Calculating the free energy of nearly jammed hard-particle packings using molecular dynamics

We present a new event-driven molecular dynamics (MD) algorithm for measuring the free energy of nearly jammed packings of spherical and non-spherical hard particles. This Bounding Cell Molecular Dynamics (BCMD) algorithm exactly calculates the free-energy of a single-occupancy cell (SOC) model in which each particle is restricted to a neighborhood of its initial position using a hard-wall bounding cell. Our MD algorithm generalizes previous ones in the literature by enabling us to study non-spherical particles as well as to measure the free-energy change during continuous irreversible transformations. Moreover, we make connections to the well-studied problem of computing the volume of convex bodies in high dimensions using random walks. We test and verify the numerical accuracy of the method by comparing against rigorous asymptotic results for the free energy of jammed and isostatic disordered packings of both hard spheres and ellipsoids, for which the free energy can be calculated directly as the volume of a high-dimensional simplex. We also compare our results to previously published Monte Carlo results for hard-sphere crystals near melting and jamming and find excellent agreement. We have successfully used the BCMD algorithm to determine the configurational and free-volume contributions to the free energy of glassy states of binary hard disks [A. Donev, F.H. Stillinger, S. Torquato, Do binary hard disks exhibit an ideal glass transition? Phys. Rev. Lett. 96 (22) (2006) 225502]. The algorithm can also be used to determine phases with locally- or globally-minimal free energy, to calculate the free-energy cost of point and extended crystal defects, or to calculate the elastic moduli of glassy or crystalline solids, among other potential applications.