TY - JOUR
T1 - Tetrahedral colloidal clusters from random parking of bidisperse spheres
AU - Schade, Nicholas B.
AU - Holmes-Cerfon, Miranda C.
AU - Chen, Elizabeth R.
AU - Aronzon, Dina
AU - Collins, Jesse W.
AU - Fan, Jonathan A.
AU - Capasso, Federico
AU - Manoharan, Vinothan N.
PY - 2013/4/4
Y1 - 2013/4/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84876008840&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84876008840&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.110.148303
DO - 10.1103/PhysRevLett.110.148303
M3 - Article
C2 - 25167045
AN - SCOPUS:84876008840
SN - 0031-9007
VL - 110
JO - Physical Review Letters
JF - Physical Review Letters
IS - 14
M1 - 148303
ER -