Biomedical Engineering Reference
In-Depth Information
E
t
I
t
Shift in
amplitude
t
Phase
shift
Figure 4.2
AC excitation signal applied and sinusoidal current response in the system
under study.
If the real part
Z
r
is plotted on the x-axis and the imaginary part
Z
i
on
the y-axis of a chart, the well-known “Nyquist plot” is obtained. In this
plot, the impedance function is represented as a vector with magnitude
Z
0
,
and a direction given by the phase angle . Another popular presentation
of impedance results is given by the Bode plot, in which both the absolute
value of the impedance and the phase shit are plotted in the y-axis versus
the frequency, which is represented in the x-axis. Albeit having the disad-
vantage of not explicitly showing the frequency information, the Nyquist
plot continues to be the most used representation for impedance data,
especially in electrochemical studies.
Figure 4.3 shows a typical example of a Nyquist plot of a generic electro-
chemical reaction taking place at an electrode. h e corner insert schematizes
the electrical equivalent circuit representing its behavior, called Randles'
equivalent circuit [56]. Each point plotted in the spectrum corresponds to
a dif erent recorded frequency. Low frequency data are on the right side of
the plot and high frequencies are on the let . h e theoretical electrical circuit
(Randles' equivalent circuit) comprises a resistance R
1
in series with the R
2
C
element which also includes a Warburg impedance (term W). h is circuit has
been extensively employed in electrochemistry for the i tting of data coming
from dif erent experiments. As stated before, each element of the circuit can
be associated to a specii c electrochemical phenomenon occurring in the cell
under study. h e parameter R
1
is generally associated to the resistance of the
electrolytic solution, R
2
corresponds in most cases to the resistance (R
ct
) to
the charge transfer between the electrolytic solution and the electrode sur-
face and C is associated to the capacitance of the double layer (due to the
interface between the electrode and the electrolytic solution).
Since the electrochemical system frequently does not conform to the
assumptions made in the models, especially those associated with electrode
