Graphic Presentations of the Total Impedance

As stated in Section 3.3.1, the total measured impedance of the system, Z, is expressed as the series combination of RB and CB. These two elements provide the real and imaginary components of Z, i.e., Zre =RB, and Ztm = l coCB. As 

Note that both the real part and the imaginary part change with frequency. Kinetic parameters can be extracted by plotting Zim versus Z, as a function of frequency (a)). Although Equations 3.90 and 3.91 look very complicated, they can be simplified at high and low frequencies. Now let us consider the behaviour for both cases. 

At very low frequencies (CO — 0), the limiting forms of Equations 3.90 and 3.91 become 

From Equations 3.92 and 3.93, we can see that the frequency dependence at low frequencies comes from Warburg impedance terms hence, the linear correlation of Zm versus Zre features a diffusion-controlled electrode process. As the frequency rises, the presupposition for Equation 3.94 will not exist. The linear correlation will deviate with increasing frequencies. 

At very high frequencies (co — °°), from Equation 3.45 we have 

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