Distributed time constant geometry-induced

It must be emphasized that the mathematical simplicity of equations (13.1) and (13.2) is the consequence of a specific time-constant distribution. As shown in this chapter, time-constant distributions can result from nonuniform mass transfer, geometry-induced nonuniform current and potential distributions, electrode porosity, and distributed properties of oxides. At first glance, the associated impedance responses may appear to have a CPE behavior, but the frequency dependence of the phase angle shows that the time-constant distribution differs from that presented in equation (13.7). 

The geometry-induced current and potential distributions cause a frequency or time-constant dispersion that distorts the impedance response of a disk elec-trode. Huang et ai, 7,i02.,205 j ye shown that current and potential distributions induce a high-frequency pseudo-CPE behavior in the global impedance response of a disk electrode with a local ideally capacitive behavior, a blocking disk electrode exhibiting a local CPE behavior, and a disk electrode exhibiting Faradaic behavior. 

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-... 

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