Spectral analysis of nonequilibrium molecular dynamics: Spectral phonon temperature and local nonequilibrium in thin films and across interfaces

Abstract

Although extensive experimental and theoretical works have been conducted to understand the ballistic and diffusive phonon transport in nanomaterials recently, direct observation of temperature and thermal nonequilibrium of different phonon modes has not been realized. Herein, we have developed a method within the framework of molecular dynamics to calculate the temperatures of phonon in both real and phase spaces. Taking silicon thin film and graphene as examples, we directly obtained the spectral phonon temperature (SPT) and observed the local thermal nonequilibrium between the ballistic and diffusive phonons. Such nonequilibrium also generally exists across interfaces and is surprisingly large, and it provides an additional thermal interfacial resistance mechanism. Our SPT results directly show that the vertical thermal transport across the dimensionally mismatched graphene/substrate interface is through the coupling between flexural acoustic phonons of graphene and the longitudinal phonons in the substrate with mode conversion. In the dimensionally matched interfaces, e.g. graphene/graphene junction and graphene/boron nitride planar interfaces, strong coupling occurs between the acoustic phonon modes on both sides, and the coupling decreases with interfacial mixing. The SPT method together with the spectral heat flux can eliminate the size effect of the thermal conductivity prediction induced from ballistic transport. Our work shows that in thin films and across interfaces, phonons are in local thermal nonequilibrium. * λQλ ,whereQ λ (t) is the time derivative of normal mode amplitude, which is given by the Fourier transform of atomic arXiv:1703.10957v1 [cond-mat.mes-hall]

A Review of Experimental and Computational Advances in Thermal Boundary Conductance and Nanoscale Thermal Transport across Solid Interfaces

“…In this regard, interfacial thermal transport has been mainly studied via either the equilibrium MD simulations with the Green–Kubo approach or the nonequilibrium MD simulations based on the “direct” method of applying heat baths on a computational domain and determining the temperature drop at the interface . A comprehensive review of the two methods is provided by Schelling et al Variations and modifications of these two methods have resulted in computational tools that are able to calculate the modal or the spectral decomposition of heat current across interfaces . Some of the most notable results and advances in our knowledge of interfacial transport through these methods will be discussed below, as this analysis approach represents a relatively new technique to advance our understanding of phonon thermal transport across interfaces.…”

“…To understand the low conductances associated with interfaces comprised of 2D materials, there have been considerable advances both from atomistic simulations as well as analytical and theoretical frameworks . One of the main findings from the MD simulations is that the conductance across the dimensionally mismatched graphene and substrate can be ascribed to the coupling between flexural acoustic phonons of graphene and the longitudinal phonons in the substrate .…”

A Review of Simulation Methods in Micro/Nanoscale Heat Conduction

“…Owing to the newly developed computational methods in the last twenty years, the temperature and heat flow can be resolved into phonon [16][17][18][19] contributions, and the spatial and time information of phonons is more accessible to give a comprehensive understanding of ballistic, hydrodynamic, coherent, localized and other unique transport [20][21][22][23][24][25] regimes.…”

Phonon branch-resolved electron-phonon coupling and the multitemperature model

“…Theoretical methods are needed to capture such modal phonon nonequilibrium. Modal and spatial Boltzmann transport equation (BTE) [41][42][43] and molecular dynamics combined with modal analysis [44,45] are rigorous and accurate methods, but they are quite complicated and this hinders their access by experimentalists. Alternatively, a simple multitemperature model (MTM) has been developed which is essentially an extension of TTM that can resolve the temperatures of different phonon branches [5,38].…”