The formula for the entropy s of the accessible volume of the phase space for frictionless hard spheres is combined with the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state for polydisperse three-dimensional packings to obtain an analytical expression for s as a function of packing density phi. Polydisperse hard-sphere packings with log-normal, Gaussian, and Pareto particle diameter distributions are generated to estimate their ideal glass transition densities phi(g). The accessible entropy s at phi(g) is almost the same for all investigated particle diameter distributions. We denote this entropy as s(g) and can predict phi(g) for an arbitrary particle diameter distribution through an equation s(phi) = s(g). If the BMCSL equation of state is used for s(phi), then phi(g) is found to depend only on the first three moments of a particle diameter distribution. (C) 2015 AIP Publishing LLC.
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