DISSERTATION
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________________________________________________________________ Experimental Work<br />
Z = |Z|exp(jθ) (5.11)<br />
Z ′ = |Z|sinθ Z ′′ = |Z|cosθ (5.12)<br />
where j = √−1, Z ′ is the real impedance component, Z′ ′ is the imaginary impedance<br />
component, |Z| is the magnitude and θ is the phase shift between potential and current.<br />
Electrochemical impedance spectroscopy is based on the application of a DC potential that is<br />
superimposed with a small amplitude AC potential and measurement of the resulting AC<br />
current signal:<br />
E = E AC sin(ωt) (5.13)<br />
i = i AC sin(ωt + θ) (5.14)<br />
where E AC and i AC are potential and current amplitude, respectively. Except in the case of a pure<br />
resistor, the measured current has a phase shift as compared with the applied potential (Figure<br />
5.6). The impedance of the system is:<br />
Z = E i = E ACsin(ωt)<br />
i AC sin(ωt + θ) = |Z| sin(ωt)<br />
sin(ωt + θ)<br />
(5.15)<br />
Figure 5.6. a) Phase diagram of the applied potential and measured current; b) impedance<br />
vector diagram.<br />
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