Gaussian approximation to single particle correlations at and below the picosecond scale for Lennard-Jones and nanoparticle fluids

TL;DR

This paper develops a theoretical and numerical framework to estimate when Gaussian approximations of single particle displacements are valid in nanoscale fluids, finding they hold up to a few picoseconds for simple fluids and longer for nanoparticle suspensions.

Contribution

It provides a theoretical estimate and numerical validation for the time scale at which Gaussian approximations are valid in nanoscale fluid systems.

Findings

Gaussian approximation valid up to 1 ps in Lennard-Jones fluids

Gaussian approximation valid up to 5-10 ps in nanoparticle suspensions

Series truncation accuracy depends on system and time scale

Abstract

To describe short-time (picosecond) and small-scale (nanometre) transport in fluids, a Green's function approach was recently developed. This approach relies on an expansion of the distribution of single particle displacements around a Gaussian function, yielding an infinite series of correction terms. Applying a recent theorem [Van Zon and Cohen, J. Stat. Phys. 123, 1-37 (2006)] shows that for sufficiently small times the terms in this series become successively smaller, so that truncating the series near or at the Gaussian level might provide a good approximation. In the present paper, we derive a theoretical estimate for the time scale at which truncating the series at or near the Gaussian level could be supposed to be accurate for equilibrium nanoscale systems. In order to numerically estimate this time scale, the coefficients for the first few terms in the series are determined in computer simulations for a Lennard-Jones fluid, an isotopic Lennard-Jones mixture and a suspension of a Lennard-Jones-based model of nanoparticles in a Lennard-Jones fluid. The results suggest that for Lennard-Jones fluids an expansion around a Gaussian is accurate at time scales up to a picosecond, while for nanoparticles in suspension (a nanofluid), the characteristic time scale up to which the Gaussian is accurate becomes of the order of five to ten picoseconds.