CHEM02200704003 Nilamadhab Pandhy - Homi Bhabha National ...

Chapter 3
The modulus of electrochemical impedance |Z|, and phase angle () are obtained by the
following Eq. 9 & 10.
|Z| = !"# $ % & "# '( % & (9)
= arctan (Z Re /Z Im ) (10)
The relationship between the modulus of impedance, frequency, and phase angle is
expressed in two ways i.e. (a) Nyquist plot, and (b) Bode plot. In the format known as Nyquist
plot, the frequency response of the complex plane is obtained by plotting the imaginary
component of the impedance (jZ im ) against the real component Z Re. In Bode plot the magnitude of
total impedance is plotted against the frequency on a log-log scale and phase angle against log
frequency. Nyquist plot allows an easy prediction of the properties of the electrode-electrolyte
interface, however it does not provide the information regarding the frequency dependence of
impedance [95,102,103]. Bode plot contains all the necessary information for clear interpretation
of the results. The interpretation of the impedance data from Nyquist or Bode plot is carried out by
means of electrical equivalent circuit consisting of circuit elements, and the whole arrangement
should represent the physical phenomenon occurring in the electrochemical cell. In general the
circuit contains following basic elements,
(a) Charge transfer resistance (R P ) whose impedance is |Z| = R
(b) Capacitance of double layer (C dl ) at electrode-electrolyte interface whose impedance is
given by |Z| = 1/jC. In order to consider non-ideal capacitance behaviour, real
capacitance is replaced by constant phase element whose impedance is given by Eq.
11,
Z CPE =
)
*"+,% (11)