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

Abstract

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. 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.

Interpretation of apparent thermal conductivity in finite systems from equilibrium molecular dynamics simulations

“…Following Refs. [27,28], the Langevin thermostat with a coupling time of 0.1 ps is used to generate the heat source and sink. The apparent thermal conductivity in the transport direction is calculated as [27]…”

Remarkable Reduction of Interfacial Thermal Resistance in Nanophononic Heterostructures

“…The effects of heat baths on molecular dynamics calculation results have attracted long term research attention. [60][61][62][63][64] In principle, these two heat baths may correspond to different experimental conditions. [64] When these two heat baths are used in NEMD simulation, different thermostating approaches result in different temperature profile.…”

“…[60][61][62][63][64] In principle, these two heat baths may correspond to different experimental conditions. [64] When these two heat baths are used in NEMD simulation, different thermostating approaches result in different temperature profile. In 2020, Hu et al presented that the Langevin heat bath produces large temperature jump between the thermostat applied and thermostat free layers in small sample, while the Nose-Hoover heat bath does not.…”

“…In 2020, Hu et al presented that the Langevin heat bath produces large temperature jump between the thermostat applied and thermostat free layers in small sample, while the Nose-Hoover heat bath does not. [64] In our current work, we focus on phononic-mismatched BP heterostructure, and the temperature jump at the holey-pristine BP interface is our main concern. Therefore, we select Nose-Hoover heat bath in our calculation.…”

Quantum mechanical modeling of anharmonic phonon-phonon scattering in nanostructures

“…In principle, NEGF and Boltzmann formalisms should provide very similar results in the transport regime where the particle picture of phonons is valid and the coherent effects are negligible. For cross-plane heat transport through a silicon thin film at room temperature, a recent study has shown that the phonon Boltzmann equation could work down to a thickness of about 10 nm [84]. This critical thickness is sound since the dominant phonon coherence length of silicon at room temperature is about 1 nm [6].…”