Biomedical Engineering Reference
In-Depth Information
200
700
600
150
500
100
400
300
50
200
0
100
0.5
1
1.5
D
fd
,
D
fd1
,
D
fd2
2
2.5
3
2.3
2.4
2.5 2.6
Fractal dimension,
D
f2
2.7
2.8
2.9
3
A
B
Figure 14.7
(a) Increase in the binding rate coefficient, k
2
, with an increase in the fractal dimension, D
f2
.
(b) Increase in the dissociation rate coefficients, k
d
, k
d1
, and k
d2
, with an increase in the fractal
dimensions, D
fd
, D
fd1
, and D
fd2
, respectively.
Once again, the estimated value of the fractal dimension in the binding phase is zero. This
indicates, once again, that the TFE-850 sensor surface acts like a Cantor-like dust (
Viscek,
1989
).
Figure 14.7a
and
Table 14.3
show the increase in the binding rate coefficient,
k
2
, with an
increase in the fractal dimension,
D
f2
, for a dual-fractal analysis. For the data shown in
Figure 14.7a
the binding rate coefficient,
k
2
, is given by:
D
5
:
643
1
:
621
k
2
¼ð
1
:
1588
0
:
3618
Þ
ð
14
:
5a
Þ
f2
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The binding rate coefficient,
k
2
, is very sensitive
to the fractal dimension or the degree of heterogeneity that exists on the bentonite-vanadium
(V) sol-gel surface as noted by the greater than five and one-half (equal to 5.643) order of
dependence exhibited.
Figure 14.7b
and
Tables 14.4
and
14.5
show the increase in the dissociation rate coefficient,
k
d
,
k
d1
, and
k
d2
, with an increase in the fractal dimension,
D
fd
,
D
fd1
, and
D
fd2
. For the data
shown in
Figure 14.7b
the dissociation rate coefficient,
k
d
,
k
d1
, and
k
d2
, is given by:
2
:
486
0
:
374
k
d
,
k
d1
, and
k
d2
¼ð
13
:
894
6
:
021
Þð
D
fd
,
D
fd1
, and
D
fd2
Þ
ð
14
:
5b
Þ
The fit is reasonable. Only four three data points are available. The availability of more data points
would lead to a more reliable fit. It is owing to the lack of points that
k
d
,
k
d1
,and
k
d2
are plotted
together on the same plot. The dissociation rate coefficients are sensitive to the degree of hetero-
geneity present on the bentonite-vanadium (V) sol-gel surface as noted by the close to two and a
half (equal to 2.486) order exhibited on the fractal dimensions present in the dissociation phase.
