Environmental Engineering Reference
In-Depth Information
On the other hand, at the room temperature, even a single
defect influences the thermal transport in carbon nanotube. The
influence of defect scattering in
thin
carbon nanotubes on the
thermal conductance is more significant than that in
thick
carbon
nanotubes.Wealsoexplainedtheinfluenceofrandomlly-distributed
13
C isotopes on the thermal transport in carbon nanotubes.
Interestingly, the phonon-transmission fluctuation in the diffusive
regime is always 0.35
±
0.02, irrespective of the average phonon
transmission, the tube chirality, and the concentrations and masses
of isotopes. We also found that the histogram, which has a Gaussian
distribution in the diffusive regime, has a lognormal distribution
in the localization regime. These features share much in common
with disordered electron systems despite the different statistics
of electrons and phonons. Moreover, we would emphasize that
the knowledges obtained here are applicable to various low-
dimensionalnanostructures other than carbon nanotubes.
Recently, novel thermal devices such as a thermal rectifier [30-
33], thermal transistor [34], and phonon waveguide [35, 36] have
been proposed. However, many characteristic features ofsuch novel
devices remain to be elucidated yet. To design practical devices, it
isessentialtogainanunderstandingoftheunderlyingmechanisms.
Theauthorshopethatthischapterwillserveasausefulguidelinefor
students and researchers who enter into this new and challenging
field.
Appendix A: NEGF Formulation of Phonon Transmission
Function
AsmentionedinSection2.23,thephonontransmissionfunctioncan
be expressed as Eq. 2.11. Here, we give a derivation of Eq. 2.11 in
detail. The system Hamiltonian
H
sys
is described as the sum of the
harmonicterm
⎡
⎣
⎤
⎦
p
i
α
(
t
)
2
M
i
s
i
α
(
t
)
−
s
j
β
(
t
)
2
k
i
α
,
j
β
2
H
har
=
+
(A.1)
∈
>
sys
α
=
i
i
β
=
xyz
j
xyz
