Order and Jamming on Curved Surfaces
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-... read morewater 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.read less