Excluded volume of the system of hard-core spheres revisited: New insights from computer simulations

The role of excluded volume in the equation of state of hard-sphere system is studied by analytical theory and computer simulations. The excluded-volume parameter b(ρ) introduced in the van der Waals equation is examined as a function of density. A number of approximations are considered and tested against Monte Carlo simulations. Parameter b(ρ) is seen to decline by a factor of 2 over the density range in which the system is still in the fluid state. Partial contributions of two- and three-sphere intersections to b(ρ) are analyzed as a function of density. The resulting series is seen to be converging very slowly. An approximation based on Padé approximants is seen to offer best accuracy at the lowest cost. It involves computation of the three lowest virial expansion coefficients B2,B3 and B4. Numerical tests reveal that this approximation is accurate in the case of ellipsoids and a number of hard-core polyhedra, supporting a potential application in phase equilibria studies of molecules with non-spherical shapes, such as cubes, pear-shaped molecules and so on. © 2022 The Author(s)