Zusammenfassung
The problem of finding the most efficient way to pack spheres has a long
history, dating back to the crystalline arrays conjectured(1) by Kepler
and the random geometries explored(2) by Bernal. Apart from its
mathematical interest, the problem has practical relevance(3) in a wide
range of fields, from granular processing to fruit packing. There are
currently numerous experiments showing that the loosest way to pack
spheres ( random loose packing) gives a density of similar to 55 per
cent(4-6). On the other hand, the most compact way to pack spheres (
random close packing) results in a maximum density of similar to 64 per
cent(2,4,6). Although these values seem to be robust, there is as yet no
physical interpretation for them. Here we present a statistical
description of jammed states(7) in which random close packing can be
interpreted as the ground state of the ensemble of jammed matter. Our
approach demonstrates that random packings of hard spheres in three
dimensions cannot exceed a density limit of similar to 63.4 per cent. We
construct a phase diagram that provides a unified view of the hard-
sphere packing problem and illuminates various data, including the
random-loose-packed state.
Nutzer