On the domain size effect of thermal conductivities from equilibrium and nonequilibrium molecular dynamics simulations

Abstract

Equilibrium molecular dynamics (EMD) simulations with the Green-Kubo formula and nonequilibrium molecular dynamics (NEMD) simulations with the Fourier's Law are two widely used methods for calculating thermal conductivities of materials. It is well known that both methods suffer from domain size effects, especially for NEMD. But the underlying mechanisms and their comparison have not been much quantitatively studied before. In this paper, we investigate their domain size effects by using crystalline silicon at 1000 K, graphene at 300 K, and silicene at 300 K as model material systems. The thermal conductivity of silicon from EMD simulations increases normally with the increasing domain size and converges at a size of around 4×4×4 nm3. The converging trend agrees well with the wavelength-accumulated thermal conductivity. The thermal conductivities of graphene and silicene from EMD simulations decrease abnormally with the increasing domain size and converge at a size of around 10×10 nm2. We ascribe the anomalous size effect to the fact that as the domain size increases, the effect of more phonon scattering processes (particularly the flexural phonons) dominates over the effect of more phonon modes contributing to the thermal conductivity. The thermal conductivities of the three material systems from NEMD simulations all show normal domain size effects, although their dependences on the domain size differ. The converging trends agree with the mean free path accumulation of thermal conductivity. This study provides new insights that other than some exceptions, the domain size effects of EMD and NEMD are generally associated with wavelength and mean free path accumulations of thermal conductivity, respectively. Since phonon wavelength spans over a much narrower range than mean free path, EMD usually has less significant domain size effect than NEMD.