Structure formation in colloidal and nanoscale systems

In biotechnology, microelectronics, and materials science, many products require intimate attention to microscopic and sub-microscopic construction. Bulk properties of interest often depend on the system microstructure, leading researchers to strive to tailor custom microstructures and predict properties from microstructure—increasingly difficult tasks as component sizes shrink. A promising paradigm for engineering small systems is the idea of designing components which self-assemble into the structures desired, similar to the way that biological systems routinely build themselves from the molecular level up to the macroscopic. In this thesis, I use numerical simulation to study the structural evolution of colloidal and nanoscopic particulate systems. I focus on problems in rheology and adsorption. In the rheological study, I use Stokesian dynamics to investigate a transition where the shear rate qualitatively changes the trajectories of a lattice of particles and imparts a discontinuous, hysteretic viscosity jump. My model shows that a particular face-centered cubic crystal configuration is necessary to reproduce experimental findings. The adsorption studies are approached with two different models. First is a two-dimensional model for the random sequential adsorption of tethered nanoparticles. Tethers provide robust physical and/or electrical connections between particles and a substrate, but they also frustrate order. Hexatic and crystal structures form with surprisingly short tethers of one and four particle radii, respectively. Polydispersities of less than 5–7% (and sufficient tether length) are necessary to form crystal phases, and polydispersities of less than 7–8% are necessary to create hexatic phases. The second set of adsorption studies employs full three-dimensional Brownian dynamics simulations to model electrostatically-repulsive particles that are attracted to a substrate. The zeta-potential of the wall is the primary control of order formation on the surface, and the particle potentials are the primary control of surface coverage. Mixtures of particles that are bidisperse in surface zeta-potential can disrupt order for significant ratio of zeta-potentials, and at large ratios the process creates interesting patterns including dots, clusters, chains, and doped crystals. In each study, system history has a significant effect on the final state of the system; careful attention must be paid to the non-equilibrium process of assembling small systems.