Solidification and structure formation in soft-core fluids

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

Structural crossover in a model fluid exhibiting two length scales: repercussions for quasicrystal formation

We investigate the liquid state structure of the two-dimensional (2D) model introduced by Barkan et al. [Phys. Rev. Lett. 113, 098304 (2014)], which exhibits quasicrystalline and other unusual solid phases, focussing on the radial distribution function $g(r)$ and its asymptotic decay $r\to\infty$. For this particular model system, we find that as the density is increased there is a structural crossover from damped oscillatory asymptotic decay with one wavelength to damped oscillatory asymptotic decay with another distinct wavelength. The ratio of these wavelengths is $\approx1.932$. Following the locus in the phase diagram of this structural crossover leads directly to the region where quasicrystals are found. We argue that identifying and following such a crossover line in the phase diagram towards higher densities where the solid phase(s) occur is a good strategy for finding quasicrystals in a wide variety of systems. We also show how the pole analysis of the asymptotic decay of equilibrium fluid correlations is intimately connected with the non-equilibrium growth or decay of small amplitude density fluctuations in a bulk fluid