Tetrahedral colloidal clusters from random aggregation of bidisperse spheres

Details Tetrahedral colloidal clusters from random aggregation of bidisperse spheres Tetrahedral colloidal clusters from random aggregation of bidisperse spheres

2012-01-19

arxiv.org/abs/1201.3952v1

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 3 figures

Scientific paper

Using experiments and simulations, we investigate the structures that form when colloidal spheres cluster around smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA sequences to form the clusters, and we vary the ratio $\alpha$ of large to small sphere radii. Near a critical size ratio $\alpha_c=(1+\sqrt{2})$, we find that 90% of the clusters produced through random aggregation are tetrahedra containing four large particles. A random sphere parking model shows that the high yield of tetrahedra, which approaches 100% in simulations at $\alpha = \alpha_c$, arises from the convergence of two geometrical bounds on the number of attached outer spheres. We show that these bounds can be derived from the solutions to the classic mathematical problems of spherical packing and covering. The phenomenon we observe might be used to mass produce tetrahedral clusters, which can be used as building blocks for isotropic optical metamaterials.

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