Collective modes in simple melts: Transition from soft spheres to the hard sphere limit

TL;DR

This study investigates how collective modes in classical particle systems evolve from soft to hard-sphere interactions by varying the IPL exponent, revealing the limitations of existing theoretical models near the hard-sphere limit.

Contribution

It provides a detailed comparison between MD simulations and the QCA approach across a range of interaction softness, highlighting the inaccuracy of QCA for steep potentials.

Findings

QCA becomes inaccurate for n ≥ 20

High-frequency elastic moduli expressions are invalid for steep potentials

Relations between elastic velocities and sound velocity are discussed

Abstract

We study collective modes in a classical system of particles with repulsive inverse-power-law (IPL) interactions in the fluid phase, near the fluid-solid coexistence (IPL melts). The IPL exponent is varied from $n=10$ to $n=100$ to mimic the transition from moderately soft to hard-sphere-like interactions. We compare the longitudinal dispersion relations obtained using molecular dynamic (MD) simulations with those calculated using the quasi-crystalline approximation (QCA) and find that this simple theoretical approach becomes grossly inaccurate for $n\gtrsim 20$. Similarly, conventional expressions for high-frequency (instantaneous) elastic moduli, predicting their divergence as $n$ increases, are meaningless in this regime. Relations of the longitudinal and transverse elastic velocities of the QCA model to the adiabatic sound velocity, measured in MD simulations, are discussed for the regime where QCA is applicable. Two potentially useful freezing indicators for classical particle systems with steep repulsive interactions are discussed.