Semicircle Rotation of the Impedance

From Equations 3.102 and 3.103, the real and imaginary parts of the total impedance can be calculated  

Dividing both denominator and nominator by (cobRctCd)2, Equation 3.105 becomes 

Adding (, ty + (—eJ—)2 to both sides of the above equation, we obtain 

Now let us calculate the length of the chord using the polar coordinates. The total complex admittance Y and complex impedance Z in the polar coordinates can be 

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In the study of impedance plots, we may observe the depression of semicircles. This is the so-called semicircle rotation of the impedance. This phenomenon is associated with electrode/electrolyte interface double-layer properties. For example, the rough surface of the electrodes or porous electrodes can result in an uneven distribution of the double-layer electric field. This semicircle rotation can be explained using the equivalent circuit presented in Figure 3.10, where R is inversely proportional to the frequency CO (and b is a constant). 

Figure 3.10. Equivalent circuit for explaining the semicircle rotation of the impedance...

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