Biomedical Engineering Reference
In-Depth Information
Fig. 1.14
Number of water molecules inside the carbon nanotube with respect to time in several
representative systems (reprinted from [
129
]. Copyright 2008 American Physical Society)
N
D
5and
N
D
6 are 0.96 and 0.90 ps, respectively, showing similar probabilities
for two states. When ı
D
0 A, the total probabilities of
N
D
5, 6 are about 52 and
48%, both close to 50%.
The free energy of occupancy fluctuations
G
(
N
) can be calculated by G.N /
D
k
B
T ln p.N /,where
p
(
N
) is the probability of
N
water molecules inside the
nanotube,
k
B
is the Boltzmann constant, and
T
is the temperature.
Figure
1.15
shows that the free energy of
N
D
5 is close to the free energy of
N
D
6forı
6
ı
c
2:0 A. Profile of free energy of occupancy shows that two
states of
N
D
5and
N
D
6aresteadyforı
6
ı
c
2:0 A. The rapid transitions
between the two states in the water permeation across the CNT are similar to those
observed in the KcsA ion channel. However, for ı>ı
c
, free energy of
N
D
4is
the minimum. The behavior of the single-filed water molecules inside the nanotube
becomes different.
