Biomedical Engineering Reference
In-Depth Information
The fit is not good. There is scatter in the data, and this is reflected in the error in the dis-
sociation rate coefficient,
k
d
. Only the positive error is presented since the dissociation rate
coefficient,
k
d
, cannot exhibit a negative value. The dissociation rate coefficient,
k
d
,
exhibits close to a first (equal to 1.102) order of dependence on the NH
3
concentration in
ppm in air. The non-integer order of dependence exhibited by the dissociation rate coeffi-
cient,
k
d
,ontheNH
3
concentration in ppm in air lends support to the fractal nature of the
system.
Figure 10.7b
and
Table 10.4
show the increase in the dissociation rate coefficient,
k
d
, with an
increase in the fractal dimension for dissociation,
D
fd
. For the data shown in
Figure 10.7b
, the
dissociation rate coefficient,
k
d
is given by:
D
1
:
243
0
:
369
k
d
¼ð
0
:
851
0
:
669
Þ
ð
10
:
7b
Þ
fd
The fit is very good. Only three data points are available. The availability of more data points
would lead to a more reliable fit. The dissociation rate coefficient,
k
d
, exhibits an order of
dependence between one and one and a half (equal to 1.243) on the fractal dimension in
the dissociation phase,
D
fd
, or the degree of heterogeneity present on the biosensor surface
during the dissociation phase.
Roy et al. (2005)
analyzed the influence of film thickness on the binding and the dissociation
of NH
3
in ppm in air to the sol-gel derived nM thin film biosensor.
Figure 10.8a
shows the
binding and the dissociation of NH
3
in ppm in air to the sol-gel derived 150 nM thin film
biosensor. A dual-fractal analysis is required to adequately describe the binding kinetics.
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 dissociation rate coefficient,
k
d
, and the fractal dimension
D
fd
, for a single-fractal
analysis, and (c) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, are given in
Tables 10.5
and
10.6
.
It is of interest to note that as the fractal dimension increases by a factor of 7.37 from a value
of
D
f1
equal to 0.22 to
D
f2
equal to 1.6212, the binding rate coefficient increases by a factor
of 16.47 from a value of
k
1
equal to 0.05949 to
k
2
equal to 0.98. In this case, the affinity,
K
1
(
¼
k
1
/
k
d
) is equal to 0.523, and
K
2
(
¼
k
2
/
k
d
) is equal to 0.861.
Figure 10.8b
shows the binding and the dissociation of NH
3
in ppm in air to the sol-gel
derived 320 nM thin film biosensor. A dual-fractal analysis is required to adequately
describe the binding kinetics. A single-fractal analysis is adequate to describe the dissocia-
tion kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
,
for a single-fractal analysis, (b) the dissociation rate coefficient,
k
d
, and the fractal dimen-
sion,
D
fd
, for a single-fractal analysis, and (c) the binding rate coefficients,
k
1
and
k
2
,and
