Biomedical Engineering Reference
In-Depth Information
0.7
0.01
0.6
0.008
0.5
0.006
0.4
0.3
0.004
0.2
0.002
0.1
0
0
0
100
200
300
400
500
0
100
200 300
Ion concentration (mM)
400
500
A
B
Ion concentration (mM)
1000
800
600
400
200
0
1.6
1.8 2 2.2
Fractal dimension ratio
D
f2
/
D
f1
2.4
2.6
2.8
C
Figure 16.16
(a) Increase in the binding rate coefficient, k
1
, for a dual-fractal analysis with an increase in the ion
concentration (in mM) in solution. (b) Increase in the binding rate coefficient, k
2
, for a dual-fractal
analysis with an Increase in the ion concentration (in mM) in solution. (c) Increase in the binding
rate coefficient ratio, k
2
/k
1
, with an increase in the fractal dimension ratio, D
f2
/D
f1
.
exhibits only a mild (less than one-half (equal to 0.378)) order of dependence on the ion con-
centration in solution in the 0.1-500 mM range.
Figure 16.16b
and
Table 16.12
show the increase in the binding rate coefficient,
k
2
, with an
increase in the ion concentration (MgCl
2
) in solution in the 0.1-500 mM range for a dual-fractal
analysis. For the data shown in
Figure 16.16b
, the binding rate coefficient,
k
2
, is given by:
0
:
123
þ
0
:
173
k
2
¼ð
01232
þ
0
:
1726
Þ½
ion concentration, mM
ð
16
:
10b
Þ
The fit is not good. There is scatter in the data, and this is reflected in the error of the
estimated rate coefficient values. Only the positive value of the errors is given. Only five data
points are available. The availability of more data points would lead to a more reliable fit.
The binding rate coefficient,
k
2
, for a dual-fractal analysis exhibits close to a zero (equal
to 0.123) order of dependence on the ion concentration in solution in the 0.1-500 mM range.
