Elastic properties of dense hard-sphere fluids

TL;DR

This paper investigates the elastic properties of dense hard-sphere fluids, revealing limitations of conventional models and exploring implications for sound propagation, Poisson's ratio, and related physical phenomena.

Contribution

It provides a new analysis based on Miller's expressions, identifying divergence issues in traditional elastic moduli formulas near the hard-sphere limit.

Findings

Conventional elastic moduli formulas diverge near the HS limit.

New analysis clarifies applicability of elastic expressions for soft vs. hard interactions.

Implications for sound wave propagation and material properties in dense fluids.

Abstract

A new analysis of elastic properties of dense hard sphere (HS) fluids is presented, based on the expressions derived by Miller [J. Chem. Phys. {\bf 50}, 2733 (1969)]. Important consequences for HS fluids in terms of sound waves propagation, Poisson's ratio, Stokes-Einstein relation, and generalized Cauchy identity are explored. Conventional expressions for high-frequency elastic moduli for simple systems with continuous and differentiable interatomic interaction potentials are known to diverge when approaching the HS repulsive limit. The origin of this divergence is identified here. It is demonstrated that these conventional expressions are only applicable for sufficiently soft interactions and should not be applied to HS systems. The reported results can be of interest in the context of statistical physics, physics of fluids, soft condensed matter, and granular materials.