Anomalous Size Dependence of the Thermal Conductivity of Graphene Ribbons

Abstract

We investigated the thermal conductivity K of graphene ribbons and graphite slabs as the function of their lateral dimensions. Our theoretical model considered the anharmonic three-phonon processes to the second-order and included the angle-dependent phonon scattering from the ribbon edges. It was found that the long mean free path of the longwavelength acoustic phonons in graphene can lead to an unusual non-monotonic dependence of the thermal conductivity on the length L of a ribbon. The effect is pronounced for the ribbons with the smooth edges (specularity parameter p>0.5). Our results also suggest that -contrary to what was previously thought -the bulk-like 3D phonons in graphite can make a rather substantial contribution to its in-plane thermal conductivity. The Umklapp-limited thermal conductivity of graphite slabs scales, for L below ~ 10 m, as log(L) while for larger L, the thermal conductivity approaches a finite value following the dependence K 0 -A×L -1/2 , where K 0 and A are parameters independent of the length. Our theoretical results clarify the scaling of the phonon thermal conductivity with the lateral sizes in graphene and graphite. The revealed anomalous dependence K(L) for the micrometer-size graphene ribbons can account for some of the discrepancy in reported experimental data for graphene.

Phonon transport effects in one-dimensional width-modulated graphene nanoribbons

“…An increase in the width of the wide region W w does not increase the unit cell any further, and thus, it does not affect the constriction resistance which is already formed. This was also observed by Nika et al [9] and Moore et al [25]. Sullivan et al using molecular dynamics in the case of Si nanowires in the presence of nano-constrictions, justified the irrelevance of large W w on the thermal conductance by explaining that the increase of the corrugation amplitude beyond a certain limit introduces atomic heat current separation between the corrugated ridges and the inner channel [23].…”

“…Examples of these features include that: i) the thermal conductivity could deviate from Fourier's law [1][2][3][4][5], ii) a crossover is observed from ballistic into diffusive transport regimes [6,7], or from nanoto macro-scale behaviors [8,9], iii) the thermal conductivity could even increase under channel width confinement [10,11], iv) band mismatch under extreme confinement could result to phonon localization and 'effective transmission bandgaps' [12], v) heat transport could be below the Casimir or the amorphous limits, and many more [13,14]. Several interesting device concepts have also emerged recently in the area of phononics, which attempt to use heat to perform transistor action [15], create heat rectifiers [16], engineer the sound velocities and phonon dispersions, etc.…”

“…For this we employ lattice dynamics based on a force-field method and the Landauer formalism. Graphene and GNRs have huge thermal conductivities in their pristine form, reaching values as high as 3080-5150 W/mK at room temperature [9,[34][35][36][37][38][39][40]. Recent theoretical works even suggest values up to ~6000 W/mK, with a large proportion of phonon mean-free-paths beyond 10μm [41][42][43].…”

Generalized Two-Temperature Model for Coupled Phonons in Nanosized Graphene

“…Recent studies 9,23,[48][49][50] showed that the thermal conductivity of graphene increases logarithmically (~logL) with the size of sample, which is taken to fit MD results shown in Fig. 3.…”

Specific heat of twisted bilayer graphene: Engineering phonons by atomic plane rotations

“…Theoretical investigations employed different models of the lattice vibrations, molecular dynamics simulations, density functional method and Boltzmann transport equation approach [13][14][19][20][21][22][23]. Recently the attention has been shifted to twisted few-layer graphene (T-FLG), which demonstrates intriguing electron [24][25][26][27] and phonon properties [28][29][30][31][32][33][34][35][36].…”