Environmental Engineering Reference
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phonon transmission, and finally compute thermal conductance as
a function of temperature.
The calculated scaled thermal conductance at 300 K versus
width for GNRs and CNTs are presented in Fig. 3.8a. It is very
interesting that thermal conductance of GNRs and CNTs show
quite different shape and width dependence. Specifically, ACNTs
have nearly the same scaled thermal conductance as ZCNTs,
consistent with previous theoretical results [41]. In addition, the
scaled thermal conductance of CNTs weakly depends on their
circumference. Based on these facts, we established that the scaled
thermal conductance of CNTs is insensitive to the change of their
chirality and ribbon width. In contrast, significant size effect and
anisotropy of thermal conductance are observed in GNRs. There,
the scaled thermal conductance decreases rapidly as the ribbon
width increases for narrow GNRs (width smaller than 2 nm),
showingstrongquantumconfinementeffects.WhileforwiderGNRs,
the size dependence becomes weaker but remains observable for
all the GNRs considered by our study. More importantly, ZGNRs
have significantly larger scaled thermal conductance than AGNRs,
indicating a strong anisotropic thermal transport in GNRs.
The appearance of anisotropy in thermal conductance is really
unexpected, if considering the fact that both graphene (i.e., the bulk
counterpartofGNRs)andCNTs(i.e.,rolled-upGNRs)areisotropicin
thermal conductance. This observation raises many interesting and
important questions. What is the origin of the anisotropy? Is this a
generalphenomenon?Howdoestheanisotropyevolveasincreasing
theribbonwidth?Canitbeusedforthermalconductiontuning?For
answering these questions, let us discuss the anisotropic thermal
conductance of GNRs in more details.
We define an anisotropy factor for the thermal conductance of
GNRs as
η
=
[(
σ/
S
)
ZGNR
/
(
σ/
S
)
AGNR
]
−
1 (3.66)
to give a quantitative description of the anisotropic thermal
conductance. As shown in Fig. 3.8b, narrower GNRs generally
exhibit stronger anisotropy, though some irregular variation of the
anisotropy factor is shown up when
W
is less than 2 nm. The
room temperature anisotropy factor changes irregularly from 31%
