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Issue 41, 2009
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High-order virial coefficients and equation of state for hard sphere and hard disk systems

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Abstract

A very simple and accurate approach is proposed to predict the high-order virial coefficients of hard spheres and hard disks. In the approach, the nth virial coefficient Bn is expressed as the sum of nD−1 and a remainder, where D is the spatial dimension of the system. When n≥ 3, the remainders of the virials can be accurately expressed with Padé-type functions of n. The maximum deviations of predicted B5B10 for the two systems are only 0.0209%–0.0044% and 0.0390%–0.0525%, respectively, which are much better than the numerous existing approaches. The virial equation based on the predicted virials diverges when packing fraction η = 1. With the predicted virials, the compressibility factors of hard sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to η = 0.545. The compressibility factors of hard disk fluid can be predicted very accurately up to η = 0.63. The simulated B7 and B10 for hard spheres are found to be inconsistent with the other known virials and therefore they are modified as 53.2467 and 105.042, respectively.

Graphical abstract: High-order virial coefficients and equation of state for hard sphere and hard disk systems

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Publication details

The article was received on 17 Jun 2009, accepted on 28 Jul 2009 and first published on 19 Aug 2009


Article type: Paper
DOI: 10.1039/B911901A
Citation: Phys. Chem. Chem. Phys., 2009,11, 9382-9390

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    High-order virial coefficients and equation of state for hard sphere and hard disk systems

    J. Hu and Y. Yu, Phys. Chem. Chem. Phys., 2009, 11, 9382
    DOI: 10.1039/B911901A

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