A branch-point approximant for the equation of state of hard spheres

Abstract

Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value, and it is as accurate as the rescaled virial expansion and better than the Padé [3/3] equations of state. Consequences regarding the convergence properties of the virial series and the use of similar equations of state for hard-core fluids in $d$ dimensions are also pointed out.

arXiv comment6 pages, 4 tables, 3 figures; v2: enlarged version, extension to other dimensionalities; v3: typos in references corrected

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Cited by in corpus (7)

• Structural and Thermodynamic Properties of Hard-Sphere Fluids
• Equation of state for hard sphere fluids offering accurate virial coefficients
• Note: Equation of state and the freezing point in the hard-sphere model
• On the relation between virial coefficients and the close-packing of hard disks and hard spheres
• Carnahan Starling type equations of state for stable hard disk and hard sphere fluids
• Asymptotic expansion based equation of state for hard-disk fluids offering accurate virial coefficients
• Application of Levin's transformations to virial series