Environmental Engineering Reference
In-Depth Information
Figure 3.7 Schematicillustrationoftwo-probetransportsystem,wherethe
centertransportregion(C)isconnectedtoleft(L)andright(R)semi-infinite
thermal leads. (a) N a -AGNR, (b) N z -ZGNR. Reprinted with permission from
Ref.[38].Copyright 2009, AIPPublishing LLC.
N a ( N z ) carbon dimer lines (zigzag carbon chains) across the
ribbon width. Since GNRs with larger ribbon width ( W ) support
more phonon transport channels and thus gives higher thermal
conductance (
σ
), we define scaled thermal conductance as thermal
conductance per unit area (
σ/
S ) for comparing thermal-transport
abilityamongdifferentGNRsorcomparingwithothermaterials.The
cross sectional area S is defined to be S = W δ ,where δ = 0.335 nm
is chosen as the layer separation in graphite. Note that CNTs can
be viewed as rolled-up GNRs. For the sake of comparison, we also
consider armchair carbon nanotubes (ACNTs) and zigzag carbon
nanotubes(ZCNTs), whose widthsrefer to their circumferences.
In the transport calculations, we first perform geometric
optimization and then calculate force constants using the second-
generationreactiveempiricalbondorderpotential[39].Thisempir-
ical potential is widely used for simulating materials composed of
carbon and hydrogen. It was proved to give phonon modes of GNRs
compatible with density functional theory calculations [40]. The
calculated force constants are used as the phonon Hamiltonian. The
complex many-body interactions (phonon-phonon and electron-
phononinteractions),whichareonlyimportantatveryhightemper-
atures, are neglected here. By following the procedures described
previously, we calculate the phonon Green's function and then
 
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