Date of Award

Spring 5-28-2014

Document Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

First Advisor

Matthew A. Glaser

Second Advisor

Paul Beale

Third Advisor

Noel A. Clark

Abstract

Three models are examined to demonstrate novel and complex behavior stemming from simple specifications. First I explore the hard-core soft-shoulder (HCSS) system where spheres interact via isotropic, purely repulsive potentials involving a hard core repulsion of range σ and a finite step "shoulder" repulsion of range σs. This system's diverse phase morphology is illustrated by the zero-temperature phase diagram calculated via a large scale simulated annealing procedure. I explore the prospect of directed design of self-assembled structures. The system's incredibly complex behavior and numerous metastable states make it ideal as a test bed for examining the computational effectiveness of various advanced Monte Carlo techniques. I apply several existing methods as well as extend the virtual move Monte Carlo (VMMC) algorithm to models with purely repulsive interactions.

Second, I examine self assembled bundles of achiral hard rods with distributed, short-range attraction. I show that in the majority of cases the equilibrium state of the bundle is chiral. I use umbrella sampling Monte Carlo and cell theory to compute the free energy as a function of a twist order parameter, and show that the formation of spontaneously chiral bundles is driven by maximization of orientational entropy through a process called orientational escape. I map out the phase diagram of bundles in terms of the density and bundle aspect ratio (L/Db) finding transitions between untwisted, weakly twisted, and strongly twisted states.

Lastly I explore the phase behavior of tilted hard rods as a model of de Vries smectic behavior and the first order smectic C (SmC) to smectic A (SmA) phase transition. The free energy cost of azimuthal rotation of a molecule away from the local tilt direction is calculated via umbrella sampling. This calculation is used to map the hard rod system onto a lattice spin system which shows a cross-over from a continuous to first order phase transition as the tilt of the rods is increased. This analysis offers a natural explanation of the first order SmA-SmC phase transition common to de Vries smectics.

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