Person:

Collins, Jesse

Using experiments and simulations, we investigate the clusters that form when colloidal spheres stick irreversibly to—or “park” on—smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA sequences, and we vary the ratio α of large to small sphere radii. Once bound, the large spheres cannot rearrange, and thus the clusters do not form dense or symmetric packings. Nevertheless, this stochastic aggregation process yields a remarkably narrow distribution of clusters with nearly 90% tetrahedra at α=2.45. The high yield of tetrahedra, which reaches 100% in simulations at α=2.41, arises not simply because of packing constraints, but also because of the existence of a long-time lower bound that we call the “minimum parking” number. We derive this lower bound from solutions to the classic mathematical problem of spherical covering, and we show that there is a critical size ratio αc=(1+√2)≈2.41, close to the observed point of maximum yield, where the lower bound equals the upper bound set by packing constraints. The emergence of a critical value in a random aggregation process offers a robust method to assemble uniform clusters for a variety of applications, including metamaterials.

In this thesis, I discuss engineering colloidal particles to have specific, isotropic interactions and studying their cluster geometries in equilibrium. I discuss light scattering experiments showing that a highly specific protein, Dscam, is unstable against thermal aggregation. This result lead me to use DNA instead to control interparticle specificity. I coated 1-micron diameter polystyrene particles uniformly with DNA. I used fluorescence microscopy with oxygen-scavenging enzymes to observe these particles self-assembling in clusters. These experiments show that a packing of 6 spheres that is rarely seen in a single-component system is observed very often in an optimized 3-species system. Then I show experiments using the same 3 species but 9 total particles, finding that the equilibrium yields of the most likely cluster relative to other stable clusters are lower than at 6 particles. I conclude from these experiments that optimizing the assembly of an otherwise unlikely configuration may require nearly as many species as particles. Finally, I investigate the scalability of self-assembly of particles with isotropic and specific interactions theoretically. I use both exact and approximate partition functions to show that spheres with specific interactions can have energy landscapes with thermodynamically large numbers of strictly local minima relative to the number of their ground states. Compared to single-component systems, these systems of many different species may spend much more time in kinetic traps and never reach their ground states. Finally, I discuss briefly some directions for further study, including questions of how the results in this thesis may be related to protein folding and complex formation.