Environmental Engineering Reference
In-Depth Information
Figure 1.11
The thermal conductivity
κ
versus the tube length
L
in log-log
scale for both (5,5)and (10,10) SWNTsat 300 K and 800 K, respectively.
interaction between the transverse modes and longitudinal modes
becomes stronger, which leads to a smaller value of
β
. For the (5,5)
tube at
T
=
300 K, because the small tube radius, the coupling
between transverse and longitudinal mode is still very weak, this
leads to the thermal conduction behavior is very close to that
one in the 1D Fermi-Pasta-Ulam-type lattice, namely, the thermal
conductivity
κ
diverges with
L
,as
L
0.4
.
The length dependent thermal conductivity was predicted by
MD simulation, then it was verified experimentally [49]. This shows
that MD simulation does not rely on any thermodynamic limit
assumptions and it thus is applicable for any system size, which
is important for the study of thermal conductivity of realistic
nanoscalesystems.
The high thermal conductivity of SWNTs is for a pure and
defect free tube. Actually, nanotubes can have natural defects and
dopingintheprocessoffabrication.Dopingwithisotopesandother
atoms has played key roles in some of the most important problems
of the materials. Since the phonon frequency depends on mass,
