title: Tetrahedral colloidal clusters from random parking of bidisperse spheres.
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 α(c) = (1 + sqrt[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.
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Nicholas B
authors.initials: NB
authors.lastname: Schade
authors.affiliation: School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Miranda C
authors.initials: MC
authors.lastname: Holmes-Cerfon
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Elizabeth R
authors.initials: ER
authors.lastname: Chen
authors.affiliation: School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Dina
authors.initials: D
authors.lastname: Aronzon
authors.affiliation: School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Jesse W
authors.initials: JW
authors.lastname: Collins
authors.affiliation: School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Jonathan A
authors.initials: JA
authors.lastname: Fan
authors.affiliation: School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Federico
authors.initials: F
authors.lastname: Capasso
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Vinothan N
authors.initials: VN
authors.lastname: Manoharan
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D004247:DNA / Q000737:chemistry*; D008956:Models, Chemical; D055672:Static Electricity
chemical_list: D003102:Colloids; D004247:DNA