Biomedical Engineering Reference
In-Depth Information
0.8960, the dissociation rate coefficient increases by a factor of 5.41 from a value of
k
d1
equal
to 0.0634 to
k
d2
equal to 0.3433.
Figure 10.6c
shows the binding and dissociation of 640 ppm of NH
3
in air to the sol-gel derived thin
film biosensor (
Roy et al., 2005
). A single-fractal analysis is adequate to describe the binding and
the dissociation kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis, and (b) the dissociation rate coefficient,
k
d
, and the fractal dimen-
sion for the dissociation phase,
D
fd
, for a single-fractal analysis are given in
Table 10.4
.
Figure 10.6d
shows the binding and dissociation of 1280 ppm NH
3
in air to the sol-gel derived
thin film biosensor. A dual-fractal analysis is required to adequately describe the binding kinet-
ics. A single-fractal analysis is adequate to describe the dissociation kinetics. The values of
(a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis,
(b) the binding rate coefficients,
k
1
and
k
2
and the fractal dimensions,
D
f1
and
D
f2
for a
dual-fractal analysis, and (c) the dissociation rate coefficient,
k
d
, and the fractal dimension
for the dissociation phase for a single-fractal analysis,
D
fd
, are given in
Tables 10.4
and
10.5
.
It is of interest to note that as the fractal dimension increases by a factor of approximately
2.15 from a value of
D
f1
equal to 1.0946 to
D
f2
equal to 2.3548, the binding rate coefficient
increases by a factor of 13.83 from a value of
k
1
equal to 0.8170 to
k
2
equal to 11.296.
Figure 10.7a
and Table
10.4
show the increase in the dissociation rate coefficient,
k
d
, with
an increase in the NH
3
concentration in ppm in air. For the data shown in
Figure 10.7a
,
the dissociation rate coefficient,
k
d
, is given by:
1
:
102
0
:
798
k
d
¼ð
0
:
000248
þ
0
:
000571
Þ½
NH
3
ð
10
:
7a
Þ
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
200
400 600
NH
3
concentration (ppm)
800
1000
1200
1400
0
0.2
0.4 0.6 0.8
Fractal dimension,
D
fd
1
1.2
1.4
A
B
Figure 10.7
(a) Increase in the dissociation rate coefficient, k
d
, with an increase in the NH
3
concentration in air
(in ppm). (b) Increase in the dissociation rate coefficient, k
d
, with an increase in the fractal
dimension for dissociation, D
fd
.
