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R0 3.6. Electrochemical Impedance Spectroscopy noted that the fit parameters obtained through this procedure have no physical meaning. The idea behind using the Voigt circuit is that each (RC)i element with associated time constant τi = RiCi represents a time constant of a distributed element, such as the CPE and the diffusion elements. An appropriate number of Voigt elements must therefore be used. Boukamp suggested 6–7 elements per frequency decade [80]. C1 Ci CN (( R1 Ri N - 2 RN Figure 3.19: Schematic of a Voigt circuit consisting of a resistor R0 and N(RC) ele- ments. Once the Kramers-Kronig transforms have been carried out, the real and imaginary parts of the experimental data are compared to the calculated Kramers-Kronig impe- dance through plots of relative residuals against frequency. If the residuals are randomly distributed around and close to 0 %, the experimental data is Kramers-Kronig compliant and of good quality. Some valuable conclusions can be drawn from the residuals if this is not the case. For example, if there is a systematic increase in residuals with decreasing frequency, the system is most likely drifting, which is not compliant with the condition of stability. An example of a Kramers-Kronig compliant and non-compliant data set is shown in Figure 3.20. Figure 3.20: Illustrative Kramers-Kronig residuals plots for (upper) a system that is Kramers-Kronig compliant and (lower) a system that is not Kramers-Kronig compliant. 43PDF Image | Organic Redox Flow Batteries 2023
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