Biomedical Engineering Reference
In-Depth Information
450
20
18
400
350
16
300
14
12
250
10
200
150
8
6
100
50
4
2.74
2.76
2.78 2.8
Fractal dimension,
D
f2
2.82
2.84
2.86
3
4
5
6 7
D
f2
/
D
f1
8
9
10
A
B
8
6
4
2
0
0
2
4
6
8
10
12
14
C
D
f
/
D
fd
;
D
f1
/
D
fd1
;
D
f2
/
D
fd2
Figure 10.2
(a) Increase in the binding rate coefficient, k
2
, with an increase in the fractal dimension, D
f2
.
(b) Increase in the binding rate coefficient ratio, k
2
/k
1
with an increase in D
f2
/D
f1
.
(c) Increase in the ratio, k/k
d
, k
1
/k
d1
, and k
2
/k
d2
with an increase in the fractal dimension
ratio, D
f
/D
fd
, D
f1
/D
fd1
, and D
f2
/D
fd2
.
For the data shown in
Figure 10.2c
, the ratio of the binding rate coefficients,
k
2
/
k
1
,is
given by:
k
=
k
d
,
k
1
=
k
d1
, and
k
2
=
k
d2
¼ð
:
þ
:
Þ
0
5943
1
203
ð
10
:
4c
Þ
0
:
997
0
:
453
ð
D
f
=
D
fd
,
D
f1
=
D
fd1
, and
D
f2
=
D
fd2
D
f2
=
D
f1
Þ
The fit is reasonable. Only four data points are available. There is scatter in the data, and this
is reflected in the error in the ratio of the binding and the dissociation rate coefficient pres-
ented. The ratio of three different coefficient values are also presented, and this too con-
tributes to the error. This is done because the number of points are so few. In any case, the
three different ratios of the binding and their corresponding dissociation rate coefficients
presented exhibit very close to a first (equal to 0.997) order of dependence on the ratio of
fractal dimensions exhibited in the binding and in the dissociation phases, respectively.
Roy et al. (2005)
recently developed a sol-gel derived thin film biosensor to detect ppm con-
centrations of NH
3
in air. They analyzed the influence of presintering temperature on gas
