Application of the scaled particle theory to the glass transition of hard spheres

In a previous article [1], an improved approach to the scaled particle theory of Reiss et al. was presented. As a result, we obtained a Pade-like expression of the compressibility factor of the fluid state. That expression contains two parameters p(1) and p(2), which we were able to calculate. In this paper we find other sets of values for p(1) and p(2). Two of these sets yield equations of state which agree with the simulation results of the glassy states obtained by Woodcock and Speedy. The calculations are based on two assumptions: firstly, that second order phase transitions may occur and secondly, that a hard sphere glass contains a fluid-like and a solid-like part. As an additional result, we found an upper and a lower limit for the fluid densities at which glass transitions may occur.