We consider the thermodynamically driven self-assembly of spheres onto the
surface of a central sphere. This assembly process forms self-limiting, or
terminal, anisotropic clusters (N-clusters) with well defined structures. We
use Brownian dynamics to model the assembly of N-clusters varying in size from
two to twelve outer spheres, and free energy calculations to predict the
expected cluster sizes and shapes as a function of temperature and inner
particle diameter. We show that the arrangements of outer spheres at finite
temperatures are related to spherical codes, an ideal mathematical sequence of
points corresponding to densest possible sphere packings. We demonstrate that
temperature and the ratio of the diameters of the inner and outer spheres
dictate cluster morphology and dynamics. We find that some N-clusters exhibit
collective particle rearrangements, and these collective modes are unique to a
given cluster size N. We present a surprising result for the equilibrium
structure of a 5-cluster, which prefers an asymmetric square pyramid
arrangement over a more symmetric arrangement. Our results suggest a promising
way to assemble anisotropic building blocks from constituent colloidal spheres.Comment: 15 pages, 10 figure
