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

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 B_n is expressed as the sum of n^D−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 B₅–B₁₀ 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.