Elastic properties of dense hard-sphere 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. 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. arXiv:1910.00338v1 [cond-mat.mtrl-sci]

Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition

“…The results are shown in Figure 1 . The following main trends are observed: (i) Very weak dependence of both longitudinal and transverse sound velocities on the softness parameter in the considered range of softness; (ii) Numerical values are comparable to those of the hard-sphere fluids at the freezing packing fraction [ 2 ]; (iii) The difference between the sound velocities in the fluid and solid phases is very tiny and can normally be neglected; (iv) the longitudinal sound velocity exhibits a minimum at , while the transverse sound velocity decreases continuously as s increases; (v) the ratio of sound velocities, , decreases monotonously from ≃0.53 to as s increases in the range considered.…”

“…They predict divergence of sound velocities as (or ), which contradicts finite values in the HS limit [ 31 , 32 ]. The origin behind the unphysical divergence of the conventional expressions for the instantaneous elastic moduli when approaching the HS limit has been identified and discussed [ 2 , 33 ]. The conventional expressions should not be applied for .…”

“…The high frequency (instantaneous) elastic moduli and the corresponding sound velocities are important characteristics of condensed fluid and solid phases, which affect and regulate wave propagation [ 1 ], the instantaneous Poisson’s ratio [ 2 ], the coefficient in the Stokes–Einstein relation [ 3 , 4 ], the Lindemann melting rule [ 5 , 6 ], as well as some other simple melting rules [ 7 ], the relaxation time in the shoving model [ 8 , 9 ], just to give few examples.…”

Isomorph invariance and thermodynamics of repulsive dense bi-Yukawa one-component plasmas

“…The numerical procedure followed for the solution of the system of Eqs. (9,10,12,20) is based on Picard iterations in Fourier space combined with standard mixing algorithms and established long-range decomposition schemes (when necessary) in order to improve convergence [23]. The upper range cut-off was selected to be R max = 20 d, the real space resolution was ∆r = 10 −3 d and the Fourier-space convergence criterion in terms of the indirect correlation function read as |γ n (k) − γ n−1 (k)| < 10 −5 ∀k.…”

“…Yukawa interactions result from the linearized Boltzmann response of isotropic plasmas around a test point charge [2]. However, even in the absence of plasma drifts, the continuous absorption of plasma fluxes on the particulate surface leads to non-Boltzmann densities for isolated dust [7][8][9] and brings forth the issue of ionizationrecombination balance for dense dust clouds [10,11]. In the latter, simple hydrodynamic models have predicted that the interaction potential acquires a double Yukawa repulsive form [12,13], where the short-range screening length is controlled by plasma shielding and the longrange screening length is controlled by plasma sink-source competition.…”