Order and Jamming on Curved Surfaces - Burke, Christopher. (2017)
Abstract: Geometric frustration occurs when a physical system's preferred ordering (e.g. spherical particles packing in a hexagonal lattice) is incompatible with the system's geometry. An example of this occurs in arrested relaxation in Pickering emulsions. Pickering emulsions are emulsions (e.g. mixtures of oil and water) with colloidal particles mixed in. The particles tend to lie at an oil-water interface, and can coat the surface of droplets within the emulsion (e.g. an oil droplet surrounded by water.) If a droplet is deformed from its spherical ground state, more particles adsorb at the surface, and the droplet is allowed to relax, then the particles on the surface can become close packed and prevent further relaxation, arresting the droplet in a non-spherical shape. The resulting structures tend to be relatively well ordered with regions of highly hexagonal packings; however, the curvature of the surface prevents perfect ordering and defects in the packing are required. These defects may influence the stability of these structures, making it important to understand how to predict and control them for applications in the food, cosmetic, oil, and medical industries. In this work, we use simulations to study the ordering and stability of sphere packings on arrested emulsions droplets. We first isolate the role of surface geometry by creating packings on a static ellipsoidal surface. Next we perform simulations which include dynamic effects that are present in the experimental Pickering emulsion system. Packings are created by evolving an ellipsoidal surface towards a spherical shape at fixed volume; the effects of relaxation rate, interparticle attraction, and gravity are determined. Finally, we study jamming on curved surfaces. Packings of hard particles are used to study marginally stable packings and the role curvature plays in constraining them. We also study packings of soft particles, compressed beyond marginal stability, and find that geometric frustration plays an important role in determining their mechanical properties.; Thesis (Ph.D.)--Tufts University, 2016.; Submitted to the Dept. of Physics.; Advisor: Timothy Atherton.; Committee: Peggy Cebe, James Adler, and Greg Grason.; Keywords: Physics, and Condensed matter physics.