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

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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.

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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.


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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.

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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.

Correspondence to Alfons van Blaaderen or Marjolein Dijkstra.

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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) doi:10.1038/nmat4072

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