Abstract
Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packing structures are known. The packing of 2D crosses does not yet belong to the category of solved problems. We demonstrate in experiments with crosses of different aspect ratios (arm width to length) which packing fractions are actually achieved by random packing, and we compare them to densest regular packing structures. We determine local correlations of the orientations and positions after ensembles of randomly placed crosses were compacted in the plane until they jam. Short-range orientational order is found over 2 to 3 cross lengths. Similarly, correlations in the spatial distributions of neighbors extend over 2 to 3 crosses. There is no simple relation between the geometries of the crosses and the peaks in the spatial correlation functions, but some features of the orientational correlations can be traced to typical local configurations.
Highlights
Prediction of packing configurations of identical objects is in general a tough problem, even for very simple particle geometries and without spatial restrictions
In sequence of increasing aspect ratio, the densest crystalline packings are the tilted square TSQ, the rhombic end-to-end (ETE) and side-by-side (SBS) lattices named after the mutual positions of arms of neighboring crosses, and the tilted rhomboid (TRH)
A few literature results obtained in numerical simulations can be used as benchmarks for our experimental results
Summary
Prediction of packing configurations of identical objects is in general a tough problem, even for very simple particle geometries and without spatial restrictions. Even shaking or shearing ensembles of spheres leaves them in arrangements where packing is random, and the packing fraction of around rcp ≈ 64% remains well below the optimum value for the crystalline configurations [21,22,23,24,25,26] This jammed state is irregular and in general much less densely packed than the optimum space-filling arrangement, for spherical particles. For more complex shapes like polygons [28, 29], ellipses and dimers [30], irregular
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
