Thermal Resistance by Transition Between Collective and Non-Collective Phonon Flows in Graphitic Materials

Abstract

Phonons in graphitic materials exhibit strong normal scattering (N-scattering) compared to umklapp scattering (U-scattering). The strong N-scattering cause collective phonon flow, unlike the relatively common cases where U-scattering is dominant. If graphitic materials have finite size and contact with hot and cold reservoirs emitting phonons with non-collective distribution, Nscattering change the non-collective phonon flow to the collective phonon flow near the interface between graphitic material and a heat reservoir. We study the thermal resistance by N-scattering during the transition between non-collective and collective phonon flows. Our Monte Carlo solution of Peierls-Boltzmann transport equation shows that the N-scattering in graphitic materials reduce heat flux from the ballistic case by around 15%, 30%, and 40% at 100, 200, and 300 K, respectively. This is significantly larger than ~ 5% reduction of Debye crystal with similar Debye temperature (~ 2300 K). We associate the large reduction of heat flux by N-scattering with the non-linear dispersion and multiple phonon branches with different group velocities of graphitic materials.

Hydrodynamic phonon transport: past, present and prospects

“…The profile is calculated by Monte Carlo method of the PBE assuming the Callaway's scattering model. The rate of N-scattering is assumed 10 10 s -1 and U-scattering is ignored [58]. The large thermal resistance by N-scattering for graphitic materials can be explained with their non-linear phonon dispersion with many phonon branches.…”

Size effect on phonon hydrodynamics in graphite microstructures and nanostructures

“…Callaway's dual relaxation model [21] represents a good approximation to the full scattering term in the phonon Boltzmann equation [10,22] and has been widely adopted in analyzing heat transport in the hydrodynamic regime by analytical or semi-analytical methods [5,[23][24][25][26][27][28][29]. The direct solution of the phonon Boltzmann equation under Callaway's model has been advanced recently by a few numerical schemes including both deterministic methods [30,31] and stochastic ones [32,33]. However, the deterministic numerical method [30,31] was designed for heat transport in 2D graphene ribbons with empirical isotropic phonon properties.…”

“…However, the deterministic numerical method [30,31] was designed for heat transport in 2D graphene ribbons with empirical isotropic phonon properties. The gray Monte Carlo simulation [32,33] was conducted in hypothetical graphitic materials due to the lack of knowledge of normal and Umklapp scattering rates and the pending development of the methodology. Thus, none of the previous methods [30][31][32][33] are available to describe heat transport in realistic anisotropic graphite ribbons.…”

“…The gray Monte Carlo simulation [32,33] was conducted in hypothetical graphitic materials due to the lack of knowledge of normal and Umklapp scattering rates and the pending development of the methodology. Thus, none of the previous methods [30][31][32][33] are available to describe heat transport in realistic anisotropic graphite ribbons. In this paper, a pertinent computational framework is developed based on a deterministic numerical solution of Callaway's model.…”

“…Within the computational framework, we investigate the hydrodynamic heat transport in graphite ribbon with finite length and width. The in-plane [19,26,30,36] (or crossplane [28,32]) heat transports along infinitely long (or wide) graphitic ribbons were widely studied previously [3]. A very important hydrodynamic phenomenon, the phonon Knudsen minimum, has been predicted in infinitely long graphene ribbons [30] and graphite ribbons [26].…”