Journal
PHYSICAL REVIEW LETTERS
Volume 103, Issue 11, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.103.118303
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Funding
- National Science Foundation [DMR-0820484]
- NSF Division of Mathematical Sciences
- DARPA [BAA 07-21]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [820484] Funding Source: National Science Foundation
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We calculate the ground states of hard-sphere clusters, in which n identical hard spherical particles bind by isotropic short-ranged attraction. Combining graph theoretic enumeration with basic geometry, we analytically solve for clusters of n <= 10 particles satisfying minimal rigidity constraints. For n <= 9 the ground state degeneracy increases exponentially with n, but for n > 9 the degeneracy decreases due to the formation of structures with >3n - 6 contacts. Interestingly, for n = 10 and possibly at n = 11 and n = 12, the ground states of this system are subsets of hexagonal close-packed crystals. The ground states are not icosahedra at n = 12 and n = 13. We relate our results to the structure and thermodynamics of suspensions of colloidal particles with short-ranged attractions.
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