2010/01/31 by Yuliang Jin, Hernán A. Makse, Hernan A. Makse · 1 citation
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Atomic packing factor #Classification of discontinuities #Condensed matter physics #Entropy (arrow of time) #Fusion #Geometry #Hard spheres #Material Dynamics and Properties #Mathematical analysis #Mathematics #Phase Equilibria and Thermodynamics #Phase transition #Physics #Pickering emulsions and particle stabilization #SPHERES #Singularity #Sphere packing #Statistical mechanics #Statistical physics #Thermodynamics #cond-mat.dis-nn #cond-mat.soft
paper · pdf · doi:10.1016/j.physa.2010.08.010
published as Physica A 389, 5362 (2010) · 33 pages, 10 figures
openalex publication_date 2010/08/20 · arxiv created 2016/03/28 · arxiv updated 2016/03/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ~64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit. Here we show that RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the "freezing point" in a first-order phase transition between ordered and disordered packing phases. Despite the athermal nature of granular matter, we show the thermodynamic character of the transition in that it is accompanied by sharp discontinuities in volume and entropy. This occurs at a critical compactivity, which is the intensive variable that plays the role of temperature in granular matter. Our results predict the experimental conditions necessary for the formation of a jammed crystal by calculating an analogue of the "entropy of fusion". This approach is useful since it maps out-of-equilibrium problems in complex systems onto simpler established frameworks in statistical mechanics.