On the relation between virial coefficients and the close-packing of hard disks and hard spheres

Abstract

The question of whether the known virial coefficients are enough to determine the packing fraction ${\eta }_{\infty }$ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Padé approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that ${\eta }_{\infty }$ is equal to the maximum packing fraction corresponding to an ordered crystalline structure.

10 pages, 6 figures; v2: discussion about hard-square and hard-hexagon systems on a lattice added; five new references

References in corpus (5)

• Simulation-based equation of state of the hard disk fluid and prediction of higher-order virial coefficients
• The analyticity region of the hard sphere gas. Improved bounds
• A branch-point approximant for the equation of state of hard spheres
• Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations
• Local and global properties of mixtures in one-dimensional systems. II. Exact results for the Kirkwood-Buff integral

Cited by in corpus (1)

• Structural and Thermodynamic Properties of Hard-Sphere Fluids