Local Structure in Hard Particle Self-Assembly and Assembly Failure

Abstract

The relationship between local order and global structure is not often a straightforward one in systems on the nano- and microscale in which interactions are usually weak and thermal fluctuations drive self-assembly. Moreover, structure in systems for which particle symmetry is broken is difficult to describe theoretically on any level higher than a pairwise one, due to the prohibitively high-dimensional nature of the relevant configuration space. However, a thorough understanding of local structure in all phases of soft matter systems is necessary to gain a complete picture of the physics of these systems and to leverage them for technological and materials science applications. In this dissertation, I investigate local structure in systems of anisotropic particles mediated exclusively by entropy maximization. Specifically, I explore the role of local structure in crystallization and its failure by tackling two related lines of inquiry.

First, I study the interplay between particle shape and spherical confinement in systems of hard polyhedral particles, to examine locally dense clusters of anisotropic particles and their possible connection to preferred local structures during unconfined self-assembly. I use Monte Carlo simulation methods to find putative densest clusters of the Platonic solids in spherical confinement, for up to N = 60 constituent particles. I find that a spherical boundary suppresses the packing influence of particle shape and produces a robust class of common cluster structures. I also find a range of especially dense clusters at so-called "magic numbers" of constituent particles, and discover that a magic-number cluster of tetrahedra is a prominent motif in the self-assembled structure of tetrahedra, the dodecagonal quasicrystal.

Second, I explore the influence of local structure in systems of hard polyhedral particles that fail to crystallize. I use a shape landscape, or a two-dimensional space of particles that are continuously interrelated by a set of shape perturbations, to investigate why slight changes to particle shape sometimes result in the vitrification rather than crystallization of dense monatomic systems of these particles. I show that assembly failure in these systems arises from a multiplicity of competing local structures, each of which is prevalent in ordered phases crystallized by particles that are only slightly different in shape. Thus, systems that fail to assemble do so because they cannot crystallize into any one ordered phase.

Third, I demonstrate that fragility in these systems, a technologically relevant measure of glass-forming ability, can be tuned by slight changes to particle shape. I relate this finding to simulations of molecular systems in which fragility is linked to intermolecular bond angle.

Finally, I detail the methods and applications of software I developed to detect multi-particle local structure in real space. This software is open-source and in current use, and has already been utilized for local structure detection in several papers by myself and others.

I conclude this dissertation by providing an outlook on the implications and future directions of my work.