Thermodynamic and dynamical properties of the hard sphere system revisited by molecular dynamics simulation

Abstract

Revised thermodynamic and dynamical properties of the hard sphere (HS) system are obtained from extensive molecular dynamics calculations carried out with large system sizes (number of particles, N) and long times.

Tethered-particle model: The calculation of free energies for hard-sphere systems

“…The reference absolute crystal entropy of s res (ρσ 3 = 1.04086)/k B = −5.9189(2) is also taken from Ref. 22. Overall the agreement is excellent, both between the methods and against literature, verifying the methods and the extrapolation to the thermodynamic limit.…”

“…III. To generate reference literature values, thermodynamic integration is performed on the current best available equations of state 22 . The reference absolute crystal entropy of s res (ρσ 3 = 1.04086)/k B = −5.9189(2) is also taken from Ref.…”

“…This estimate for the crystal free-energy can be used with the latest equations of state 22 to estimate the fluid-solid coexistence point at a reduced liquid number density of 0.93890 (7), a reduced solid density of 1.03715( 9), a reduced chemical potential of 16.053(4), and a reduced pressure of 11.550 (4). The uncertainties on these values result from a propogation of uncertainty from the reference crystal energy above, and not any uncertainty in the equations of state.…”

Elastic properties of dense hard-sphere fluids

“…Recent MD simulations [39] reported α in the range from 1/2π 0.159 to 1/6 0.167 for a similar range of φ, which is somewhat above the theoretical expectations. It should be noted, however, that the effect of a finite particle number in simulations of the transport coefficients of HS fluids and the way how these coefficients are approaching the thermodynamic limit are not very thoroughly investigated (note, however, a very recent paper [43], where this thematics has been addressed). This can be one of the possible reasons behind the observed discrepancy.…”

Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids

“…Extensive data on the self-diffusion, shear viscosity, and thermal conductivity coefficients have been published and discussed in the literature. For the HS system, we use the recent comprehensive simulation study by Pieprzyk et al [14,15]. For the OCP model we use the shear viscosity data tabulated by Daligault et al [16] and thermal conductivity data tabulated by Scheiner and Baalrud [17].…”