Impedance-experimental parameters range

The frequency K = 1 at which the current distribution influences the impedance response is shown in Figure 13.7 with k/Co as a parameter. As demonstrated in Example 13.2, the influence of high-frequency geometry-induced time-constant dispersion can be avoided for reactions that do not involve adsorbed intermediates by conducting experiments below the characteristic frequency given in equation (13.57). The characteristic frequency can be well within the range of experimental measurements. The value k/Cq = 10 cm/s, for example, can be obtained for a capacitance Co = 10 (corresponding to the value expected for the dou-... 

The potential benefit of impedance studies of porous GDEs for fuel applications has been stressed in Refs. 141, 142. A detailed combined experimental and theoretical investigation of the impedance response of PEFC was reported in Ref. 143. Going beyond these earlier approaches, which were based entirely on numerical solutions, analytical solutions in relevant ranges of parameters have been presented in Ref. 144 which are convenient for the treatment of experimental data. It was shown, in particular, how impedance spectroscopy could be used to determine electrode parameters as functions of the structure and composition. The percolation-type approximations used in Ref. 144, were, however, incomplete, having the same caveats as those used in Ref. 17. Incorporation of the refined percolation-type dependencies, discussed in the previous section, reveals effects due to varying electrode composition and, thus, provides diagnostic tools for optimization of the catalyst layer structure. 

Impedance analysis is also suggested when properties of an attached film, a liquid, or interfaces are of interest. Due to the weak frequency dependence of the acoustic load within a typical measurement range of some 10 kHz at fundamental mode, one measurement point would be sufficient to calculate Zl (Eq. 2). An effective method to decrease statistical errors is to first fit a theoretical curve to the experimental curve or a specific segment, secondly to calculate Zl from the fit, and finally to extract (material) parameters of interest using separate models describing how the acoustic load is generated [37]. 

The same ventricle may be coupled to a pathological arterial system, for example, one with doubled peripheral resistance R. As expected, increased peripheral resistance raises arterial pulse pressure (to 140/95 mmHg) and impedes the ventricle s ability to eject blood (Figure 8.6). The ejection fraction decreases to 50% in this experiment. Other experiments, such as altered arterial stiffness, may be performed. The model s flexibility allows description of heart pathology as well as changes in blood vessels. This one equation (Equation 8.8) with one set of measured parameters is able to describe the wide range of hemodynamics observed experimentally [11],... 

For polymers with a glass transition temperature well above room temperature, the dipole contribution to the dielectric constant will be weak. However, low Tg polymers exhibit a strong contribution as shown in Figure 4 for the composite DMNPAA PVK ECZ TTSIF with Tg = 16°. The frequency-dependence of the dielectric constant has been deduced for this material from frequency-dependent impedance measurements and the sample was approximated to a capacitor and a resistor in parallel. In the range of frequencies / = cy / 2 r = 0 to 1000 Hz, a good fit to the experimental data is found with the superposition of just two Debye functions with the following parameters = 3.55, Cdc = 6.4, Aj = 0.8, A2 = 0.2, r = 0.004 s and... 

In many situations it is preferable to obtain values for the fundamental equivalent circuit parameters via a nonlinear least squares fitting protocol applied to the raw experimental impedance data. The latter can be accomplished if we obtain an analytical expression for the real and imaginary components of the impedance that is valid over the entire frequency range. Initial estimates of circuit parameters can be obtained from data analysis using the approximate expressions previously outlined. 

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