Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement


Icosahedral symmetry, which is not compatible with truly long-range order, can be found in many systems, such as liquids, glasses, atomic clusters, quasicrystals and virus-capsids1,2,3,4,5,6,7,8,9,10,11,12. To obtain arrangements with a high degree of icosahedral order from tens of particles or more, interparticle attractive interactions are considered to be essential1,3,6,7,8,9,10,11,12. Here, we report that entropy and spherical confinement suffice for the formation of icosahedral clusters consisting of up to 100,000 particles. Specifically, by using real-space measurements on nanometre- and micrometre-sized colloids, as well as computer simulations, we show that tens of thousands of hard spheres compressed under spherical confinement spontaneously crystallize into icosahedral clusters that are entropically favoured over the bulk face-centred cubic crystal structure13,14. Our findings provide insights into the interplay between confinement and crystallization and into how these are connected to the formation of icosahedral structures.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Secondary electron scanning transmission electron microscopy (SE-STEM) images of typical supraparticles containing cobalt iron oxide nanoparticles.
Figure 2: Core and surface structure of the icosahedral clusters.
Figure 3: Size dependence of the cluster structure.
Figure 4: Crystallization process of icosahedral clusters.


  1. 1

    Nelson, D. R. & Halperin, B. I. Pentagonal and icosahedral order in rapidly cooled metals. Science 229, 233–238 (1985).

    CAS  Article  Google Scholar 

  2. 2

    Steinhardt, P. J., Nelson, D. R. & Ronchetti, M. Bond-orientational order in liquids and glasses. Phys. Rev. B 28, 784–805 (1983).

    CAS  Article  Google Scholar 

  3. 3

    Doye, J. P. K. & Wales, D. J. The structure and stability of atomic liquids: From clusters to bulk. Science 271, 484–487 (1996).

    CAS  Article  Google Scholar 

  4. 4

    Karayiannis, N. C., Malshe, R., Kröger, M., de Pablo, J. J. & Laso, M. Evolution of fivefold local symmetry during crystal nucleation and growth in dense hard-sphere packings. Soft Matter 8, 844–858 (2012).

    CAS  Article  Google Scholar 

  5. 5

    Bernal, J. D. & Finney, J. L. Random close-packed hard-sphere model. II. Geometry of random packing of hard spheres. Discuss. Faraday Soc. 43, 62–69 (1967).

    Article  Google Scholar 

  6. 6

    Mackay, A. L. A dense non-crystallographic packing of equal spheres. Acta Crystallogr. 15, 916–918 (1962).

    CAS  Article  Google Scholar 

  7. 7

    Doye, J. P. K. & Wales, D. J. Thermally-induced surface reconstructions of Mackay icosahedra. Z. Phys. D 40, 466–468 (1997).

    CAS  Article  Google Scholar 

  8. 8

    Meng, G., Arkus, N., Brenner, M. P. & Manoharan, V. N. The free-energy landscape of clusters of attractive hard spheres. Science 327, 560–563 (2010).

    CAS  Article  Google Scholar 

  9. 9

    Hendy, S. C. & Doye, J. P. K. Surface-reconstructed icosahedral structures for lead clusters. Phys. Rev. B 66, 235402 (2002).

    Article  Google Scholar 

  10. 10

    Wang, Y., Teitel, S. & Dellago, C. Melting of icosahedral gold nanoclusters from molecular dynamics simulations. J. Chem. Phys. 122, 214722 (2005).

    Article  Google Scholar 

  11. 11

    Lacava, J., Born, P. & Kraus, T. Nanoparticle clusters with Lennard-Jones geometries. Nano Lett. 12, 3279–3282 (2012).

    CAS  Article  Google Scholar 

  12. 12

    Frank, F. C. Supercooling of liquids. Proc. R. Soc. Lond. A 215, 43–46 (1952).

    CAS  Article  Google Scholar 

  13. 13

    Pusey, P. N. & Van Megen, W. Phase behaviour of concentrated suspensions of nearly hard colloidal spheres. Nature 320, 340–342 (1986).

    CAS  Article  Google Scholar 

  14. 14

    Bolhuis, P. G., Frenkel, D., Mau, S-C. & Huse, D. A. Entropy difference between crystal phases. Nature 388, 235–236 (1997).

    CAS  Article  Google Scholar 

  15. 15

    Conway, J. H. & Sloane, N. J. A. Sphere Packings, Lattices and Groups (Springer, 1998).

    Google Scholar 

  16. 16

    McGinley, J. T., Jenkins, I., Sinno, T. & Crocker, J. C. Assembling colloidal clusters using crystalline templates and reprogrammable DNA interactions. Soft Matter 9, 9119–9128 (2013).

    CAS  Article  Google Scholar 

  17. 17

    O’Malley, B. & Snook, I. Crystal nucleation in the hard sphere system. Phys. Rev. Lett. 90, 085702 (2003).

    Article  Google Scholar 

  18. 18

    Hubert, H. et al. Icosahedral packing of B12 icosahedra in boron suboxide (B6O). Nature 391, 376–378 (1998).

    Article  Google Scholar 

  19. 19

    Doye, J. P. K. & Calvo, F. Entropic effects on the structure of Lennard-Jones clusters. J. Chem. Phys. 116, 8307–8317 (2002).

    CAS  Article  Google Scholar 

  20. 20

    Hofmeister, H. Forty years study of fivefold twinned structures in small particles and thin films. Cryst. Res. Technol. 33, 3–25 (1998).

    CAS  Article  Google Scholar 

  21. 21

    Langille, M. R., Zhang, J., Personick, M. L., Li, S. & Mirkin, C. A. Stepwise evolution of spherical seeds into 20-fold twinned icosahedra. Science 337, 954–957 (2012).

    CAS  Article  Google Scholar 

  22. 22

    Tang, J. et al. Hard-sphere packing and icosahedral assembly in the formation of mesoporous materials. J. Am. Chem. Soc. 129, 9044–9048 (2007).

    CAS  Article  Google Scholar 

  23. 23

    Wales, D. J. Surveying a complex potential energy landscape: Overcoming broken ergodicity using basin-sampling. Chem. Phys. Lett. 584, 1–9 (2013).

    CAS  Article  Google Scholar 

  24. 24

    Fortini, A. & Dijkstra, M. Phase behaviour of hard spheres confined between parallel hard plates: Manipulation of colloidal crystal structures by confinement. J. Phys. Condens. Matter 18, L371–L378 (2006).

    CAS  Article  Google Scholar 

  25. 25

    Löwen, H., Oguz, E. C., Assoud, L. & Messina, R. Colloidal crystallization between two and three dimensions. Adv. Chem. Phys. 148, 225–249 (2012).

    Google Scholar 

  26. 26

    Bodnarchuk, M. I. et al. Exchange-coupled bimagnetic wüstite/metal ferrite core/shell nanocrystals: Size, shape, and compositional control. Small 5, 2247–2252 (2009).

    CAS  Article  Google Scholar 

  27. 27

    Van Blaaderen, A. & Vrij, A. Synthesis and characterization of colloidal dispersions of fluorescent, monodisperse silica spheres. Langmuir 8, 2921–2931 (1992).

    CAS  Article  Google Scholar 

  28. 28

    Farges, J., De Feraudy, M. F., Raoult, B. & Torchet, G. Noncrystalline structure of argon clusters. II. Multilayer icosahedral structure of ArN clusters 50 < N < 750. J. Chem. Phys. 84, 3491–3501 (1986).

    CAS  Article  Google Scholar 

  29. 29

    Friedrich, H. et al. Quantitative structural analysis of binary nanocrystal superlattices by electron tomography. Nano Lett. 9, 2719–2724 (2009).

    CAS  Article  Google Scholar 

  30. 30

    Van Blaaderen, A. & Wiltzius, P. Real-space structure of colloidal hard-sphere glasses. Science 270, 1177–1179 (1995).

    CAS  Article  Google Scholar 

  31. 31

    Schilling, T. & Schmid, F. Computing absolute free energies of disordered structures by molecular simulation. J. Chem. Phys. 131, 231102 (2009).

    CAS  Article  Google Scholar 

  32. 32

    Cacciuto, A., Auer, S. & Frenkel, D. Onset of heterogeneous crystal nucleation in colloidal suspensions. Nature 428, 404–406 (2004).

    CAS  Article  Google Scholar 

  33. 33

    Manoharan, V. N., Elsesser, M. T. & Pine, D. J. Dense packing and symmetry in small clusters of microspheres. Science 301, 483–487 (2003).

    CAS  Article  Google Scholar 

  34. 34

    Lauga, E. & Brenner, M. P. Evaporation-driven assembly of colloidal particles. Phys. Rev. Lett. 93, 238301 (2004).

    Article  Google Scholar 

  35. 35

    Bai, F. et al. A versatile bottom-up assembly approach to colloidal spheres from nanocrystals. Angew. Chem. Int. Ed. 46, 6650–6653 (2007).

    CAS  Article  Google Scholar 

Download references


We thank R. J. A. Moes (who is funded by the FOM programme Control over Functional Nanoparticle Solids (FNPS)) for synthesis of the semiconductor particles, A. Kuijk for the synthesis of the silica colloids, and T. H. Besseling for the two-dimensional tracking. We thank J. R. Edison, W. Vlug and R. v. Roij for critical reading of the manuscript. B.d.N. acknowledges financial support from a ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek’ (NWO) CW grant. M.D. and F.S. acknowledge financial support from an NWO-VICI grant. S.D. and M.D. acknowledge financial support from an NWO-CW-Echo grant.

Author information




A.I. and A.v.B. initiated the experimental part of the project. B.d.N. and D.J.G. performed the experiments under the supervision of A.I. and A.v.B. B.d.N. and J.D.M. performed the electron microscopy analysis. S.D. and F.S. carried out the simulations under the supervision of L.F. and M.D. B.d.N., S.D., F.S., L.F., M.D. and A.v.B. co-wrote the paper. All authors analysed and discussed results.

Corresponding authors

Correspondence to Alfons van Blaaderen or Marjolein Dijkstra.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 5498 kb)

Supplementary Information

Supplementary Movie 1 (MOV 10977 kb)

Supplementary Information

Supplementary Movie 2 (MOV 17310 kb)

Supplementary Information

Supplementary Movie 3 (MOV 21318 kb)

Supplementary Information

Supplementary Movie 4 (MOV 27620 kb)

Supplementary Information

Supplementary Information (HTML 1835 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

de Nijs, B., Dussi, S., Smallenburg, F. et al. Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement. Nature Mater 14, 56–60 (2015).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing