On the thermodynamics of hard spheres

Pártay, LB and Bartók, AP and Csányi, G (2012) On the thermodynamics of hard spheres.

Abstract

We use the recently introduced nested sampling Monte Carlo algorithm to calculate the partition function of the three dimensional periodic hard sphere system. Given the partition function, we evaluate the compressibility and the free energy as functions of the packing fraction and local order, showing that the transition to crystallinity is barrierless, and that the entropic contribution of the jammed states to the free energy is negligible for packing fractions above the phase transition. We also identify quantitatively the extent of the region of jammed states, and find that the maximally random jammed configuration is surprisingly disordered.

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