Biomedical Engineering Reference
In-Depth Information
rate coefficient,
k
d
, and the fractal dimension for the dissociation phase for a single-fractal
analysis,
D
fd
, 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 10.4
and
10.5
.
It is of interest to note that as the fractal dimension increases by a factor of approximately
two from a value of
D
f1
equal to 1.0774 to
D
f2
equal to 2.14, the binding rate coefficient
increases by a factor of 9.44 from a value of
k
1
equal to 0.264 to
k
2
equal to 2.4922.
Figure 10.6b
shows the binding and dissociation of 320 ppm 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 kinetics. A dual-fractal analysis is required to adequately 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
for dissociation,
D
fd
, for a single-fractal analysis, and (c) the dissociation rate coefficients,
k
d1
and
k
d2
, and the fractal dimensions for dissociation,
D
fd1
and
D
fd2
, for a dual-fractal anal-
ysis are given in
Tables 10.4
and
10.5
.
It is of interest to note that for a dual-fractal analysis in the dissociation phase, as the fractal
dimension increases by a factor of 4.90 from a value of
D
fd1
equal to 0.1828 to
D
fd2
equal to
25
50
20
40
15
30
10
20
5
10
0
0
0
50
100
Time (s)
150
200
0
50
100
Time (s)
150
200
A
B
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
0
50
100
Time (s)
150
200
0
50
100
Time (s)
150
200
C
D
Figure 10.6
Binding and dissociation of different NH
3
concentrations (in ppm) in air to a sol-gel derived thin
film (
Roy et al., 2005
): (a) 160 (b) 320 (c) 640 (d) 1280. When only a solid line (--) is used then a
single-fractal analysis applies. When both a dashed (- - -) and a solid (--) line are used then the
dashed line represents a single-fractal analysis and the solid line represents a dual-fractal analysis.
