title: Clusters of polyhedra in spherical confinement.
abstract: Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to [Formula: see text] constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem.
authors.affiliation: Applied Physics Program, University of Michigan, Ann Arbor, MI 48109;
authors.forename: Erin G
authors.initials: EG
authors.lastname: Teich
authors.affiliation: Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109;
authors.forename: Greg
authors.initials: G
authors.lastname: van Anders
authors.affiliation: Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109;
authors.forename: Daphne
authors.initials: D
authors.lastname: Klotsa
authors.affiliation: Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109;
authors.forename: Julia
authors.initials: J
authors.lastname: Dshemuchadse
authors.affiliation: Applied Physics Program, University of Michigan, Ann Arbor, MI 48109; Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109; Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109; Biointerfaces Institute, University of Michigan, Ann Arbor, MI 48109 sglotzer@umich.edu.
authors.forename: Sharon C
authors.initials: SC
authors.lastname: Glotzer
keywords: clusters; colloids; confinement; nanoparticles; packing
references.citation: Phys Rev Lett. 2013 Mar 29;110(13):137801
references.pmid: 23581374
references.citation: Nat Mater. 2007 Sep;6(9):692-7
references.pmid: 17618289
references.citation: Small. 2009 Mar;5(6):646-64
references.pmid: 19306458
references.citation: Nat Rev Genet. 2001 Apr;2(4):292-301
references.pmid: 11283701
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 1):050302
references.pmid: 22181358
references.citation: Langmuir. 2008 Apr 1;24(7):3661-70
references.pmid: 18294020
references.citation: Small. 2014 Aug 13;10(15):3058-63
references.pmid: 24733721
references.citation: Science. 2004 Feb 13;303(5660):990-3
references.pmid: 14963324
references.citation: J Phys Condens Matter. 2010 Jul 21;22(28):283102
references.pmid: 21399272
references.citation: ACS Nano. 2013 Dec 23;7(12):11064-70
references.pmid: 24219591
references.citation: Biophys J. 2013 Apr 2;104(7):1576-84
references.pmid: 23561534
references.citation: Science. 2003 Jul 25;301(5632):470-1
references.pmid: 12881559
references.citation: Phys Rev Lett. 2001 Jun 18;86(25):5719-22
references.pmid: 11415341
references.citation: J Phys Chem B. 2011 Jan 27;115(3):422-32
references.pmid: 21186830
references.citation: Nat Mater. 2011 Nov 20;11(2):131-7
references.pmid: 22101811
references.citation: Science. 2006 Jun 23;312(5781):1780-2
references.pmid: 16728597
references.citation: Soft Matter. 2014 Oct 14;10(38):7468-79
references.pmid: 25034966
references.citation: ACS Appl Mater Interfaces. 2014 Mar 26;6(6):4134-42
references.pmid: 24533909
references.citation: Nano Lett. 2012 Oct 10;12(10):5318-24
references.pmid: 22947109
references.citation: Nat Mater. 2015 Jan;14(1):56-60
references.pmid: 25173580
references.citation: Phys Rev Lett. 2015 Jul 10;115(2):025702
references.pmid: 26207482
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 1):061317
references.pmid: 23367942
references.citation: Soft Matter. 2015 Feb 28;11(8):1481-91
references.pmid: 25601423
references.citation: J Mol Biol. 2010 Feb 19;396(2):384-95
references.pmid: 19944702
references.citation: Science. 2006 Jul 28;313(5786):502-4
references.pmid: 16873661
references.citation: Nat Nanotechnol. 2012 Jun 10;7(7):433-7
references.pmid: 22683842
references.citation: Nature. 2012 Nov 1;491(7422):51-5
references.pmid: 23128225
references.citation: Nano Lett. 2008 Aug;8(8):2321-7
references.pmid: 18630973
references.citation: Science. 1996 Jun 28;272(5270):1924-6
references.pmid: 8662492
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jan;83(1 Pt 1):011304
references.pmid: 21405690
references.citation: Science. 2003 Jul 25;301(5632):483-7
references.pmid: 12881563
references.citation: Nucleic Acids Res. 2013 Feb 1;41(3):1569-80
references.pmid: 23258701
references.citation: Nat Mater. 2010 Mar;9(3):193-204
references.pmid: 20168343
references.citation: Phys Rev Lett. 2000 Oct 23;85(17):3652-5
references.pmid: 11030973
references.citation: J Am Chem Soc. 2005 Nov 16;127(45):15968-75
references.pmid: 16277541
references.citation: J Am Chem Soc. 2006 Nov 22;128(46):14863-70
references.pmid: 17105296
references.citation: Soft Matter. 2015 May 21;11(19):3746-66
references.pmid: 25869864
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041124
references.pmid: 23214546
references.citation: Proc Natl Acad Sci U S A. 2014 Nov 11;111(45):E4812-21
references.pmid: 25344532
references.citation: Phys Rev Lett. 2007 May 4;98(18):188304
references.pmid: 17501616
references.citation: Nature. 2009 Aug 13;460(7257):876-9
references.pmid: 19675649
references.citation: J Am Chem Soc. 2001 Sep 12;123(36):8718-29
references.pmid: 11535076
references.citation: J Am Chem Soc. 2004 Jul 21;126(28):8648-9
references.pmid: 15250706
references.citation: J Am Chem Soc. 2012 Aug 29;134(34):14043-9
references.pmid: 22839450
references.citation: Opt Express. 2007 Oct 17;15(21):14129-45
references.pmid: 19550686
references.citation: Science. 2000 Mar 24;287(5461):2240-3
references.pmid: 10731141
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jun;73(6 Pt 1):062301
references.pmid: 16906885
references.citation: Trends Biochem Sci. 2001 Oct;26(10):597-604
references.pmid: 11590012
references.citation: Nature. 2004 Oct 7;431(7009):647-52
references.pmid: 15470418
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Mar;91(3):030201
references.pmid: 25871031
references.citation: Langmuir. 2006 Jan 3;22(1):32-41
references.pmid: 16378396
references.citation: Proc Natl Acad Sci U S A. 2001 Nov 20;98(24):13671-4
references.pmid: 11707588
references.citation: Phys Rev Lett. 2015 May 8;114(18):188302
references.pmid: 26001021
references.citation: J Phys Chem B. 2008 Nov 20;112(46):14583-92
references.pmid: 18817438
references.citation: Nano Lett. 2013 Sep 11;13(9):4399-403
references.pmid: 23977943
references.citation: Blood. 2014 Mar 6;123(10):1596-603
references.pmid: 24335500
references.citation: Science. 2002 Nov 1;298(5595):1006-9
references.pmid: 12411700
references.citation: ACS Nano. 2012 Jan 24;6(1):609-14
references.pmid: 22098586
references.citation: J Am Chem Soc. 2005 Mar 16;127(10):3268-9
references.pmid: 15755130
references.citation: Phys Rev Lett. 2013 Jul 5;111(1):015501
references.pmid: 23863011
references.citation: Phys Rev Lett. 2015 Oct 9;115(15):158001
references.pmid: 26550753
references.citation: Proc Natl Acad Sci U S A. 2006 Aug 15;103(33):12388-93
references.pmid: 16885211
references.citation: Chromosome Res. 2007;15(7):899-916
references.pmid: 17926137
references.citation: Proc Natl Acad Sci U S A. 2013 Apr 23;110(17):6640-5
references.pmid: 23569275
references.citation: Science. 2012 Jul 27;337(6093):453-7
references.pmid: 22837525
references.citation: Proc Natl Acad Sci U S A. 2007 Jan 16;104(3):717-22
references.pmid: 17215354
references.citation: Nature. 2009 Dec 10;462(7274):773-7
references.pmid: 20010683
references.citation: Langmuir. 2011 Feb 1;27(3):917-27
references.pmid: 21190338
references.citation: PLoS Biol. 2005 May;3(5):e157
references.pmid: 15839726
references.citation: Phys Rev Lett. 2004 Dec 3;93(23):238301
references.pmid: 15601211
references.citation: Phys Rev Lett. 2011 Oct 7;107(15):155501
references.pmid: 22107298
references.citation: Langmuir. 2005 Jul 19;21(15):6669-74
references.pmid: 16008373
references.citation: Science. 2005 Apr 22;308(5721):534-7
references.pmid: 15845849
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Mar;75(3 Pt 1):031903
references.pmid: 17500722
references.citation: Phys Rev Lett. 2011 Mar 18;106(11):115704
references.pmid: 21469881
references.citation: J Phys Chem B. 2005 Jan 13;109(1):188-93
references.pmid: 16851003
references.citation: Nano Lett. 2013 Sep 11;13(9):4137-41
references.pmid: 23919764
references.citation: J Am Chem Soc. 2008 Jun 4;130(22):6949-51
references.pmid: 18465860