Tetrahedral colloidal clusters from random parking of bidisperse spheres

Nicholas B. Schade, Miranda Holmes-Cerfon, Elizabeth R. Chen, Dina Aronzon, Jesse W. Collins, Jonathan A. Fan, Federico Capasso, Vinothan N. Manoharan

Research output: Contribution to journalArticle

Abstract

Using experiments and simulations, we investigate the clusters that form when colloidal spheres stick irreversibly to - or "park" on - smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA sequences, and we vary the ratio α of large to small sphere radii. Once bound, the large spheres cannot rearrange, and thus the clusters do not form dense or symmetric packings. Nevertheless, this stochastic aggregation process yields a remarkably narrow distribution of clusters with nearly 90% tetrahedra at α=2.45. The high yield of tetrahedra, which reaches 100% in simulations at α=2.41, arises not simply because of packing constraints, but also because of the existence of a long-time lower bound that we call the "minimum parking" number. We derive this lower bound from solutions to the classic mathematical problem of spherical covering, and we show that there is a critical size ratio αc=(1+√2) ≈2.41, close to the observed point of maximum yield, where the lower bound equals the upper bound set by packing constraints. The emergence of a critical value in a random aggregation process offers a robust method to assemble uniform clusters for a variety of applications, including metamaterials.

Original languageEnglish (US)
Article number148303
JournalPhysical Review Letters
Volume110
Issue number14
DOIs
StatePublished - Apr 4 2013

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parking
Stochastic Processes
Complementary DNA
tetrahedrons
complementary DNA
random processes
stochastic processes
charged particles
coverings
simulation
radii

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Medicine(all)

Cite this

Schade, N. B., Holmes-Cerfon, M., Chen, E. R., Aronzon, D., Collins, J. W., Fan, J. A., ... Manoharan, V. N. (2013). Tetrahedral colloidal clusters from random parking of bidisperse spheres. Physical Review Letters, 110(14), [148303]. https://doi.org/10.1103/PhysRevLett.110.148303

Tetrahedral colloidal clusters from random parking of bidisperse spheres. / Schade, Nicholas B.; Holmes-Cerfon, Miranda; Chen, Elizabeth R.; Aronzon, Dina; Collins, Jesse W.; Fan, Jonathan A.; Capasso, Federico; Manoharan, Vinothan N.

In: Physical Review Letters, Vol. 110, No. 14, 148303, 04.04.2013.

Research output: Contribution to journalArticle

Schade, NB, Holmes-Cerfon, M, Chen, ER, Aronzon, D, Collins, JW, Fan, JA, Capasso, F & Manoharan, VN 2013, 'Tetrahedral colloidal clusters from random parking of bidisperse spheres', Physical Review Letters, vol. 110, no. 14, 148303. https://doi.org/10.1103/PhysRevLett.110.148303
Schade, Nicholas B. ; Holmes-Cerfon, Miranda ; Chen, Elizabeth R. ; Aronzon, Dina ; Collins, Jesse W. ; Fan, Jonathan A. ; Capasso, Federico ; Manoharan, Vinothan N. / Tetrahedral colloidal clusters from random parking of bidisperse spheres. In: Physical Review Letters. 2013 ; Vol. 110, No. 14.
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