Environmental Engineering Reference
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the lowest position and has the largest intensity among the peaks.
Similarly, ζ SW ( ω ) has some dips at particular energies coinciding
withpositionsof the LDOS peak due to the SW defect.
The dip at 7.0 meV indicated by the blue arrow lies at the lowest
position among the LDOS peaks associated with the SW defect. As
showninthetop-leftinsetinFig.2.6,thephonondensityat7.0meV
isstrongly localized around the SW defect.
Substitutingthe
ζ
ω
(
)obtainedintoEq.2.7,wecandeterminethe
κ
thermal conductance
( T ) as a function of temperature T . The low-
temperaturebehaviorof
κ
( T )normalizedbytheuniversalquantum
κ 0 for (6,6), (8,8) and (10,10) SWNTs with and without defects are
showninFig.2.7.Thered(blue)curvesrepresent κ vac(SW) /
κ
0 for the
CNTs with the vacancy (SW defect). The dashed curves represent
κ p / κ 0 for perfect CNTs. Asdiscussed above, all thermal conductance
curvesapproach4inthelimitof T 0,eveninthepresenceoflocal
defects. In the temperature region shown in Fig. 2.7, the thermal
conductance κ SW / κ 0 is slightly lower than κ vac / κ 0 .Thisisbecause
propagating phonons in this region are dominantly scattered by the
phonon localized state associated with the SW defects at 7.0 meV,
and not by the phonon localized states associated with a vacancy at
the higher energy of 11.6 meV (Fig. 2.6).
We next describe the tube diameter dependence of defect
scattering on thermal conductance for moderate temperatures up
to 300 K. Figure 2.8 shows the ratios κ vac / κ p and κ SW / κ p for (6,6),
(8,8), and (10,10) SWNT s as a function of T . The black, red, and
blue solid (dashed) curves are the ratios κ vac(SW) / κ p for (6,6), (8,8),
and (10,10) SWNTs with the vacancy (SW defect), respectively. All
the
κ p curves decrease rapidly with increasing temperature
and become nearly independent of the temperature at
κ vac(SW) /
300 K. The
κ p also decreases as the CNT gets thinner.
In other words, the influence of defect scattering in thin CNTs
on the thermal conductance is more significant than that in thick
CNTs. Interestingly, κ vac / κ p is clearly lower than κ SW / κ p at moderate
temperatures, which is in sharp contrast with the low temperature
case. That is, the incident phonons are scattered more strongly by
the vacancy than by the SW defect. This result is consistent with
results obtained by classical molecular dynamics simulations at
room temperature [23].
κ vac(SW) /
terminal value of
 
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