On standardised moments of force distribution in simple liquids

TL;DR

This paper derives analytical expressions for the standardized force moments of a tagged atom in a Lennard-Jones fluid, exploring their dependence on density and temperature through theory and simulations, including clustering effects.

Contribution

It provides explicit analytical formulas for force moment dependence on physical parameters and investigates their behavior in different regimes using molecular dynamics simulations.

Findings

Analytical expressions for force moments as functions of density and temperature.

Leading order behavior of force moments at low density and temperature.

Clustering effects influence the force distribution moments.

Abstract

The force distribution of a tagged atom in a Lennard-Jones fluid in the canonical ensemble is studied with a focus on its dependence on inherent physical parameters: number density ($n$) and temperature ($T$). Utilising structural information from molecular dynamics simulations of the Lennard-Jones fluid, explicit analytical expressions for the dependence of standardised force moments on $n$ and $T$ are derived. Leading order behaviour of standardised moments of the force distribution are obtained in the limiting cases of small density ($n \rightarrow 0$) and low temperature ($T \rightarrow 0$), while the variations in the standardised moments are probed for general $n$ and $T$ using molecular dynamics simulations. Clustering effects are seen in molecular dynamics simulations and their effect on these standardised moments is discussed.