Environmental Engineering Reference
In-Depth Information
210 nm-long (8,0) SWNT
with 9.4% C
(a)
(b)
625 nm-long (5,5) SWNT
with 15% C
0.6
14
13
0.4
0.2
0
0
400
800
1200
1600
0
400
800
1200
1600
ω
(cm )
ω
(cm )
-1
-1
Figure 2.10
The root-mean-square phonon transmission for (a) a 625 nm-
long (5,5) SWNT with 15%
13
C, and (b) a 210 nm-long (8,0) SWNT with
9.4%
14
C.Thetriangles,circles,andrectanglesrepresentnumericaldatafor
ζ
(
ω
) in the ballistic, diffusive, and localization regimes, respectively. The
dashed linesare the universal phonon-transmission fluctuation in Eq. 2.33.
2.3.3.2 Universal phonon-transmission fluctuation
We now discuss the phonon-transmission fluctuation, which is
defined by a standard deviation
ζ
(
ω
)
2
−
ζ
(
ω
)
2
.
ζ
(
ω
)
=
(2.32)
Figure 2.10 shows
ζ
(
ω
) for (a) 625 nm-long (5,5) SWNT with
15%
13
C and (b) 210 nm-long (8,0) SWNT with 9.4%
14
C. The
fluctuation of a physical quantity generally decreases as its average
value increases. However, the fluctuation of phonon transmission
is constant within the frequency region in the diffusive regime
although
<ζ
ω
>
ω
(
)
varies depending on
(Fig. 2.9a). The constant
value isestimated to be
ζ
(
ω
)
=
0.35
±
0.02
(2.33)
and is indicated by the dashed lines in Fig. 2.10a,b. Thus,
ζ
(
ω
)
in the diffusive regime is universal and does not depend on the
background phonon transmission, the tube chirality and length,
theisotopeconcentration,anddifferencesbetween
13
Cand
14
C.The
universal phonon-transmission fluctuation is realized only in the
diffusive regime and not in the ballistic and localization regimes.
Interestingly, the value in Eq. 2.33 is the same as the value of
the universal conductance fluctuation (UCF) for coherent electron
