Influence of thermostatting on nonequilibrium molecular dynamics simulations of heat conduction in solids

Li, Zhen; Xiong, Shiyun; Sievers, C.; Hu, Yunfeng; Fan, Zheyong; Wei, Ning; Bao, Hua; Chen, Shunda; Donadio, Davide; Ala-Nissilä, Tapio

doi:10.1063/1.5132543

Cited by 147 publications

(94 citation statements)

References 78 publications

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“…3 changes geometry. We show in the inset of cous heat equations predict a steeper-than-Fourier's law or non-linear temperature gradient that is reminiscent of that obtained in molecular dynamics simulations [88][89][90][91][92][93][94][95][96][97] and in explicit solutions of the LBTE [34].…”

Section: Case Studysupporting

confidence: 59%

Generalization of Fourier’s Law into Viscous Heat Equations

2020

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Heat conduction in dielectric crystals originates from the propagation of atomic vibrational waves, whose microscopic dynamics is well described by linearized or generalized phonon Boltzmann transport. Recently, it was shown that the thermal conductivity can be resolved exactly and in a closed form as a sum over relaxons, i.e. the collective phonon excitations that are eigenvectors of Boltzmann equation's scattering matrix [Cepellotti and Marzari, Phys. Rev. X 6, 041013 (2016)]. Relaxons have a well-defined parity and only odd relaxons contribute to the thermal conductivity. Here, we show that the complementary set of even relaxons determines another quantity -the thermal viscosity -that enters into the description of heat transport in the hydrodynamic regime, where dissipation of crystal momentum by Umklapp scattering phases out. We also show how the thermal viscosity and conductivity parametrize two novel viscous heat equations -two coupled equations for the local temperature and drift velocity fields -which represent the thermal counterpart of the Navier-Stokes equations of hydrodynamics in the linear, laminar regime. These viscous heat equations are derived from a coarse-graining of the linearized Boltzmann transport equation for phonons, and encompass both limits of Fourier's law or second sound for strong or weak Umklapp dissipation, respectively. Last, we introduce the Fourier deviation number, a dimensionless parameter that quantifies the steady-state deviations from Fourier's law due to hydrodynamic effects. We showcase these findings in a test case of a complex-shaped device made of silicon or diamond. This formulation generalizes rigorously Fourier's heat equation, and extends the reach of microscopic computational techniques to characterize the fundamental parameters governing heat conduction. * michele.simoncelli@epfl.ch ics. Sussmann and Thellung [12], starting from the linearized BTE (LBTE) in absence of momentumdissipating (Umklapp) phonon-phonon scattering events, derived mesoscopic equations in terms of temperature and phonon drift velocity, the thermal counterpart of pressure and fluid velocity in liquids. Further advances came from Gurzhi [13,14] and Guyer & Krumhansl [15,16] who, including the effect of weak crystal momentum dissipation, obtained equations for damped second sound and Poiseuille heat flow. Among early works, we also mention the discussions on phonon hydrodynamics using approaches different from the LBTE of Refs. [17,18]. While correctly capturing the qualitative features of phonon hydrodynamics, all the theoretical investigations mentioned above are heuristic, e.g. they assume simplified phonon dispersion relations (either power-law [13,14] or linear isotropic [12,15,16]), or neglect momentum dissipation. A more rigorous and general formulation -albeit valid only in the hydrodynamic regime of weak Umklapp scattering -was introduced by Hardy, who extended the discussion of second sound [19] and, together with Albers, of Poiseuille flow in terms of mesoscopic transport equations...

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Section: Case Studysupporting

confidence: 59%

Generalization of Fourier’s Law into Viscous Heat Equations

2020

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“…Here, Q is the energy exchange rate between the thermostat and the atoms in the thermostatted region and S is the cross-sectional area. The thermal conductivity of a sample of length L is then computed as [31] The calculated thermal conductivity values for SWCNT and CNP samples are shown in Fig. 2.…”

Section: Results From Nemd Simulationsmentioning

confidence: 99%

Thermal conductivity reduction in carbon nanotube by fullerene encapsulation: A molecular dynamics study

Dong

Fan

Qian

et al. 2020

Carbon

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Single-walled carbon nanotubes (SWCNTs) in their pristine form have high thermal conductivity whose further improvement has attracted a lot of interest. Some theoretical studies have suggested that the thermal conductivity of a (10, 10) SWCNT is dramatically enhanced by C 60 fullerene encapsulation. However, recent experiments on SWCNT bundles show that fullerene encapsulation leads to a reduction rather than an increase in thermal conductivity. Here, we employ three different molecular dynamics methods to study the influence of C 60 encapsulation on heat transport in a (10, 10) SWCNT. All the three methods consistently predict a reduction of the thermal conductivity of (10, 10) SWCNT upon C 60 encapsulation by 20% − 30%, in agreement with experimental results on bundles of SWCNTs. We demonstrate that there is a simulation artifact in the Green-Kubo method which gives anomalously large thermal conductivity from artificial convection. Our results show that * Corresponding authors

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“…Such agreement allows us to unify the phonon interpretation of the non-Fourier heat conduction effects in the two methods. Moreover, we clarify why different thermal reservoirs in NEMD simulations give different results, which has been a subject of debate for a long time [19,21,37,38].…”

Section: Introductionmentioning

confidence: 89%

“…II, NEMD simulations with sufficiently large thermal reservoirs are described, and we revisit the difference among the Langevin thermostat, the Nose-Hoover chain (NHC) thermostat, and the velocity rescaling (VR) method. Especially, we study the heat flux profiles and phonon modal temperature inside sufficiently large reservoirs, which were not considered in previous work [21,33,37]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

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

Feng

et al. 2020

Phys. Rev. B

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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.

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Influence of thermostatting on nonequilibrium molecular dynamics simulations of heat conduction in solids

Cited by 147 publications

References 78 publications

Generalization of Fourier’s Law into Viscous Heat Equations

Generalization of Fourier’s Law into Viscous Heat Equations

Thermal conductivity reduction in carbon nanotube by fullerene encapsulation: A molecular dynamics study

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

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