Impedance-experimental parameters Relaxation time

Two such circuits having different relaxation time constants and connected in series lead to two semicircles as shown in Fig. 2.55(b). As in the case of any other spectroscopic analysis the separate responses may overlap and the experimental curve must then be resolved into its separate constituent semicircles. Impedance spectroscopy makes use of other electrical parameters, including the admittance (Y = Z 1), to assist in quantifying the circuit parameters. 

In many cases, complex systems present a distribution of relaxation times and the resulting plot is a depressed semicircle, which is associated with a nonideal capacitor or a constant phase element (CPE), and its impedance is expressed by Q(a) = To(7(o)" , where Tq represents the admittance and n is an experimental parameter (0 < < 1)... 

Distributions of relaxation times can be simulated using equation (34) for different p(02). The series of distribution functions is then compared to distributions obtained from electrochemical impedance measurements carried out under the same variation of experimental conditions as shown in Figure 9.11. The peaks in the distribution function are characterised by their frequency, shape and area. By comparing dependencies of these peak parameters on the experimental variables, that were varied in the measurement series, with the same parameter variation from simulation, physical processes described by the model may be attributed to relaxation peaks in the distribution function calculated from the impedance response of the system. 

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