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Examined graphene GBs constructed using mirror reflection of GNRs with different chiralities: (a) grain-4, (b) grain-7, (c) grain-10, and (d) LD. (e) Example for the chirality of the GNR underlying grain-4.
Phonon transmission along graphene structures with periodic boundary conditions in the transverse direction (also see Fig. 1 ). (a) Computed dispersion showing phonon energy ℏω vs. wave vector q. L, T, and Z labels correspond to longitudinal, transverse, and out-of-plane phonon displacements. A and O labels are for acoustic and optical phonons, respectively. (b) Corresponding transmission function (i.e., number of modes per width) across pristine graphene of chiralities from Fig. 1 . Individual chiralities are not labeled because all display the same transmission spectrum. The subset of out-of-plane ZA and ZO modes is shown separately. (c) Computed transport across grains from Fig. 1 , revealing that transmission depends on the grain structure. Grain-4 (g-4) and grain-7 (g-7) have similar transmission, grain-10 (g-10) exhibits lower transmission, and LD has the worst transmission.
(a) Thermal conductance vs. temperature across various defects (GBs and LD) corresponding to Fig. 1 . Calculations are performed using periodic boundary conditions in the transverse direction (width 6.5 nm) based on transmission spectra of Fig. 2 . The upper limit of ballistic conductance in graphene with no defects ( ) is displayed for comparison. (b)Thermal conductance vs. temperature along graphene with a defect, normalized by the ballistic conductance of the same case with no defects ( ). At room temperature, the grain-4 and grain-7 GB structures show the largest thermal conductance (∼80% of pristine graphene), and the LD the lowest (∼50% of pristine graphene).
Thermal properties of structures calculated without using periodic boundary conditions in the transverse direction. (a) Ballistic thermal conductance in pristine GNRs of the chirality indicated, see Fig. 1 . (b) Phonon transmission in GNRs with a GB or LD normalized by transmission of the same GNRs without defects (T GB) as a function of phonon energy, ℏω. (c)Thermal conductance vs. temperature along GNRs with a defect, normalized by the ballistic conductance of the same GNRs with no defects ( ).
(a) Simulation results (without GBs, lines) fitted against experimental data (Ref. 31 , symbols) for thermal conductivity of monocrystalline graphene on SiO2 substrate. (b) Corresponding thermal conductivity of polycrystalline graphene as a function of average grain size ℓ G, calculated using the thermal conductance of GBs from Fig. 4 . The thermal conductivity depends on defect type (GB or LD) and becomes strongly affected when grain sizes are below dimensions a few times the intrinsic phonon mean free path in substrate-supported graphene (∼100 nm at room temperature) (also see Ref. 3 ).
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