On the Asymptotic Properties of a Hard Sphere Fluid

An analysis of the expected divergences in thermodynamic properties at the close-pack density (ηcp = π2½/6) along with the known virial coefficients up to 10th order, suggests a weak logarithmic singularity in the excess fluid entropy. The corresponding equation of state (EOS) also possesses a singularity at ηcp. The new EOS accurately describes extant molecular dynamics data up to the fluid-solid transition (η ≈ 0.494) with differences of less than 1 part per thousand. This accuracy is maintained into the metastable fluid regime up to η ≈ 0.52. In terms of accuracy, the new EOS is no better than Padé approximants, but the new EOS, unlike the Padé approximants, diverges at ηcp. In addition, a new order parameter is defined that enables all system configurations to be classified as either disordered or ordered. Monte Carlo simulations are used to determine this order parameter in the metastable fluid range. Using this new order parameter, evidence is presented to support a thermodynamic glass transition at ηcp = 0.54. With respect to this transition, congruence is found with the traditional ideas espoused by Gibbs & DiMarzio and Adam & Gibbs. It is the rapid disappearance of disordered (random) configurations with increasing density that drives the glass transition and slows the dynamics.