STATISTICAL-MECHANICS OF HARD-SPHERES

A theoretical equation of state for a system of hard spheres is proposed. It is based on the ideas of the scaled-particle theory that has been developed by Reiss et al. [J. Chem. Phys. 31, 369 (1959)]. In this paper, their method is generalized by expanding the function G(y,r) in a set of functions t i(r) so that the low-density behavior is described exactly, not only for asymptotically large values of r, but for the full range of r values. As a consequence the virial coefficients B3 and B4 come out exactly in the approach to the scaled particle theory. For the compressibility factor, a Padé-like expression is obtained that gives exact values for B3 and B4 and reproduces B5, B6, B7, and B8 to within 1.3%, 1.4%, 0.74%, and 5.5%, respectively. Furthermore, the equation of state agrees with the simulation data up to high densities, where the fluid is metastable. An expression for the surface tension is also found. © 1995 American Institute of Physics.