In this thesis we explore two different theories for modelling soft matter systems. We start by discussing density functional theory (DFT) and dynamical density functional theory (DDFT) and consider the thermodynamics underpinning these theories as well as showing how the main results may be derived from the microscopic properties of soft matter. We use this theory to set up a model for the evaporation of the solvent from a thin film of a colloidal suspension. The general background for such systems is discussed and we display some of the striking nanostructures which self-assemble during the evaporation process. We show that our theory successfully reproduces some of these patterns and deduce the various mechanisms and transport processes behind the formation of the different structures.
In the second part of this thesis we discuss results for a second model; the phase field crystal (PFC) model. The model equations are discussed, showing how they may be derived from DDFT as well as discussing the general background of PFC models. We present some results for the PFC model in its most commonly used form before going on to introduce a modified PFC model. We show how the changes in the model equations are reflected in the thermodynamics of the model. We then proceed by demonstrating how this modified PFC model may be used to qualitatively describe colloidal systems. A two component generalisation of the modified PFC model is introduced and used to investigate the transition between hexagonal and square ordering in crystalline structures. We conclude by discussing the similarities and connections between the two models presented in the thesis.
A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.