On the asymptotic properties of a hard sphere fluid

An analysis of the expected divergences in thermodynamic properties at the close-pack density (eta(cp) = pi square root(2)/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 eta(cp). The new EOS accurately describes extant molecular dynamics data up to the fluid-solid transition (eta approximately 0.494) with differences of less than 1 part per thousand. This accuracy is maintained into the metastable fluid regime up to eta approximately 0.52. In terms of accuracy, the new EOS is no better than Pade approximants, but the new EOS, unlike the Pade approximants, diverges at eta(cp). 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 eta approximately 0.54. With respect to this transition, congruence is found with the traditional ideas espoused by Gibbs and DiMarzio and Adam and Gibbs. It is the rapid disappearance of disordered (random) configurations with increasing density that drives the glass transition and slows the dynamics.