Thermal conductance at the interface between crystals using equilibrium and non-equilibrium molecular dynamics

TL;DR

This study compares equilibrium and non-equilibrium molecular dynamics methods for calculating interfacial thermal conductance, revealing significant differences and analyzing their physical implications for heat transfer at solid interfaces.

Contribution

It demonstrates the contrasting results of EMD and NEMD methods for interfacial conductance and links these to physical models, highlighting size effects and the importance of out-of-equilibrium conditions.

Findings

NEMD and EMD give inconsistent conductance results, differing by up to a factor of 5.

Equilibrium simulations are more affected by finite size effects than NEMD.

EMD results align with the diffuse mismatch model, while NEMD results match an out-of-equilibrium acoustic mismatch model.

Abstract

In this article, we compare the results of non-equilibrium (NEMD) and equilibrium (EMD) molecular dynamics methods to compute the thermal conductance at the interface between solids. We propose to probe the thermal conductance using equilibrium simulations measuring the decay of the thermally induced energy fluctuations of each solid. We also show that NEMD and EMD give generally speaking inconsistent results for the thermal conductance: Green Kubo simulations probe the Landauer conductance between two solids which assumes phonons on both sides of the interface to be at equilibrium. On the other hand, we show that NEMD give access to the out-of-equilibrium interfacial conductance consistent with the interfacial flux describing phonon transport in each solid. The difference may be large and reaches typically a factor 5 for interfaces between usual semi-conductors. We analyze finite size effects for the two determinations of the interfacial thermal conductance, and show that the equilibrium simulations suffer from severe size effects as compared to NEMD. We also compare the predictions of the two above mentioned methods -EMD and NEMD- regarding the interfacial conductance of a series of mass mismatched Lennard-Jones solids. We show that the Kapitza conductance obtained with EMD can be well described using the classical diffuse mismatch model (DMM). On the other hand, NEMD simulations results are consistent with a out-of-equilibrium generalisation of the acoustic mismatch model (AMM). These considerations are important in rationalizing previous results obtained using molecular dynamics, and help in pinpointing the physical scattering mechanisms taking place at atomically perfect interfaces between solids, which is a prerequesite to understand interfacial heat transfer across real interfaces.