When do soft spheres become hard spheres?

TL;DR

This paper investigates the transition from soft to hard sphere behavior in fluids with repulsive interactions, revealing a crossover at specific interaction exponents and providing a model for the hard sphere regime.

Contribution

It identifies the soft-hard sphere crossover point and develops an accurate model for the hard sphere regime based on extensive simulations.

Findings

Crossover occurs at interaction exponent n ≈ 10-20.

Elastic moduli of true hard sphere fluids are finite.

Developed a simple model for the hard sphere regime.

Abstract

The conventional (Zwanzig-Mountain) expressions for instantaneous elastic moduli of simple fluids predict their divergence as the limit of hard sphere (HS) interaction is approached. However, elastic moduli of a true HS fluid are finite. Here we demonstrate that this paradox reveals the soft- to hard-sphere crossover in fluid excitations and thermodynamics. With extensive \emph{in-silico} study of fluids with repulsive power-law interactions ($\propto r^{-n}$), we locate the crossover at $n\simeq 10-20$ and develop a simple and accurate model for the HS regime. The results open novel prospects to deal with the elasticity and related phenomena in various systems, from simple fluids to melts and glasses.