Impedance spectra with change

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. 

Figure 7.6 shows Nyquist representations of the impedance spectrum for such nanotubes in contact with 7 M aqueous KOH. A semicircle appears at high frequency and abruptly changes to an almost vertical line at low frequency, this last denoting the capacitive behavior typical of CNTs. 

With increasing interest in time-resolved impedance measurements but also with the demand of parallel measurements, fast methods based on time domain approach move more and more into the focus. Although time and frequency domain are well defined, they are often not clearly presented. Especially, when the impedance spectrum changes with time, a joint analysis in terms of time and frequency dependence is often accompanied by uncertainties in wording. 

A comparison of the results obtained from these two models is shown in Fig. 10.3. Of course, in such cases, at each potential the complete impedance spectrum must be obtained, which leads to longer experiments and possible changes in the surface layer with time. 

Adsorption processes which are slow on a time scale (defined as the time it takes to measure an impedance spectrum within a reasonable frequency interval) can be monitored by impedance analysis. In Figure 6.22 such spectra are shown for the adsorption of carbon monoxide (CO, 3.7) on activated carbon (AC) Norit R1 taken at T = 298 K for a gas pressure of p = 7.5 MPa, the initial state referring to vacuum (p < 1 Pa), [6.13, 6.33]. The time it took to monitor the real part of the capacitance (ReC(v)) within the frequency interval 0.1 MHz < V <1 MHz, At was about 20 minutes. The adsorption process itself, monitored simultaneously with a magnetic suspension balance, Cp. Sect. 3.2, lasted about 24 h. However, the impedance spectra of the system showed considerable changes for a much longer time and actually have been observed for 41 h, or 2460 minutes, or 123 At. 

Experimentally, there are several ways to determine the ohmic cell resistance. If the V-I curve has a substantial linear portion (in the center), the slope of this curve usually closely approximates the ASR of the cell. Only in such a linear portion of the V-I curve the ohmic resistance is dominant, and hence the determination of the ASR valid. Sometimes, a more accurate way to determine the ohmic resistance is from impedance spectroscopy. In an impedance spectrum of a fuel cell, the ohmic resistance is the real value of the impedance of the point for which the imaginary impedance is zero (Figure 2-5). As can be seen in the example, the ohmic resistance is invariant with gas concentration. The part of the impedance that is related to mass transport and kinetics, however, changes markedly with anode feed composition. 

Extensive efforts have been directed toward the search for oxide materials that allow fabrication of an SOFC with low activation and ohmic losses. To determine the role of new materiak in the overall fuel cell performance, electrochemical impedance spectroscopy (EIS) has been used to measure the activation and/ or ohmic resktance contributed by the specific new material. An impedance spectrum k obtained by applying a periodic change in voltage and monitoring the current response at varying frequencies. The impedance spectra obtained... 

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