Pore-size entropy of random hard-sphere packings

We introduce a method for calculating the entropy of random hard-sphere packings, also referred to as pore-size entropy. The method is applicable to packings of monodisperse or polydisperse spheres as well as non-spherical particles. Pore-size entropy allows us to analyze the packing microstructure and provides deep insight into the traditional concept of pore-size distribution. Specifically, the logarithm of the pore-size distribution's tail area is equal to the packing entropy. We reveal a local minimum in the plot of pore-size entropy vs. packing density (phi) for monodisperse frictionless sphere packings at a critical density of phi(C) approximate to 0.65, independent of the employed packing generation protocol (Lubachevsky-Stillinger, Jodrey-Tory, and force-biased algorithms), which is a density with minimal number of available packing configurations. This entropy minimum is followed by an entropy increase as phi increases up to similar to 0.68, corresponding to the emergence of crystalline structures in the coexistence region; beyond this packing density the entropy decreases again. In a complementary study we modify the Lubachevsky-Stillinger protocol and reproduce the random-close packing limit at phi(RCP) approximate to 0.64. We conclude that phi(RCP) approximate to 0.64 is the jamming point of the glassy states with the lowest density, whereas phi(C) approximate to 0.65 is the jamming point of the densest glassy state (the ideal glass state).