Impedance plane plots

Fig. 6 Impedance plane plots for TDDA membranes with TPB (top) and without TPB (bottom) as a function of bathing solution pH.

Impedance plane plots have been introduced to analyse the effect of... 

The constant phase element (CPE) is a non-intuitive circuit element that was discovered in the course of investigations into responses from real systems. In general, a Nyquist plot (also called a Cole-Cole plot or complex impedance plane plot) should be a semicircle with the centre on the x-axis. However, the observed plot for some real systems was indeed the arc of a circle but with the centre located somewhere below the x-axis. Figure 4.1 shows the impedance spectra of a circuit of a resistor and a constant phase element connected in parallel. The centre of the semicircle is located at (l-n)x90° below the real axis. 

The asymptotic limits of the real part of the impedance for the reactive circuit of Table 16.1(b) are Re at high frequencies and Re + R at low frequencies. These limits are indicated in the complex-impedance-plane plot, and the characteristic... 

Remember 16.2 Complex-impedance-plane plots should have orthonormal axes, and characteristic frequencies should be labeled. 

The real part of the impedance for the blocking circuit shown in Table 16.1(a) is equal to Rg for all frequencies. The tendency of the imaginary part to approach —00 as frequency tends toward zero appears as a vertical line in the complex-impedance-plane plot. 

The logarithmic scale used in Figure 18.4 emphasizes the scatter seen in the imaginary impedance at Icnv frequencies. The impedance response is seen to be a strong function of temperature. The impedance-plane plots shown in Figure 18.5, for data collected at 320 and 340 K, show the classic semicircle associated with a single relaxation process. 

Figure 10.4.3 Impedance plane plot for the equivalent circuit of Figure 10.4.2.

Figure 10.4.5 Impedance plane plots for actual chemical systems. Numbers by points are...

Figure 9 shows a complex impedance plane plot of the water-nitrobenzene interface that contains 0.01-mol/L LiCl in the aqueous phase and 0.01-mol/L tetrabutylammonium teraphenylborate (TBATPB) in the nitrobenzene phase as the supporting electrolytes (filled circles). Upon addition of 3-ppm BSA (open circles) dramatically changes the low-frequency values, which implies that addition of the protein to the system causes a change in the interfacial structure, especially in the capacitance of the interface. 

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. 

For an ideally polarized electrode, the impedance consists of the double-layer capacity Cd and the solution resistancein series. In the impedance plane plot, a straight vertical line results intersecting the Z -axis at Z =. At solid electrodes, especially... 

Figure 6.4 Impedance plane plot for a Randles equivalent circuit with charge transfer resistance and Warburg impedance. First region is a kinetics-governed semicircle tall. Last region Is a mass transfer-capacitive tall. Region between two Is a diffusion governed. Reproduced from Ref. 161 with permission of The Royal Society of Chemistry.

As the frequency of voltage perturbation is increased, one may limit the penetration depth (D/jco) of a concentration wave generated by the redox reaction so that it is much smaller than the thickness of the electroactive polymer film. In this region, one measures the kinetics of the charge injection process at the surface (Region III). The impedance characteristic is a semicircle in the Zreal vs —Zjmag impedance plane plot. For the impedance measurement, one may obtain Rct, the charge transfer resistance, and the double layer capacitance Cdl- This procedure was used to calculate the... 

Figure 1.3.1. Figures 1.3.1a and d show two common RC circuits. Parts b and e show their impedance plane plots and c and/their admittance plane plots. Arrows indicate the direction of...

Figure 1.3.2. Impedance plane plot for a depressed circular arc showing definitions of quantities used in its analysis.

Figure 8 shows the general form of the impedance plane plot following from the present theory. The various arcs can be of any size relative to each other and all three do not necessarily show up simultaneously. Arc 1, which occurs at the... 

Fig. 8. Typical form of normalized impedance plane plot following from detailed SCP theory without recombination.

Fig. 9. Normalized impedance plane plot showing calculated arc 2,...

Fig. 10. Calculated normalized impedance plane plot for several values of M. Arc 1 not shown completely.

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