Thermal Conductivity of Graphene and Graphite: Collective Excitations and Mean Free Paths

Abstract

We characterize the thermal conductivity of graphite, monolayer graphene, graphane, fluorographane, and bilayer graphene, solving exactly the Boltzmann transport equation for phonons, with phonon-phonon collision rates obtained from density functional perturbation theory. For graphite, the results are found to be in excellent agreement with experiments; notably, the thermal conductivity is 1 order of magnitude larger than what found by solving the Boltzmann equation in the single mode approximation, commonly used to describe heat transport. For graphene, we point out that a meaningful value of intrinsic thermal conductivity at room temperature can be obtained only for sample sizes of the order of 1 mm, something not considered previously. This unusual requirement is because collective phonon excitations, and not single phonons, are the main heat carriers in these materials; these excitations are characterized by mean free paths of the order of hundreds of micrometers. As a result, even Fourier's law becomes questionable in typical sample sizes, because its statistical nature makes it applicable only in the thermodynamic limit to systems larger than a few mean free paths. Finally, we discuss the effects of isotopic disorder, strain, and chemical functionalization on thermal performance. Only chemical functionalization is found to play an important role, decreasing the conductivity by a factor of 2 in hydrogenated graphene, and by 1 order of magnitude in fluorogenated graphene.

Temperature-Dependent Mean Free Path Spectra of Thermal Phonons Along the c-Axis of Graphite

“…Considering the measured thermal conductivity is independent of thickness, these boundaries must consist of internal grain boundaries. The trend of the curve as well as the peak position are consistent with prior experimental and theoretical works [32,33]. The measured bulk thermal conductivity at room temperature is between 6.4 W/mK to 7.0 W/mK, in agreement with the accepted value of 6.8 W/mK [14].…”

Thermal conductivity of graphene mediated by strain and size

“…Moreover, unlike the work of Ref. 28, we find qualitatively uniform dependences of k on strain from the full BPE solution and the SMRTA, consistent with that found in strained 3D diamond [40]. Unless specified otherwise, all the results shown below are for N 1 =301 for unstrained and strained is due partly to decreasing magnitude of the anharmonic IFCs with tensile strain [23], which reduces the scattering matrix elements, and partly to the reduction in ZA phonon density of states caused by zone center dispersion linearization [22], which leads to less scatterings of ZA phonons [18].…”

“…The results are 4 partly different with aforementioned MD predictions [18] that k of infinite graphene diverges only under large tensile strain (> 0.02). We note that the SMRTA incorrectly treats the momentum-conserving Normal (N) processes as independent resistive processes on the same footing as Umklapp (U) processes [33], and it can not be used to appropriately present the phonon thermal transport in graphene, as justified by Lindsay et al [23] and Fugallo et al [28]. Based on a full iterative solution of the linearized Boltzmann-Peierls Equation (BPE), Lindsay et al [23] found that ZA phonons give the dominant contributions to k in finite graphene up to 50 μm with strong dependence of k on boundary scattering.…”

“…On the theoretical side, fundamental problems concerning the details of thermal transport in graphene have been subjects of debate [17][18][19][20][21][22][23][24][25][26][27][28][29][30], including the convergence behavior of k with system size, the extent of the diffusive and ballistic transport regimes, the role of flexural acoustic (ZA) phonons for thermal transport and strain effects on the convergence of k. It is generally believed that acoustic phonons [31] dominate the thermal transport in graphene. Based on this, 2D models give a logarithmic divergence with system size [27] but neglect the contributions from ZA phonons due to their low group velocities near the center of first Brillouin zone (FBZ) and their large Grüneisen parameters [32].…”

“…First-principles lattice dynamics calculations [22][23][24]28] of k of graphene within three-phonon scattering framework have also been conducted. Using the single-mode relaxation time approximation (SMRTA), Bonini et al [22] showed that k of infinite graphene diverges under infinitesimal isotropic tensile strains, while k converges to ~550 W/m-K for infinite unstrained graphene at room temperature.…”