Phonon transport in molecular dynamics simulations: Formulation and thermal conductivity prediction.

Abstract

Atomic-level thermal transport is explored using lattice dynamics theory and molecular dynamics (MD) simulations. Due to the classical nature of the simulations and the small system sizes considered, a formulation different than the standard quantum-particle based approach is required. This is addressed by using real and phonon space analysis techniques to develop links between the atomic structure of dielectric materials and their thermal conductivities. Crystalline, liquid, and amorphous Lennard-Jones phases, and silica-based crystals (including zeolites) are considered. In predicting the thermal conductivity using the Green-Kubo method (a real space approach), two thermal transport mechanisms are identified. The first is temperature independent, related to short length and time scales, and governed by the atomic coordination. The second is temperature dependent, related to long length and time scales, and typically dominates the thermal transport. In the zeolites, the presence of cage structures, and disorder and anisotropy at sub-unit cell length scales, are found to inhibit the second mechanism, resulting in room temperature thermal conductivities of order 1 W/m-K, an order of magnitude less than that of quartz. The thermal conductivity of the Lennard-Jones crystal is also predicted with the Boltzmann transport equation under the single mode relaxation time approximation. Results from the simulations are used to specify all of the parameters in this phonon space model. Due to the inherent anharmonic nature of the simulations, the inclusion of anharmonic effects is straightforward. By comparing the predictions to those from the Greek-Kubo method, the quantitative validity of this model is established. Prior work required simplifying assumptions and the fitting of the results to experimental data, leading to a masking of the underlying physics. Using unsteady, steady non-equilibrium, and equilibrium simulations, three-phonon interactions are observed. Little attention has previously been given to their description in the MD system. The selection process is found to be governed strictly by the mode wave vectors. In determining the strength of an allowed interaction, consideration must be given to the polarizations and frequencies; the latter in the context of internal resonance.