Comparison of structure and transport properties of concentrated hard and soft sphere fluids

TL;DR

This study compares the structural and transport properties of concentrated hard and soft sphere fluids using simulations, revealing that scaling by freezing point collapses key parameters at high densities and that short-range differences do not affect macroscopic transport coefficients.

Contribution

It demonstrates that density scaling at the freezing point effectively unifies the properties of hard and soft spheres at high densities, regardless of microscopic dynamics.

Findings

Scaling by freezing point collapses transport parameters for $n extgreater 18$

Long-range structure is identical at freezing points when measured in units of interparticle distance

Short-range differences affect correlation functions but not macroscopic transport coefficients

Abstract

Using Newtonian and Brownian dynamics simulations, the structural and transport properties of hard and soft spheres have been studied. The soft spheres were modeled using inverse power potentials ($V\sim r^{-n}$, with $1/n$ the potential softness). Although the pressure, diffusion coefficient and viscosity depend at constant density on the particle softness up to extremely high values of $n$, we show that scaling the density with the freezing point for every system effectively collapses these parameters for $n\geq 18$ (including hard spheres), for large densities. At the freezing points, the long range structure of all systems is identical, when the distance is measured in units of the interparticle distance, but differences appear at short distances (due to the different shape of the interaction potential). This translates into differences at short times in the velocity and stress autocorrelation functions, although they concur to give the same value of the corresponding transport coefficient (for the same density to freezing ratio); the microscopic dynamics also affects the short time behaviour of the correlation functions and absolute values of the transport coefficients, but the same scaling with the freezing density works for Newtonian or Brownian dynamics. For hard spheres, the short time behaviour of the stress autocorrelation function has been studied in detail, confirming quantitatively the theoretical forms derived for it.