Colloidal crystallization in bulk, gravity and spherical confinement

This thesis investigates, using computer simulations, various aspects of colloidal crystallization in unconfined bulk systems, in a gravitational field, and inside a spherical confinement, with a particular focus on photonic crystals. Photonic crystals show a photonic band gap as a consequence of alternating regions of high and low dielectric contrasts. Colloidal photonic crystals, due to the size of the building blocks, display a photonic band gap in the visible or infrared range of the electromagnetic spectrum, and have numerous applications as optical wave guides, optical sensors, telecommunications, energy storage and conversion. We introduce the ideas and challenges associated with the self-assembly of colloidal photonic crystals in Chapter 1. The face-centered-cubic (FCC) crystal has a narrow photonic band gap, which is susceptible to defects. In Chapter 2, we show that that monodisperse hard spheres sedimenting at high velocities onto a FCC(100) template form single large FCC crystals with very few extended defects, which is desirable for photonics. In Chapter 3, we study a colloidal self-assembly route for the binary MgCu2 Laves phase (LP) via templated sedimentation of binary hard spheres. The MgCu2 LP is a champion photonic precursor as its large and small species sublattices are the diamond and pyrochlore structures respectively, both of which show wide photonic bandgaps at low refractive index contrasts. In Chapter 4, we discuss how to avoid a random stacking of the FCC and its thermodynamically competing structure (hexagonal-close-packed) upon crystallization, by adding polymer chains to the colloidal crystal structures in order to stabilise one over the other. The addition of polymer chains incurs a free-energy cost which is different for the two crystals owing to the difference in the distribution of voids in the structures. In Chapter 5, we investigate the role of attractions in nanoparticle self-assembly inside a spherical confinement, using spheres with a hard core and an attractive corona. We observed four completely different kinetic pathways on tuning the strength of attraction between the spheres from -3 kBT to 0 (hard spheres). In Chapter 6, we return to investigating purely repulsive systems. Binary crystal nucleation in repulsive systems occurs at very high densities and is therefore often hampered by glassy dynamics. We show that by introducing a degree of softness into the hard-sphere potential one can spontaneously nucleate binary Laves phases. We then show how our soft repulsive systems are a good approximation for hard spheres from the presence of isomorphic curves on the thermodynamic phase diagram. We extend the discussion of isomorphs to attempt to answer why spontaneous nucleation of LPs have never been observed in `brute force' computer simulations of binary hard spheres. Finally, in Chapter 7, we show that the same binary mixture of repulsive spheres which forms LPs in bulk, spontaneously crystallizes into an icosahedral quasicrystal (iQC) inside a spherical confinement. This is particularly interesting for photonics as not only does an iQC possess a photonic band gap, but also the iQC cluster is made up of twenty tetrahedral domains with the local symmetry of the MgCu2 LP