Environmental Engineering Reference
In-Depth Information
Figure 2.6
Phonon transmission function
ζ
(
ω
) for the (8,8) SWNTs. Red
and blue curves represent
ζ
(
ω
) for SWNTs with vacancy and SW defect,
respectively. The dashed curves are for the perfect SWNT. The top-left inset
describes the phonon density around the SW defect at 7.0 meV indicated
by the blue arrow, and the bottom-right inset is that around the vacancy at
11.6 meV indicated by the red arrow. The red shading on the atom spheres
indicates the phonon density. (The red shading is not on the same scale for
the two insets.)
the low-energy region below 2.4 meV, being the energy gap of the
lowest optical modes, the dashed curve shows
ζ
p
(
ω
)
=
4 indicating
the number of acoustic branches corresponding to the longitudinal,
twisting, anddoubly degenerated flexural modes.
The transmission function
ζ
vac
(
ω
) for the (8,8) SWNT with the
vacancy and
ζ
SW
(
ω
) for the (8,8) SWNT with the Stone-Wales (SW)
defects [22] are described by the red and blue curves, respectively,
in Fig. 2.6. The
ζ
vac/SW
(
ω
) is dramatically deformed from
ζ
p
(
ω
)
owing to defect scattering particularly at high energies. However,
it remains unchanged in the low-energy region. This is because the
longwavelengthacousticphononswithlowenergiesintheCNTsare
notscatteredbylocaldefectssuchasvacanciesandSWdefects.This
leads to the important conclusion that the thermal conductance of
