Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

摘要

We generate jammed disordered packings of 100 u0002 N u0002 2000 monodisperse hard spheres in three dimensionsnwhose strictly jammed backbones are demonstrated to be exactly isostatic with unprecedented numerical accuracy.nThis is accomplished by using the Torquato-Jiao (TJ) packing algorithm as a means of studying the maximallynrandom jammed (MRJ) state. The rattler fraction of these packings converges towards 0.015 in the infinite-systemnlimit, which is markedly lower than previous estimates for the MRJ state using the Lubachevsky-Stillingernprotocol. This is because the packings that the TJ algorithm creates are closer to the true MRJ state, as shownnusing bond-orientational and translational order metrics. The rattler pair correlation statistics exhibit stronglyncorrelated behavior contrary to the conventional understanding that they be randomly (Poisson) distributed.nDynamically interacting “polyrattlers” may be found imprisoned in shared cages as well as interacting throughn“bottlenecks” in the backbone and these clusters are mainly responsible for the sharp increase in the rattlernpair correlation function near contact. We discover the surprising existence of polyrattlers with cluster sizesnof up to five rattlers (which is expected to increase with system size) and present a distribution of polyrattlernoccurrence as a function of cluster size and system size.We also enumerate all of the rattler interaction topologiesnwe observe and present images of several examples, showing that MRJ packings of monodisperse spheresncan contain large rattler cages while still obeying the strict jamming criterion. The backbone spheres thatnencage the rattlers are significantly hypostatic, implying that correspondingly hyperstatic regions must existnelsewhere in these isostatic packings. We also observe that rattlers in hard-sphere packings share an apparentnconnection with the low-temperature two-level system anomalies that appear in real amorphous insulators andnsemiconductors.