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Unification of nonequilibrium molecular dynamics and the mode-resolved phonon Boltzmann equation for thermal transport simulations

Journal Article · · Physical Review B
 [1];  [2];  [1];  [3];  [4];  [4];  [2];  [1]
  1. Shanghai Jiao Tong Univ., Shanghai (China)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Energy and Transportation Science Division
  3. Aalto Univ. (Finland)
  4. Purdue Univ., West Lafayette, IN (United States)
+ Show Author Affiliations

Nano-size confinement induces many intriguing non-Fourier heat conduction phenomena, such as nonlinear temperature gradients, temperature jumps near the contacts, and size-dependent thermal conductivity. Over the past decades, these effects have been studied and interpreted by nonequilibrium molecular dynamics (NEMD) and phonon Boltzmann transport equation (BTE) simulations separately, but no theory that unifies these two methods has ever been established. In this work, we unify these methods using a quantitative mode-level comparison and demonstrate that they are equivalent for various thermostats. We show that different thermostats result in different non-Fourier thermal transport characteristics due to the different mode-level phonon excitations inside the thermostats, which explains the different size-dependent thermal conductivities calculated using different reservoirs, even though they give the same bulk thermal conductivity. Specifically, the Langevin thermostat behaves like a thermalizing boundary in phonon BTE and provides mode-level thermal-equilibrium phonon outlets, while the Nose-Hoover chain thermostat and velocity rescaling method behave like biased reservoirs, which provide a spatially uniform heat generation and mode-level nonequilibrium phonon outlets. These findings explain why different experimental measurement methods can yield different size-dependent thermal conductivity. They also indicate that the thermal conductivity of materials can be tuned for various applications by specifically designing thermostats. Finally, the unification of NEMD and phonon BTE will largely facilitate the study of thermal transport in complex systems in the future by, e.g., replacing computationally unaffordable first-principles NEMD simulations with computationally less expensive spectral BTE simulations.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE Office of Energy Efficiency and Renewable Energy (EERE); National Natural Science Foundation of China (NNSFC)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1616819
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 15 Vol. 101; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (67)

Fast Parallel Algorithms for Short-Range Molecular Dynamics journal March 1995
Moment model and boundary conditions for energy transport in the phonon gas journal September 2013
Homogeneous NEMD algorithm for thermal conductivity—Application of non-canonical linear response theory journal October 1982
Effect of the accuracy of interatomic force constants on the prediction of lattice thermal conductivity journal October 2017
Enhanced thermal conduction and influence of interfacial resistance within flexible high aspect ratio copper nanowire/polymer composites journal May 2017
Impacts of potential models on calculating the thermal conductivity of graphene using non-equilibrium molecular dynamics simulations journal April 2017
Decompose the electron and phonon thermal transport of intermetallic compounds NiAl and Ni 3 Al by first-principles calculations journal February 2018
Dual-wavelength flash Raman mapping method for measuring thermal diffusivity of suspended 2D nanomaterials journal November 2019
Heat Flux for Many-Body Interactions: Corrections to LAMMPS journal August 2019
Thermally and Molecularly Stimulated Relaxation of Hot Phonons in Suspended Carbon Nanotubes journal February 2006
Length-dependent thermal conductivity in suspended single-layer graphene journal April 2014
Nanoscale thermal transport journal January 2003
Intrinsic lattice thermal conductivity of semiconductors from first principles journal December 2007
Transient ballistic and diffusive phonon heat transport in thin films journal July 1993
Molecular dynamics simulation of thermal energy transport in polydimethylsiloxane journal April 2011
A unified formulation of the constant temperature molecular dynamics methods journal July 1984
Nosé–Hoover chains: The canonical ensemble via continuous dynamics journal August 1992
Nanoscale thermal transport. II. 2003–2012 journal March 2014
Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films journal May 2015
Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations journal March 2016
Role of energy distribution in contacts on thermal transport in Si: A molecular dynamics study journal December 2016
Thermal transport at the nanoscale: A Fourier's law vs. phonon Boltzmann equation study journal January 2017
Modeling quasi-ballistic transient thermal transport with spatially sinusoidal heating: A McKelvey-Shockley flux approach journal May 2017
Resolving different scattering effects on the thermal and electrical transport in doped SnSe journal July 2019
Influence of thermostatting on nonequilibrium molecular dynamics simulations of heat conduction in solids journal December 2019
Heat transport in low-dimensional systems journal September 2008
Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface journal February 1994
Phonon Dynamics at Surfaces and Interfaces and Its Implications in Energy Transport in Nanostructured Materials—An opinion Paper journal April 2015
A Review of Thermal Transport in Low-Dimensional Materials Under External Perturbation: Effect of Strain, Substrate, and Clustering journal January 2017
Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations journal May 2014
Electrons and Phonons book January 2001
Canonical dynamics: Equilibrium phase-space distributions journal March 1985
Revisiting phonon-phonon scattering in single-layer graphene journal August 2019
Modeling solid-state chemistry: Interatomic potentials for multicomponent systems journal March 1989
Molecular-dynamics calculation of the thermal conductivity of vitreous silica journal June 1999
Simulation of thermal conductivity and heat transport in solids journal February 1999
Molecular-dynamics simulation of thermal conductivity of silicon crystals journal January 2000
Comparison of atomic-level simulation methods for computing thermal conductivity journal April 2002
Phonon transport in nanowires coated with an amorphous material: An atomistic Green’s function approach journal December 2003
Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation journal March 2004
Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations journal February 2009
Kapitza conductance of silicon–amorphous polyethylene interfaces by molecular dynamics simulations journal March 2009
Thermal boundary resistance predictions from molecular dynamics simulations and theoretical calculations journal October 2009
Tuning the thermal conductivity of polymers with mechanical strains journal May 2010
Size effects in molecular dynamics thermal conductivity predictions journal June 2010
Length-dependent thermal conductivity of single extended polymer chains journal September 2012
Finite-size effects on molecular dynamics interfacial thermal-resistance predictions journal August 2014
Role of anharmonic phonon scattering in the spectrally decomposed thermal conductance at planar interfaces journal October 2014
Frequency-dependent phonon mean free path in carbon nanotubes from nonequilibrium molecular dynamics journal March 2015
Force and heat current formulas for many-body potentials in molecular dynamics simulations with applications to thermal conductivity calculations journal September 2015
Quantitatively analyzing phonon spectral contribution of thermal conductivity based on nonequilibrium molecular dynamics simulations. I. From space Fourier transform journal November 2015
Reliability of Raman measurements of thermal conductivity of single-layer graphene due to selective electron-phonon coupling: A first-principles study journal March 2016
Full quantification of frequency-dependent interfacial thermal conductance contributed by two- and three-phonon scattering processes from nonequilibrium molecular dynamics simulations journal March 2017
Spectral analysis of nonequilibrium molecular dynamics: Spectral phonon temperature and local nonequilibrium in thin films and across interfaces journal May 2017
Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon journal March 2018
Understanding the mechanism of diffuse phonon scattering at disordered surfaces by atomistic wave-packet investigation journal October 2018
Unexpected high inelastic phonon transport across solid-solid interface: Modal nonequilibrium molecular dynamics simulations and Landauer analysis journal January 2019
Application of atomic stress to compute heat flux via molecular dynamics for systems with many-body interactions journal May 2019
Conductance viewed as transmission journal March 1999
Molecular Dynamics Study of Solid Thin-Film Thermal Conductivity journal March 2000
Computation of Sub-Micron Thermal Transport Using an Unstructured Finite Volume Method journal December 2002
Submicron Heat Transport Model in Silicon Accounting for Phonon Dispersion and Polarization journal December 2004
Microscale Heat Conduction in Dielectric Thin Films journal February 1993
Effect of Phonon Dispersion on Thermal Conduction Across Si/Ge Interfaces journal October 2011
Molecular Dynamics Simulations of Heat Conduction in Nanostructures: Effect of Heat Bath journal July 2010
Thermal Conductivity Calculation with the Molecular Dynamics Direct Method I: More Robust Simulations of Solid Materials journal October 2011
Thermal Interface Conductance Between Aluminum and Silicon by Molecular Dynamics Simulations journal February 2015

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Boltzmann theory
ballistic transport
heat transfer
lattice thermal conductivity
molecular dynamics
nanostructures
phonons
thin films