Biomedical Engineering Reference
In-Depth Information
Fig. 1.15
Free energy of
occupancy fluctuation for
different ı (reprinted from
[
129
]. Copyright 2008
American Physical Society)
Now, we consider the question why the water density distribution is so flat for
the unperturbed nanochannel and the wavelike pattern becomes obvious as the CNT
is deformed by external force.
For the unperturbed CNT with 14.6 A in length, there are two steady states of
N
D
5and
N
D
6. Their probabilities are both close to 50%. From Fig.
1.16
, we can
see that the water probability densities of
N
D
5and
N
D
6 show obvious wavelike
pattern. The average amplitude is about 0.32 A
1
. The distance between troughs
and crests of the waves is about 2.6 A, close to the length of the hydrogen bonds
between water molecules. However, the wave profiles of
N
D
5and
N
D
6 are not
in the same phase. The phase difference between them is about 1/2 period. Thus,
the total water probability density becomes flat from the superposition of those two
cases, especially in the middle region.
When the middle part of the CNT is pressed by the external force, the density
distribution pattern changes correspondingly. It is noted that the crest of the water
probability density of
N
D
5 just locates in the middle part of the CNT, while the
corresponding position is the trough of the water probability density of
N
D
6. Thus,
the wavelike pattern of
N
D
6 almost keeps the initial profile of ı
D
0 A, while the
amplitude of
N
D
5 becomes smaller. Thus, the flat profile of the total water density
distribution is broken, showing a new wavelike pattern.
In the case of ı
D
2:4 A, the middle portion of the CNT becomes narrower. There
are clear valleys in the middle portion for all the cases of
N
, resulting in a big valley
in the total water density distribution.
So now we know the reason why the total water density distribution in the middle
part is flat and becomes wavelike pattern when the middle portion of the nanotube is
narrowed. It results from the phase difference between the two states of
N
D
5and
N
D
6, and the deformed portion just locates in the middle. But the origins of the
wavelike pattern of water density distribution of
N
D
5and
N
D
6 are still not clear.
First, we calculate the water-CNT interaction along the nanotube axis. The
results are shown in Fig.
1.17
.
“U”-like profile of water-CNT shows that the more middle water molecule
locates in, the stronger the CNT attracts water molecules. When the middle portion
