

Fig. ML Complex-plane-impedance plot for an equivalent circuit with...

Fig. I5L Complex-plane impedance plots showing the gradual change from charge-transfer to mass-transport limitation with decreasing concentration. 10 < id < 10 Radis. C =20 uFIcn, R =...

Fig. 16L Complex-plane impedance plot with depressed semicircle. A -B is the diameter of the semicircle, depressed by an angle a.

FIGURE 5.32. Complex plane impedance plots forp-Si (3 x lO Vcm ) in 1% HF solution. The corresponding i-V curve is shown in Fig. 5.33. After Searson and Zhang. (Reproduced by permission of The Electrochemical Society, Inc.)... 

Figure 12.5 Complex-plane impedance plots for p-Si in 1.0 mol dm NH4F (pH 4.5). Note that the faradaic resistance (derived from the low-frequency intercept on the real axis) can be positive or negative. The negative value at 1.75 V indicates that the current decreases with increasing potential in this region of the current-potential curve (see Fig. 12.4). Adapted from Bailes et al (1998).

Examples of the complex plane plots obtained for fractal electrodes are presented in Fig. 33. With a decrease in parameter ([), the semicircles become deformed (skewed). The complex plane impedance plots obtained from Eq. (183) are formally similar to those found by Davidson and Cole " in their dielectric studies. Kinetic analysis of the hydrogen evolution reaction on surfaces displaying fractal ac impedance behavior was... 

Figure 9. Complex plane impedance plots of the water-nitrobenzene interface (negative imaginary impedance vs. real impedance) with and without bovine serum albumin. The filled circles denote the supporting electrolyte only 0.01 mol/L LiCl in water 0.01 mol/L TBATPB in nitrobenzene. The open circles indicate addition of 3 ppm BSA in water. The applied interfacial potential is 0.30 V (vs. TBA+ ion selective electrode) t = 25.0 °C. The frequency of the measurement for selected values is indicated at the data points. (Reproduced with permission from reference 32. Copyright 1990 Elsevier.)...

The real and imaginary impedances ZR and Zl are directly accessible from the impedance measurement. Rs, the solution resistance, has to be obtained from examination of the complex plane impedance plot (cf., Figure 9). In the impedance plane plot, the imaginary value decreases with increasing frequency until the curve approaches the real impedance axis. The real impedance is equal at this point to the solution resistance Rs. The value is independent of applied interfacial potential, but it depends on the position of the reference electrodes (different uncompensated resistance). Because the calculated capacitance is very sensitive to the calculated Rs, the placement of the reference electrodes must be carefully controlled. 

Figure 6. Sequential complex plane impedance plots under active SRB condition.

The following problem arises in the interpretation of such semicircles in the complex plane impedance plots every parallel combination of a constant resistance and constant capacity leads to a semicircle in the Nyquist plot of the impedance. To verify a charge transfer, for instance, the potential dependence of the charge-transfer resistance should be investigated to demonstrate the Butler-Volmer potential dependence of the exchange current. 

Double-layer charging of the pores only (non-faradaic process) and inclusion of a pore-size distribution leads to complex plane impedance plots, as in Fig. n.5.7, i.e. at high frequencies, a straight line results in an angle of 45° to the real axis and, at lower frequencies, the slope suddenly increases but does not change to a vertical line [16]. 

Fig. 3.7 The complex-plane impedance plot representation (also called the Argand diagram or Nyquist diagram) of the ideal impedance spectra in the case of reflective boundary conditions. Effect of the ratio of the film thickness (L) and the diffusion coefiicient (D). L/D (7) 0.005 (2) 0.1 (2) 0.2 4) 0.5 and (5) 1 s /. i o = 2 Q, 7 ct = 5 Q, (7 = 50 cm fis / Cdi = 20 pFcm. The smaller numbers refer to frequency values in Hz...

However, taking the impedance at each potential produces series of data values at different frequencies. Examples of complex plane impedance plots that is imaginary versus real part at various frequencies for different fuel cells are presented in Fig. 1.2. The polarization resistance is the only point corresponding to zero frequency, as indicated in the plots. One may observe that the impedance plots, besides R, produce much more information that is not available in steady-state measurements. Impedance plots display complex curves that are rich in information. Such information is contained in every point, not only in one value of R. However, one must know how to find this information on the system being studied. This is a more complex problem and can be solved by the proper physicochemical modeling. 

Fig. 1.2 Examples of complex plane impedance plots fOT fnel cells arrows polarization resistance also foimd in steady-state measurements impedances are in 2...

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