Structural and entropic insights into the nature of the random-close-packing limit

Abstract

Disordered packings of equal sized spheres cannot be generated above the limiting density (fraction of volume occupied by the spheres) of rho approximately 0.64 without introducing some partial crystallization. The nature of this "random-close-packing" limit (RCP) is investigated by using both geometrical and statistical mechanics tools applied to a large set of experiments and numerical simulations of equal-sized sphere packings. The study of the Delaunay simplexes decomposition reveals that the fraction of "quasiperfect tetrahedra" grows with the density up to a saturation fraction of approximately 30% reached at the RCP limit. At this limit the fraction of aggregate "polytetrahedral" structures (made of quasiperfect tetrahedra which share a common triangular face) reaches it maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctuations, decreases uniformly and vanishes at the (extrapolated) limit rho(Kappa) approximately 0.66 . Before such limit, and precisely in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline phases is observed.