Abstract
This thesis investigates the early stages of crystallisation in the bulk, at surfaces and in pores. The main motivation is to achieve a greater understanding of the crystallisation of proteins in the presence of disordered porous media, although this research is applicable to a wide range of research fields. Metropolis Monte Carlo simulation is used in conjunction with techniques such as forward flux sampling to measure the rate of nucleation of crystals. Initially, the 2d Ising model is used to simulate nucleation in rectangular pores with one open end. By calculating the rate of nucleation from pores with different pore widths we show that the overall rate of nucleation peaks at a certain pore width. To investigate effects from crystallisation we used a simple system of spherical particles interacting via the Lennard-Jones potential. Our typical conditions of study are below the triple point temperature where the equilibrium phase is crystal. As a pre-requisite to investigating crystallisation in pores we studied bulk transitions and surface transitions at planar surfaces. We find that, starting from a bulk supersaturated vapour, crystallisation occurs via two distinct steps. In the first step, a liquid droplet nucleates from the vapour. Then, the crystal phase nucleates in the liquid droplet, provided that this liquid droplet exceeds a minimum size. Since it has been shown that similar sized crystallites have lower free energies in highly defected structures such as icosahedral and decahedral ordering we investigated the role of defects in our- nucleated crystallites. Crystallites with defects patterns similar to those seen in decahedral ordering are found to have lower relative free energies than those with fcc ordering. We also observe non-equilibrium effect which we suggest are due to the slow dynamics associated with defect formation. At a planar surface crystallisation is studied from liquid phase. We find that the surface behaviour, such as freezing and pre-freezing transitions, directly effects the nature of crystallisation. Far below freezing nucleation is well described by Classical Nucleation Theory but as the surface-particle interaction becomes more attractive the nuclei become more 2 dimensional. At surfaces with a strongly attractive surface-particle interaction, the formation of a surface crystal phase removes the barriers to bulk crystallisation. Whilst crystallisation behaviour in the bulk and at a planar surface appears qualitatively similar to that of liquid nucleation, this thesis shows that crystal nucleation in a wedge shaped pore is drastically different. Due to intrinsic angles in the crystal lattice, crystallisation is enhanced at angles that allow a defect-free unstrained piece of crystal to fit into the wedge. At other angles the formation of defects and strain causes a decrease in the rate of crystallisation. Our simulation using both the Ising and Lennard-Jones model show that crystallisation is enhanced from pores with a particular size and shape. Therefore, disordered porous media with a wide distribution of pore sizes and shapes may be needed as there is a greater chance that they will contain pores with the required geometry.