Environmental Engineering Reference
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the bonding environment at edges, we can qualitatively compare
the delocalization degree of phonons between quasi-1D transport
systemswithdifferentboundaryconditions.Theapproachissimple
and can explain the different scaled thermal conductance observed
for GNRs and CNTs. In GNRs, the bonds that are cut off due to
the formation of edges are perpendicular to the transport direction
for zigzag edges, while they have components along the transport
direction for armchair edges. According to our approach, ZGNRs
wouldgivehigherscaledthermalconductancethanAGNRs.Ifrolling
up GNRs into CNTs, the bonding configuration of the bulk (i.e.,
graphene) is preserved in the whole system. We would expect that
the scaled thermal conductance of CNTs is close to that of ZGNRs,
andweaklydependsonthechiralityanddiameterofCNTs.Allthese
expectations given by this approach are consistent with the results
of ourcalculations.
We have shown that thermal conductance is anisotropic in
GNRs due to the different boundary conditions at edges. The
appearance of anisotropy is independent of phonon scattering and
bulk phonon structure. Actually, the anisotropy found here is not
limited to GNRs, but is expected to also exist in other materials. For
instance, similar anisotropy is found in boron nitride nanoribbons
as revealed by our calculations [44]. Our study demonstrates that
by controlling bonding environments at edges, the delocalization
degree of phonons, and thus the thermal conductance, can be
tuned. This conclusion generally works for any materials. Another
important observation is that the boundary effects on phonon
systems are very long range. Using GNRs as an example, the room
temperatureanisotropyinthermalconductanceissignificantlylarge
(13%) even for GNRs as wide as 35 nm and would only disappear
at
W
>
140 nm. The difference in thermal conductance, caused by
different edge shapes, can be very large for wide GNRs. All these
indicate that thermal conductance can be tuned in a wide range by
edge control.
3.4.2
Origin of High Thermal Conductivity in Graphene
Graphenepossessesextremelyhighthermalconductivity,asdemon-
stratedexperimentallyandtheoretically.Thermalconductivity(
κ
)is
