Numerical Studies of Models of Self-Assembling Systems

Abstract

Self-assembly processes are of great interest in numerous fields. This work attempts to better understand the aggregation of Janus ellipsoids, the parameter space which Janus ellipsoids can be used for encapsulation, and the adsorption of Y-shaped molecules on a two-dimensional lattice. We first employ Canonical Monte Carlo simulations to approximate a ``micellization temperature, cluster distributions, as well as orientation correlation of interacting Janus ellipsoids with an aspect ratio of $0.6$ and an interaction range of $0.2\sigma$. The phase diagram of this system was also approximated through a system of $B_{2}$ scaling and a phase diagram calculated for a model of Janus spheres with an interaction range of $0.5\sigma$. Seeing a possibility of encapsulation, we explore parameters of temperature, sphere size, inter-particle interaction range and strength and determine the most efficient areas in parameter space for encapsulation of spheres by Janus ellipsoids. The adsorption of a model of Y-shaped particles on a two-dimensional lattice implemented Grand Canonical Monte Carlo simulations, using histogram reweighting and biasing techniques to determine the phase diagram of this system. The critical temperature of this system was also determined through finite-size scaling. We also explore the effects of patterned lattices on the critical temperature of the system