Biomedical Engineering Reference
In-Depth Information
C
-
Z
i
R
1
R
2
1/R
2
C
X
w
IZI
Z
r
R
1
R
2
W
Figure 4.3
Nyquist plot in the complex plane and Randles equivalent circuit (top right)
used for the i tting.
uniformity, a constant phase element (CPE) is ot en introduced in the elec-
trical circuit to replace the capacitor (C) and to compensate for the behav-
ior of a non-homogeneous electrode surface [48].
h e impedance of a CPE is given in the following equation:
Z
CPE
= (
j
·
)
-
/
C
(4.5)
(ω: radial frequency; C: capacitance; α: empirical coei cient corresponding
to 1 for ideal capacitors;
j
=
1
imaginary unit).
In the right part of the Nyquist plot, corresponding to the low frequen-
cies, a diagonal line with a slope of 45º can be observed. h is is called
“Warburg impedance” and is associated with the dif usion of the species
from the solution to the electrode. h e equation for the Warburg imped-
ance is the following:
)
-
Z
w
=
·(
·
(1-
j
)
(4.6)
(ω: radial frequency; σ: Warburg coei cient constant for a dei ned system;
j
=
1
imaginary unit).
As a general rule, EIS is commonly measured using small excitation sig-
nals in order to obtain a pseudo-linear cell's response. h us, the current
response to a sinusoidal potential will be a sinusoid at the same frequency
but shit ed in phase. In this way it is possible to perform the impedance
analysis using linear assumptions, which provides a much easier interpre-
tation of the system under study [49].
As mentioned above, so far impedance spectroscopy is a versatile technique
which has been widely used in dif erent studies, such as corrosion, semi-con-
ducting electrodes, surface coatings, batteries and fuel cells, electrochemical
kinetics and mechanism, biomedical and biological systems, electronic and
ionic conducting polymers, data processing or solid-state systems [57].
