Biomedical Engineering Reference
In-Depth Information
Fig. 5.1
(
a
) The Randles circuit. R
s
;C
dl
,andR
ct
denote the resistance of the electrolyte
solution, the double layer capacitance, and the charge transfer resistance, respectively. (
b
) Nyquist
representation of impedance data calculated from the Randles circuit
The charge transfer resistance R
ct
is related to the current flow caused by the redox
reaction at the interface.
Using the resistance R
s
in series with the parallel combination of the resistance
R
ct
and the capacitance C
dl
, as shown in Fig.
5.1
a, the total impedance can be
given by
1
R
ct
C
j!C
dl
1
R
ct
!R
ct
C
dl
Z
D
R
s
C
D
R
s
C
.!R
ct
C
dl
/
2
j
.!R
ct
C
dl
/
2
: (5.1)
1
C
1
C
The real part and the imaginary part of the impedance are expressed as
R
ct
!R
ct
C
dl
Z
Re
D
R
s
C
.!R
ct
C
dl
/
2
;Z
im
D
j
.!R
ct
C
dl
/
2
:
(5.2)
1
C
1
C
Impedance data can be represented in Nyquist form as shown in Fig.
5.1
b[
4
]. Each
data point corresponds to a different frequency value. The impedance is limited to
R
s
at high frequencies and R
s
C
R
ct
at low frequencies. As shown in Fig.
5.1
b,
the limited impedance at low frequency increases as R
ct
increases. The maximum
of the semicircle or the maximum of
Z
Im
occurs when the frequency is equal to
(R
ct
C
dl
/
1
.
AsshowninFig.
5.2
a, receptors, recognition elements, are immobilized on the
surface of the transducer electrode. When analytes, target biomolecules, bind to
the receptors, the charge transfer between the redox mediator and the electrode is
interrupted, resulting in an increased value of R
ct
. Concomitantly, C
dl
decreases
because the biomolecular thickness increases. By monitoring the impedance change,
the binding of the analyte to the receptor at the interface of the electrode can be
detected. However, in the presence of the insulator at the interface of the electrode
or the absence of the redox mediator, no charge transfer occurs due to the blocking
