Geometric Templating and Frustration of Two-Dimensional Colloidal Crystals

Abstract

In this thesis, I explore how template geometry can assist or frustrate depletion-mediated self-assembly of two-dimensional (2D) colloidal crystals. To understand geometric frustration, it is useful to seed the position and orientation of colloidal crystal nuclei. However, existing experimental methods disrupt crystallization dynamics or do not work on highly curved substrates. Using focused ion beam (FIB) nanofabrication, I deposit seeds that control the position and orientation of 2D colloidal crystals. I show that different nucleation pathways can occur at the seed, while the growth behavior is unaffected by the seed. I use this technique to study geometric frustration on curved surfaces by seeding crystal growth on a thin glass fiber.

Although FIB nanofabrication enables seeding of colloidal crystals on curved templates, FIB is an inherently low throughput process. Therefore, I use simulations to systematically probe how various geometric parameters affect the growth of seeded crystals. I use a greedy algorithm to study how crystals of hard disks grow from a seed placed on a cone. The simulations show that tilt grain boundaries emerge when the crystals wrap around the cone. I find that initially ordered crystals transition into disordered packings near the tip of the cone. Surprisingly, the defect density depends on the circumference only. This finite-size effect appears at small circumferences for both cones and cylinders. In addition, crystals seeded close to the cone tip can temporarily escape the finite-size effect. These findings reveal that cones can frustrate crystal growth, but the frustration can be alleviated by judicious choice of seed placement.

In the absence of a seed, the fiber itself can act as a template. I show experimentally that colloidal crystals growing on conical fibers are geometrically frustrated by the conical closure condition. Whereas crystals on a cylinder can form perfect commensurate bands, crystals on a high-angle cone form a tilt-boundary seam with a predictable grain-boundary angle. At intermediate, near-cylindrical cone angles, crystals can still form perfect commensurate bands, but the widths of these crystalline bands are limited by the emergence of dislocations. The gradient in circumference for conical fibers imposes curvature-induced elastic stress on crystals, and therefore, crystals that reach the critical width incorporate dislocations to release that stress. These dislocations enable the crystal to continue growing beyond the critical width.

Spherical templates and bidisperse suspensions can also geometrically frustrate crystals. Using molecular dynamics simulations, I show that crystallization within a droplet is a competition between heterogeneous nucleation at the interface and homogeneous nucleation in the bulk. I show that crystallization of larger particles is favorable at the droplet interface for short-ranged interactions, resulting in a core-shell structure composed of a shell of larger particles and a core of smaller particles. By increasing the interaction range, I can drive crystallization of the larger particles to occur at the interior of the droplet, resulting in an inverted core-shell structure. In a bidisperse system assembling by depletion interactions, the surface presentation of the droplet can be inverted by simply changing the size of depletants without modifying the particles themselves.

My work demonstrates how geometric parameters can affect the grain orientation, defect structure, and crystal morphology of self-assembled colloidal crystals. In addition, focused ion beam methods can directly template particles for experiments requiring high spatial control. These results enable future fundamental studies in geometric frustration and applied studies in crystal and defect engineering at the colloidal scale.