Biomedical Engineering Reference
In-Depth Information
dimension,
D
f
, for a single-fractal analysis, (b) the dissociation rate coefficient,
k
d
, and the
fractal dimension for the dissociation phase for a single-fractal analysis, (c) the binding rate
coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, and
(d) the dissociation rate coefficients,
k
d1
and
k
d2
, and the fractal dimensions,
D
fd1
and
D
fd2
,
for the dissociation phase for a dual-fractal analysis.
The values of the binding and the dissociation rate coefficients and the fractal dimensions for
the binding phase presented in
Tables 10.1
and
10.2
were obtained from a regression analysis
using Corel Quattro Pro 8.0 (1997) to model the data using
Equations. (10.1)-(10.3)
. wherein
ð
kt
ð
3
D
f
Þ
for a single-fractal analysis, and
k
1
t
ð
3
D
f1
Þ
for time,
t
Ab
Ag
Þ¼
ð
Ab
Ag
Þ¼
<
t
1
,
k
2
t
ð
3
D
f2
Þ
for time,
t
and
t
c
for a dual-fractal analysis. The binding
and the dissociation rate coefficients presented in
Table 10.1
are within 95% limits. For
example, for the binding (and dissociation) of LPG to sample S
1
the binding rate coefficient,
k
1
, is equal to 0.1825
ð
Ab
Ag
Þ¼
¼
t
1
<
t
<
t
2
¼
0.0166. The 95% confidence limit indicates that the
k
1
value lies
between 0.1659 and 0.1991. This indicates that the values are precise and significant.
An increase in the fractal dimension for a dual-fractal analysis by a factor of 3.44 from
a value of
D
f1
equal to 0.8196 to
D
f2
equal to 2.8210 leads to an increase in the binding rate
coefficient by a factor of 105.93 from a value of
k
1
equal to 0.1825 to
k
2
equal to 19.334.
Note that changes in the fractal dimension or the degree of heterogeneity on the ZnO-glass
substrate and in the binding rate coefficient are in the same direction. In other words, and
as indicated elsewhere in the different chapters in this topic, an increase in the degree of het-
erogeneity on the sensing surface leads to an increase in the binding rate coefficient.
Figure 10.1b
shows the binding and dissociation of 0.15 volume %LPG in the gas phase to sample S
2
(0.15 M zinc nitrate solution used in the spray pyrolysis method) (
Shinde et al., 2007
). A dual-fractal
analysis is required to adequately describe the binding kinetics. A single-fractal analysis is adequate
to describe the dissociation kinetics.
Tables 10.1
and
10.2
show (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.
Once again, for the binding phase an increase in the fractal dimension by a factor of 3.44
from a value of
D
f1
equal to 0.308 to
D
f2
equal to 2.849 leads to an increase in the binding
rate coefficient by a factor of 400.7 from a value of
k
1
equal to 0.0351 to
k
2
equal to 14.066.
An increase in the degree of heterogeneity on the biosensor surface leads, once again, to an
increase in the binding rate coefficient.
Figure 10.1c
shows the binding and dissociation of 0.2 volume percent LPG in the gas phase
to sample S
3
(0.2 M zinc nitrate solution used in the spray pyrolysis method) (
Shinde et al.,
2007
). A dual-fractal analysis is required to adequately describe the binding and the dissoci-
ation kinetics.
Tables 10.1
and
10.2
show (a) the binding rate coefficient,
k
, and the fractal
