DISSERTATION

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