Analysis of Impedance and Modulation Spectroscopic Signals

Combined Analysis of Impedance and Modulation Spectroscopic Signals 

The refined method of analysis of co-dependent ER signal data set to obtain described in the last part of the previous section is in principle the combined use of ac impedance and the modulated spectroscopic signal. A similar calculation was reported by Yamada and Finklea and their colleagues [21, 71]. We describe below in detail the procedure for a concerted use of these two potential modulation techniques in the kinetic analysis. 

We now use an equivalent circuit shown in Fig. 2.21. As opposed to Fig. 2.18, the faradaic impedance Zf and double-layer non-faradaic impedance Z j are used without any specified constituent represented by constant resistance and capacitance elements. That is, it is unnecessary to specify each of the elements involved in these two partial impedance units. We assume that we have a data set of Zt including the frequencies at the high limit from which we can determine the value of (this frequency is usually called the high frequency Umif in the ac impedance analysis protocol). Then, the ac potential difference across Zf, 

In Eqs. (30)-(32), was expressed in reference to the ac potential modulation of Fac- In the light of Eq. (37), Rac can now be alternatively analyzed with reference to the ac potential difference modulation of In latter analysis, the effects of Rg and double-layer charging upon Rac have aheady been excluded. This exclusion is independent of the form of Za. Therefore, a complex quantity of Rac/ ac has a phase 0 that is nothing else than the phase of the optical signal in reference to Thus, if Zf has a form such that the rate constant is represented by Eq. (34), 0 satisfies the following equation  

It is clear that the problems in the use of the plot of -co cot as a function of -o/ listed in the previous section are well resolved. 

---