Self-assembly in colloidal hard-sphere systems

Abstract

In this thesis, we examine the phase behaviour and nucleation in a variety of hard-sphere systems. In Chapter 1 we present a short introduction and describe some of the simulation techniques used in this thesis. One of the main difficulties in predicting the phase behaviour in colloidal, atomic and nanoparticle systems is in determining the stable crystalline phases. To address this problem, in Chapters 2 and 4 we present two different methods for predicting possible crystal phases. In Chapter 2, we apply a genetic algorithm to binary hard-sphere mixtures and use it to predict the best-packed structures for this system. In Chapter 4 we present a novel method based on Monte Carlo simulations to predict possible crystalline structures for a variety of models. When the possible phases are known, full free-energy calculations can be used to predict the phase diagrams. This is the focus of Chapters 3 and 5. In Chapter 3, we examine the phase behaviour for binary hard-sphere mixtures with size ratios of the large and small spheres between 0.74 and 0.85. Between size ratios 0.76 and 0.84 we find regions where the binary Laves phases are stable, in addition to monodisperse face-centered-cubic (FCC) crystals of the large and small spheres and a binary liquid. For size ratios 0.74 and 0.85 we find only the monodisperse FCC crystals and the binary liquid. In Chapter 5 we examine the phase behaviour of binary hard-sphere mixtures with size ratios between 0.3 and 0.42. In this range, we find an interstitial solid solution (ISS) to be stable, as well as FCC crystals of the small and large spheres, and a binary fluid. The ISS phase consists of an FCC crystal of the large particles with some of the octahedral holes filled by smaller particles. We show that this filling fraction can be tuned from 0 to 100%. Additionally, we examine the diffusive properties of the small particles in the ISS for size ratio 0.3. In contrast to most systems, we find a region where the diffusion increases as a function of the packing fraction. Finally, in Chapters 6, 7, and 8 we examine nucleation in colloidal systems. In Chapter 6, we examine the crystal nucleation for hard spheres using a variety of simulation techniques, namely, umbrella sampling (US), forward flux sampling (FFS), and molecular dynamics (MD). We compare the resulting nucleation rates with previous experimental and simulated rates. and find agreement between all the theoretically predicted nucleation rates. However, the experimental results display a markedly different behaviour for low supersaturation. In Chapter 7, we examine in more detail the FFS technique, in particular, the effect measurement error has on the resulting nucleation rates. In Chapter 8, we examine the crystal nucleation of the Weeks-Chandler-Andersen (WCA) model with ?? = 40 using Brownian dynamics, US and FFS. This WCA potential is softer than the hard-sphere potential, but is frequently used to approximate hard spheres. Our predicted nucleation rates for this potential are in agreement with those found for hard spheres.