Colloidal clusters, aggregates of a few micrometer-sized spherical particles, are a model experimental system for understanding the physics of self-assembly and processes such as nucleation. Colloidal clusters are well suited for studies on these topics because they are the simplest colloidal system with internal degrees of freedom. Clusters made from particles that weakly attract one another continually rearrange between different structures. By characterizing these internal dynamics and the structures connected by the rearrangement pathways, we seek to understand the statistical physics underlying self-assembly and equilibration.

In this thesis, we examine the rearrangement dynamics of colloidal clusters and analyze the equilibrium distributions of ground and excited states. We prepare clusters of up to ten microspheres bound by short-range depletion interactions that are tuned to allow equilibration between multiple isostatic arrangements. To study these clusters, we use bright-field and digital holographic microscopy paired with computational post-processing to amass ensemble-averaged and time-averaged probabilities.

We study both two-dimensional (2D) and three-dimensional (3D) clusters composed of either one or two species of particles. To learn about geometrical nucleation barriers, we track rearrangements of particles within freely rotating and translating 3D clusters. We show that rearrangements occur on a timescale of seconds, consistent with diffusion-dominated internal dynamics. To better understand excited states and transition pathways, we track hundreds of rearrangements between degenerate ground states in 2D clusters. We show that the rearrangement rates can be understood using a model with two parameters, which account for the diffusion coefficient along the excited-state rearrangement pathways and the interaction potential. To explore new methods to control self-assembly, we analyze clusters of two species with different masses and different interactions. We find that the interactions allow for control over the intracluster placement of each species, while the masses have no influence. To provide a theoretical framework for understanding these observations, we derive the classical partition function of colloidal clusters in terms of translational, rotational, and vibrational degrees of freedom. We show that the masses of the particles enter the partition function through the kinetic energy but have no effect on the probabilities of states that differ only in where the masses are placed. This result is consistent with our experiments.

Overall, this work shows that the equilibrium distribution of self-assembled colloidal clusters is well-modeled by classical statistical physics, and that the rearrangement dynamics of colloidal clusters can be understood by incorporating diffusion and the effect of the interaction potential. Because both the structures and dynamics can be accurately predicted, these clusters are a promising system for self-assembling novel materials and for studying the emergence of phase transitions.