+ Site Statistics
+ Search Articles
+ PDF Full Text Service
How our service works
Request PDF Full Text
+ Follow Us
Follow on Facebook
Follow on Twitter
Follow on LinkedIn
+ Subscribe to Site Feeds
Most Shared
PDF Full Text
+ Translate
+ Recently Requested

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



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



Journal of Chemical Physics 134(8): 084502



The question of whether the known virial coefficients are enough to determine the packing fraction η(∞) 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 η(∞) is equal to the maximum packing fraction corresponding to an ordered crystalline structure.

Please choose payment method:






(PDF emailed within 0-6 h: $19.90)

Accession: 054739796

Download citation: RISBibTeXText

PMID: 21361546

DOI: 10.1063/1.3558779


Related references

Virial coefficients of hard spheres and hard disks up to the ninth. Physical Review. E Statistical Nonlinear and Soft Matter Physics 71(2 Pt 1): 021105, 2005

Virial coefficients and equations of state for mixtures of hard discs, hard spheres and hard hyperspheres. Molecular Physics 99(23): 1959-1972, 2001

Monte-Carlo integration for virial coefficients re-visited: hard convex bodies, spheres with a square-well potential and mixtures of hard spheres. Molecular Physics 100(20): 3313-3324, 2002

Adsorption kinetics of hard disks from virial coefficients. Physical Review. E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics 51(2): 873-883, 1995

Second virial coefficients of dipolar hard spheres. Journal of Physics. Condensed Matter 22(32): 325104, 2010

Fifth to eleventh virial coefficients of hard spheres. Physical Review. E Statistical Nonlinear and Soft Matter Physics 90(2): 023301, 2014

Third and fourth virial coefficients for hard disks in narrow channels. Journal of Chemical Physics 140(24): 244504, 2014

Thermodynamics and structure of a fluid of hard rods, disks, spheres, or hyperspheres from rescaled virial expansions. Physical Review. A General Physics 36(8): 3912-3925, 1987

Bulk and interior packing densities of random close packing of hard spheres. Journal of Materials Science 38(9): 2019-2025, 2003

Calculation of high-order virial coefficients with applications to hard and soft spheres. Physical Review Letters 110(20): 200601, 2013

Analytical representation of the higher virial coefficients of binary mixtures of additive hard spheres. Molecular Physics 101(10): 1545-1549, 2003

Close packing density of polydisperse hard spheres. Journal of Chemical Physics 131(24): 244104, 2009

Entropy of hard spheres in the close-packing limit. Molecular Physics 113(9-10): 1061-1068, 2015

High-order virial coefficients and equation of state for hard sphere and hard disk systems. Physical Chemistry Chemical Physics 11(41): 9382-9390, 2009

Random close packing fractions of lognormal distributions of hard spheres. Powder Technology 245: 28-34, 2013