Predicting maximally random jammed packing density of non-spherical hard particles via analytical continuation of fluid equation of state

Abstract

Dense packings of hard particles are useful models for condensed matters including crystalline and glassy state of solids, simple liquids, granular materials and composites. It is very challenging to devise predictive theories of random packings, due to the intrinsic non-equilibrium and non-local nature of the system. Here, we develop a formalism for accurately predicting the density (i.e., fraction of space covered by the particles) η_MRJ of the maximally random jammed (MRJ) packing state of a wide spectrum of congruent non-spherical hard particles in three-dimensional Euclidean space ³, via analytical continuation of the corresponding fluid equation of state (EOS). This formalism is based on the assumption that the fluid branch of the EOS can be analytically extended into the meta-stable region, which leads to a diverging pressure at the jamming point (i.e., the MRJ state). This allows us to estimate η_MRJ as the pole in the EOS, which can be expressed in terms of the virial coefficients encoding intrinsic local n-body packing information of the particles, and depending alone on particle shape. The accuracy of our formalism is verified using the hard sphere system and is subsequently applied to a wide spectrum of non-spherical shapes. The predictions are compared to numerical results whenever possible, and excellent agreements are found.