Biomedical Engineering Reference
In-Depth Information
We now come to exploit the question why the location of the narrow portion
plays a key role in water transportation through the nanotube. We have known that
the transportation behavior of water molecules is mainly determined by the profile
of the total interaction potential (it is denoted by the symbol
P
in this chapter). In
this section, potential includes two parts: one is the water-water interactions (the
interaction energies of the water molecule at position
z
inside the SWNT with its
neighboring water molecules), denoted by
P
WW
, and the other part is the water-
SWNT interactions (the interactions of the confined water at position
z
with the
carbon atoms of SWNT), denoted by
P
WC
. It is consistent with the results shown
in Fig.
1.17
that the potential energy curve of
P
WC
for the unperturbed SWNT
has a symmetrical “U-like” shape, and the lowest is located in the middle of the
SWNT (the position of
z
D
0 A). When the SWNT is narrowed at
d
, the potential
barrier appears at
z
D
d
. The profile of the curve of
P
WC
changes from a “U-like”
shape into a “W-like” shape. As the location of the narrow portion moves to the
ends of the nanotube, the peak of
P
WC
moves to the openings of the nanotube
correspondingly, and the height of the peak increases due to a “U-like” shape of
P
WC
for the unperturbed SWNT.
Water molecules inside the CNT are connected by hydrogen bond. The strength
of the energy is about 10
k
B
T
.For
j
d
j 6
2:5 A, the hydrogen-bonding chain
structure inside the SWNT is still perfect because the water-SWNT interaction
potential
P
WC
is negligible compared to the strength of the hydrogen bond.
However, if the location of the deformation moves out from the middle region,
the water-SWNT interaction energy increases obviously. Thus, for
j
d
j >
4:9 A,
the possibility of producing defects by breaking the hydrogen bond increases
dramatically. Figure
1.27
shows that
P
WW
for
d
D
4.9 A peaks at
z
D
2.1 A,
which is
2.8 A (about the size of a water molecule) away from the deformed
position of
z
D
d
D
4.9 A, indicating that the hydrogen bond that connects between
the water molecule at
z
D
2.1 A and its left one (the water molecule at
z
D
4.9 A)
usually is violated. Correspondingly, for
d
D
4.9 A, the value of
P
WW
(
z
D
4.9 A)
is lower than that of
P
WW
(
z
D
2.1 A). In fact, it results mainly from that the
possibility of the water molecule located in
z
D
2.1 A is larger than that in
z
D
4.9 A due to
P
WC
(
z
D
4.9 A) >
P
WC
(
2.1 A). Certainly, the average number
of the hydrogen bonds of the water molecule at
z
D
2.1 A is larger than that of
the water molecule at
z
D
4.9 A. In other words, when there is a water molecule
near
z
D
4.9 A, usually there exist water molecules in two sides of it (near
z
D
2.1
˚
Aand
z
D
7.7 A), rather than vice versa.
P
WW
(
z
<
4.9 A) is lower
than
P
WW
(
z
>
4.9 A) because the water molecules in the region of
z
<
4.9 A
are closer to the bulk water than those in the region of
z
>
4.9 A. The same
mechanism (water molecules near
z
D
7.9 A are closer to the bulk water than
those near
z
D
4.9 A) makes the height of the peak of
P
WW
for
d
D
7.4 A
lower than that for
d
D
4.9 A. The total interaction potential
P
(
z
)isgivenby
P
(
z
)
D
P
WC
(
z
)
C
P
WW
(
z
). For
d
D
7.4,
4.9, 4.9, and 7.4 A, the distributions of
P
(
z
) are lifted up. The higher the total interaction potential is, the less the water flux
through the CNT is. In the case of
d
D
0 A, the average interaction potential is lower
than that in the others, which results in the largest net flux. In the cases of
d
D
4.9
