When do soft spheres become hard spheres?

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.

6 pages, 4 figures

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• Quasi-universal behaviour of shear relaxation times in simple fluids
• Comparing zero-parameter theories for the WCA and harmonic-repulsive melting lines
• Variational approach to Yukawa fluids. II. Instantaneous elastic moduli and sound velocities
• Excess entropy scaling of the transverse sound speed in simple fluids