Biomedical Engineering Reference
In-Depth Information
The water density distribution along the tube axis (
z
) can be calculated by
N.
z
/
NL
;
.
z
/
D
where L is the bin length and
N
(
z
) is the number of water molecules appearing
at the bin at
z
for the total of
N
snapshots from simulation. In order to compute
the water density distribution near two openings of the CNT, we can extend the
CNT from each end to bulk by 11.3 A to construct a virtual cylinder with 8.1
˚
Ain
diameter. The whole cylinder was divided into 1,000 bins. In the case of ı
D
0 A, the
distribution has a wavelike structure with minimal values at the openings and five
peaks, which is consistent with the average value of the water occupancy
N
(
N
5
for ı
D
0 A from Fig.
1.5
). For 0
ı<2.0 A, the distribution changes gradually
and the peak move leftward as ı increases, but the values of the peaks do not
change much. This is conforming to the stable value of water occupancy
N
at the
range of 0
ı<2.0
˚
AinFig.
1.5
. The water distribution at
P
, the location facing
the forced-atom, decreases corresponding to the narrowing of the nanotube at
P
.
When ı
2.0 A, the distribution at
P
is smaller than that of the other dips, and
the wavelike pattern is considerably deformed; the values of the peaks decrease
obviously corresponding to the decrease in
N
in Fig.
1.5
at the same range of ı.The
distribution at
P
is very close to zero when ı
D
2.5 A. However, we still observe
that about one water molecule enters from one side and leaves from the other side
per nanosecond when ı
D
2.5 A. Further inspection of the data shows that water
molecules can pass the position of
P
very rapidly without staying.
The gating behavior can also be understood from the distance between the two
water molecules, one left to the forced-atom and the other right to the forced-
atom. As shown in Fig.
1.7
, the distance almost keep the initial value without
the deformation of the SWNT of 2-2.8
˚
Aforı<2.0 A. Further increase in ı
makes the distance increases rapidly, breaking the connection (hydrogen bonding)
between those two water molecules. It is just the strong interaction of the hydrogen
bonds that keeps the distance almost as a constant when ı<2.0 A. Thus the water
transportation across the nanotube stops.
As we have mentioned before, the water molecules form hydrogen bonds with
neighboring water molecules, and the water molecules inside the CNT form a single
hydrogen-bonded chain. The dipoles of the water molecules are nearly aligned along
the nanotube axis. Due to the deformation of the nanotube, the total number of
hydrogen bonds inside the nanotube decreases as ı increases (Fig.
1.8
). The average
number of the hydrogen bonds, denoted by
N
Hbond
, decreases very slowly in a
linear fashion as
N
Hbond
D
3.16-0.136 A in the range of ı<2.0 A. In the range of
2.0 A
ı<2.5 A,
N
Hbond
decreases sharply from 2.87 to 1.43. This sharp decrease
results from the decrease in the total water molecules inside the nanotube
N
as well
as the increase in the distance between those two water molecules neighbor to the
position
P
. The linear decrease in
N
Hbond
in the range of ı<2.0 A mainly results
from the increase in the distance between those two water molecules neighbor to the
position
P
, for the value of
N
keeps stable in this range. The effect of the increase
