THEORY OF THE GLASS-TRANSITION AND THE AMORPHOUS STATE .1. THE HARD-SPHERE FLUID

A thermodynamically-based criterion for the location of the glass transition in the system of hard spheres is proposed and its structural consequences are investigated. By re-analyzing existing computer simulation data and theoretical results, we estimate the hard-sphere glass transition reduced density to be rho(g) congruent-to 0.965, corresponding to a reduced pressure beta-P congruent-to 13.11. The capability of the Ornstein-Zernike integral equation to describe the structure and thermodynamics of both the supercooled liquid and amorphous solid and the glass transition between them is examined in detail. The detailed relationship between the bridge function B and the structure is elucidated, enabling us to introduce a B for the amorphous phase which correctly yields the divergence of the pressure at the random closest packing density. We call this procedure the alpha-B-OZ theory, and it produces a B that causes the contact value g* of the pair correlation function, and hence the pressure and other g*-related properties, to exhibit a slope discontinuity at the glass transition density. We examined structural indicators, based on the pair correlation function g(r), of the onset of the glass transition and found that the empirical Wendt-Abraham ratio and similar quantities are not useful. The only possible indicator of some utility is the point of onset of the split second peak in g(r), which we found to occur in the alpha-B-OZ theory at rho(a) congruent-to 1.008.