Biomedical Engineering Reference
In-Depth Information
N
Fig. 1.9
0.0, 2.0,
2.3, and 2.5 A (reprinted from
[
40
]. Copyright 2005
American Chemical Society)
for ı D
consistent with the observation that the water molecules in CNT are nearly aligned.
If we define a flip as
N
passing through 90
ı
, we can calculate the number of flips
per nanosecond, denoted by the flipping frequency
f
flip
.
The flipping frequency
f
flip
is governed by the potential barrier against flipping.
And the increment of ı leads to two aspects of the potential change, decrease due
to the breakage of hydrogen bonds inside the nanotube and increase due to the
narrowing of the nanotube that confines water molecules to a smaller space. As
isshowninFig.
1.8
,
N
Hbond
decreases very slowly with respect to ı for ı
1.4 A.
The confinement of water molecules is the main reason for the slow decrease in
f
flip
in this range.
As ı further increases,
f
flip
increases. The dependence of
f
flip
on
N
Hbond
is shown
in Fig.
1.10
. In the range of 2.0 A
ı<2.2 A, the function
f
flip
/
exp.
N
Hbond
E
Hbond
=kT /
can fit the data quite well, where
E
Hbond
is the average energy of a hydrogen bond in
the nanotube for ı
D
2.0, 2.1, and 2.2 A. Numerically, we find
E
Hbond
D
12.96
kT
.
This exponential decay indicates that the change of the potential barrier mainly
results from the decrease in the number of hydrogen bonds inside the nanotube
in this parameter range. For even larger ı,say2.5 A, the water chain is frequently
ruptured (Fig.
1.11
). Only for a small period of time,
N
falls into the two parameter
