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We study experimentally what is arguably the simplest yet non-trivialcolloidal system: two-dimensional clusters of 6 spherical particles bound bydepletion interactions. These clusters have multiple, degenerate ground stateswhose equilibrium distribution is determined by entropic factors, principallythe symmetry. We observe the equilibrium rearrangements between ground statesas well as all of the low-lying excited states. In contrast to the groundstates, the excited states have soft modes and low symmetry, and theiroccupation probabilities depend on the size of the configuration space reachedthrough internal degrees of freedom, as well as a single "sticky parameter"encapsulating the depth and curvature of the potential. Using a geometricalmodel that accounts for the entropy of the soft modes and the diffusion ratesalong them, we accurately reproduce the measured rearrangement rates. Thesuccess of this model, which requires no fitting parameters or measurements ofthe potential, shows that the free-energy landscape of colloidal systems andthe dynamics it governs can be understood geometrically.

Two-Dimensional Clusters of Colloidal Spheres: Ground States, Excited States, and Structural Rearrangements