This thesis analyses the structure, phase behaviour and dynamics of two dimensional (2D) systems of interacting soft-core particles, focussing in particular on how these can solidify and the properties of the resulting crystalline structures. Classical density functional theory (DFT) and dynamical density functional theory (DDFT) is used in the analysis, and an introduction to these is given. The first systems studied are particles interacting via the generalised exponential model of index n (GEM-n) pair potential, including binary mixtures of different types of GEM-n particles. We confirm that a simple mean-field approximate DFT (the RPA-DFT) provides a good approximation for the structure and thermodynamics. We study how solidification fronts advance into the unstable liquid after a temperature quench. We find that the length scale of the density modulations chosen by the front is not necessarily the length scale corresponding the equilibrium crystal structure. This results in the presence of defects and disorder in the structures formed. We analyse how these evolve over time, after the front has passed. We also find that for the binary mixtures, the defects and disorder persists for much longer and in-fact can remain indefinitely.
In the final part of this thesis we analyse the Barkan-Engel-Lifshitz (BEL) model, which consists of particles interacting via a soft core potential that is more complicated than the GEM-n potential and can include a minimum in the potential and soft repulsion over several competing length scales. The form of the BEL potential gives good control over the shape of the dispersion relation, which allows it to be tuned to the regime where the system forms quasicrystals. In this regime, we study in detail the nature of the liquid state pair correlations and in particular the form of the asymptotic decay as the distance between the particles r tends to infinity. The usual approach used for fluids in three dimensions has to be generalised, in order to be applicable in 2D. It is found that there is a line in the phase diagram at which the asymptotic decay crosses over from being oscillatory with one wavelength to oscillatory with a different wavelength. We expect this to be a general characteristic of systems that form quasicrystals.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.