Impedance models finite-length diffusion

As was shown earlier, the presence of the CPE of fractal impedance produces a distribution of the time constants. In addition, other elements such as the Warburg (semi-infinite or finite-length) linear or nonlinear diffusion, porous electrodes, and others also produce a dispersion of time constants. Knowledge about the nature of such dispersion is important in the characterization of electrode processes and electrode materials. Such information can be obtained even without fitting the experimental impedances to the corresponding models, which might be still unknown. Several methods allow for the determination of the distribution of time constants [378, 379], and they will be briefly presented below. 

The residual errors are presented in Figures 20.11(a) and (b) for the real and imaginary parts of the impedance, respectively. The dashed lines represent the experimentally determined noise level of the measurement. The scales used to present the results in Figure 20.11 are in stark contrast to the scales used in Figure 20.5. The residual error plots show that the measurement model provides a substantially better fit to the data than does the finite-diffusion-length model. 

As described in Sections 20.2.1 and 20.2.2, the quality of the regressions can be assessed to varying degrees of success by inspection of plots. The Nyquist or complex-impedance-plane representation given in Figure 20.13 reveals the difference between the finite-diffusion-length model and the models based on numerical solution of the convective-diffusion equation, but cannot be used to distinguish the models based on one-term, two-term, and three-term expansions. 

---