Biomedical Engineering Reference
In-Depth Information
0.1
0.0
−
0.1
−
0.2
−
0.3
−
0.4
−
0.5
0
2
4
6
t
−
1/2
(s
−
1/2
)
8
10
12
FIGURE 7.6
The current,
i
(
t
), versus
t
-1/2
(chronoamperometry data). Note that
A
= 6.45 cm
2
and
E
= -3 V.
the electrodes and the associated processes, particularly within a few micron depth,
play an important role in the sensing characteristics of IPMNCs.
Mass transfer of cations and their hydrated water molecules involved as they
move into and out of the bulk material and through the porous electrodes is another
important feature of the sensor. Diffusion can be considered as the sole transport
process of electroactive species (cations and hydrated water). The plausible treatment
of diffusion is to use the Cottrell equation having a form of
12
/
nFAD
C
it
()
=
=
Kt
12
/
(7.4)
()
12
/
π
t
and the number of electrons
involved in the process, the surface area, diffusivity, concentration, and Faraday
constant, respectively. Equation (7.4) states that the current is inversely proportional
to the square root of time.
Figure 7.6 shows the overall current versus the square root of time. Also, it states
that the product
where
i
(
t
),
n
,
A
,
D
,
C
, and
F
are the current at time
t
for a diffusional electrode. Deviation
from this constancy could be caused by a number of factors, including slow capacitive
charging of the electrode during the step voltage input and coupled chemical reactions
(hydrolysis). This figure is constructed under a step potential of -3 V for a typical
IPMNC. As can be seen, the characteristics clearly follow the simple Cottrell equation
that confirms the fact that the electrochemical process is diffusion controlled.
A more recent equivalent circuit proposed by Paquette and Kim (2002) is shown
in figure 7.7. The two loops that include R1, C1, R3, and C2 represent the two
composited effective electrodes of the IPMNC. R2 represents the effective resistance
of the polymer matrix. The value of
i
(
t
)
×
t
should be a constant
K
is the electric field applied across the material
for actuation:
E
=
V
/
h
, where
V
is the voltage applied and
h
is the membrane thickness.
E
