Environmental Engineering Reference
In-Depth Information
0.2
<τ <
300 for Nose-Hoover heat bath and 1
<λ<
100 for
Langevin heat bath, are recommended.
1.5.3
Some Applications
ThethermalconductionisdescribedbyFourier'slaw,wherethermal
conductivity is defined as one intrinsic property of a material. For
a certain material with definite composition and structure, the
thermal conductivity is believed to be an intensive property that
should be independent on the size and geometry. This belief has
received great success in describing macroscopic heat transport in
the past two hundred years.
However, a rigorous proof for Fourier's law from microscopic
Hamiltonian dynamics is still lacking, even though it is already 200-
year old. Therefore, it is still an open and much debated question
whether Fourier's law is valid or applicable in low-dimensional
systems. In past two decades, size dependent thermal conductivity
has already been observed in many theoretical models. The
discovery of this anomalous behavior in general low-dimensional
model has inspired enormous studies. Low-dimensional nanoscale
systems have been extensively studied due to their promising
potential applications for future electronic, optoelectronic, and
phononic/thermal devices. Thus these low-dimensional nanoscale
systems are ideal platforms to verify the fundamental physics.
Byusingnon-equilibriummoleculardynamicssimulation,Zhang
and Li [48] studied thermal conductivity of single-walled carbon
nanotubes(SWNTs).Itisclearthat,unlikeitselectroniccounterpart,
the thermal conductivity of SWNTs does not depend on the chirality
both at low temperature and room temperature. The thermal
conductivity
κ
versus the tube length
L
is shown in log-log scale
in Fig. 1.11 for both (5,5) and (10,10) SWNTs at 300 K and 800 K,
respectively. It is interesting to see that thermal conductivity
κ
diverges with SWNT length
L
as
κ
∼
L
β
, and the value
β
depends
on temperature as well as tube radius. For a SWNT,
β
decreases as
temperature increases; and at the same temperature,
β
decreases
as the tube radius increases. This can be qualitatively explained
by the mode coupling theory. At high temperature, the transverse
vibrations are much larger than that at low temperature, thus the
