Dynamic properties of C
60
cl usters i n DMPC membrane. The
translational motion of C
highly depends on their interesting
structural behavior as discussed in the previous section. Figure
3 shows the mean square displacements of both C
60
60
and a single
DMPC lipid in the direction parallel to the membrane. When
the nanoparticle moves inside the membrane as seen in Fig. 3(a),
a single C
60
in dilute concentration diffuses in the same pace
as a single DMPC lipid. The similar behavior was also observed
from the motion of a flat nanoparticle with the similar molecular
weight.
43
The dynamic coupling between a single C
60
(a flat naHowever, in high C
60
concentration, C
moves 2.4 times as
fast as that in dilute concentration. As mentioned above, this
interesting phenomenon results from the widening of the membrane
center region due to the
presence
of the dispersed
fullerenes.
This
gap
facilitates the
translational
motion
of
fullerenes
60
in the direction parallel to the membrane plane.
On the other hand, in the water region as seen in Fig. 3(b), a
single C
in dilute concentration shows higher mobility than
that in concentrated solution, which is the result of the cluster
formation of C
60
.
The structural behavior of C
60
in both dilute and concentrated
solutions also plays a significant role in the rotational motion
of C
60
60
. It has been reported that the rotational relaxation time
τ of C
is 3.1 ps in the gas phase and 15.5 ps in a 1,1,2,2-tetra-
chloroethane at 283 K.
C
60
60
56-57
The temperature dependence of the
rotation in the solid state can also be approximated by τ = τ
exp(T
a
/T),
56
where τ
0
= 0.81 ± 0.10 ps and T
= 695 ± 45 K.
According to the expression, the rotational relaxation time at
T = 308 K is expected to be τ = 7.7 ps in the solid state. We have
also obtained the rotational relaxation time by fitting the time
a
0