Environmental Engineering Reference
In-Depth Information
instead of bulk property or phonon scattering that gives rise to the
anisotropy in thermal conductance.
Boundary condition affects thermal transport in a very compli-
cated way due to the collective nature of lattice vibrations. Every
phononmodewillbeinfluencediftheboundaryconditionvaries.To
analyze the influence on thermal conductance, which is a weighted
integration of the contribution of all the phonon modes excited,
we look at the whole phonon transmission spectra rather than
focus on individual phonon modes. For comparison we select two
GNRs, 16-ZGNR and 28-AGNR, which share the same ribbon width
(
W
∼
3.3 nm) but different edge shape. The former one gives
higher thermal conductance than the latter one. The influence of
the different boundary condition on their phonon transmission,
as shown in Fig. 3.9a, is strongly frequency-dependent. Negligible
difference in phonon transmission is observed at low-frequency
region (
ω<
100 cm
−
1
), explaining the nearly zero anisotropy
at very low temperatures. While phonon transmission of 16-
ZGNR is obviously higher than that of 28-AGNR at high-frequency
region (especially at 400
∼
600 cm
−
1
and 1400
∼
1650 cm
−
1
). The
differenceinthermalconductanceofthetwoGNRsisobviousathigh
temperatures, as shown in Fig. 3.9b.
Next, we artificially modify the boundary conditions of GNRs
to further understand its effect on the anisotropy in thermal
conductance. This is achieved by setting the mass of edge atoms to
infinitely large (10
7
atomic mass units in the calculation) so as to
impose fixed boundary condition on the above two GNRs (i.e., 16-
ZGNRand28-AGNR).AsshownintheinsetofFig.3.9b,duetothefix
of edge atoms in GNRs, the scaled thermal conductance decreases
for both GNRs. Differently, the decrease is relatively smaller in 28-
AGNR than in 16-ZGNR, indicating that the boundary condition
imposed by armchair edge is more like fixed boundary condition.
The anisotropy becomes smaller but does not disappear after
imposing fixed boundary condition. This, on the other hand, shows
that the anisotropy is robust even under this extreme condition,
which is substantially different from the free or periodic boundary
condition generally used.
Finally we show that the boundary effects on thermal con-
ductance can be qualitatively compared for different edge shapes.
