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Abstract
This article reviews recent numerical studies of thermal transport in graphene, with a focus on molecular dynamics simulation, the atomistic Green’s function method, and the phonon Boltzmann transport equation method. The mode-wise phonon contribution to the intrinsic thermal conductivity (κ) of graphene and the effects of extrinsic mechanisms—for example, substrate, isotope, impurities, and defects—on κ are discussed. We also highlight the insights from numerical studies aimed at bridging the gaps between 1D, 2D, and 3D thermal transport in carbon nanotubes/graphene nanoribbons, graphene, and graphite. Numerical studies on thermal transport across the interface between graphene and other materials and nonlinear thermal transport phenomena such as thermal rectification and negative differential thermal resistance are also reviewed.
| NOMENCLATURE | ||
| A | = | cross-sectional area |
| Cp | = | heat capacity |
| c | = | specific heat |
| d | = | diameter of carbon nanotube |
| G | = | thermal conductance |
| GI | = | interfacial thermal conductance |
| ħ | = | reduced Planck’s constant |
| J | = | heat current |
| k | = | wave vector |
| kB | = | Boltzmann constant |
| L | = | length |
| N | = | number of layers in multi-layer graphene |
| NA | = | Avogadro’s number |
| n | = | phonon occupation number |
| RI | = | interfacial thermal resistance |
| Δr | = | root-mean-square height of edge variations in graphene nanoribbons |
| T | = | temperature |
| ΔT | = | temperature bias |
| = | temperature gradient | |
| t | = | time |
| V | = | volume |
| = | group velocity | |
| w | = | width of graphene nanoribbons |
| Greek Symbols | = | |
| α | = | exponent of the power law function for the length dependence of the thermal conductivity |
| δ | = | thickness of single-layer graphene or the wall of single-walled carbon nanotube, 0.335nm |
| η | = | thermal rectification ratio |
| = | Debye temperature | |
| κ | = | thermal conductivity |
| λ | = | phonon mean free path |
| ν | = | index of phonon branches |
| Ξ | = | transmission function |
| ρ | = | mass density |
| τ | = | phonon relaxation time |
| ω | = | angular frequency |
| NOMENCLATURE | ||
| A | = | cross-sectional area |
| Cp | = | heat capacity |
| c | = | specific heat |
| d | = | diameter of carbon nanotube |
| G | = | thermal conductance |
| GI | = | interfacial thermal conductance |
| ħ | = | reduced Planck’s constant |
| J | = | heat current |
| k | = | wave vector |
| kB | = | Boltzmann constant |
| L | = | length |
| N | = | number of layers in multi-layer graphene |
| NA | = | Avogadro’s number |
| n | = | phonon occupation number |
| RI | = | interfacial thermal resistance |
| Δr | = | root-mean-square height of edge variations in graphene nanoribbons |
| T | = | temperature |
| ΔT | = | temperature bias |
| = | temperature gradient | |
| t | = | time |
| V | = | volume |
| = | group velocity | |
| w | = | width of graphene nanoribbons |
| Greek Symbols | = | |
| α | = | exponent of the power law function for the length dependence of the thermal conductivity |
| δ | = | thickness of single-layer graphene or the wall of single-walled carbon nanotube, 0.335nm |
| η | = | thermal rectification ratio |
| = | Debye temperature | |
| κ | = | thermal conductivity |
| λ | = | phonon mean free path |
| ν | = | index of phonon branches |
| Ξ | = | transmission function |
| ρ | = | mass density |
| τ | = | phonon relaxation time |
| ω | = | angular frequency |