The primary focus of this work is to develop an understanding of crystallisation in hard sphere systems. The thesis is presented in two parts. The first section is an investigation of the liquid/crystal interface at equilibrium using molecular dynamical simulations. The objective is to understand how the interface might bridge between the disordered and ordered states in liquid/crystal environments. Topological measures of structure are used to investigate whether any precursor structures are present in the liquid phase, close to the interface, that would allow transition from disorder to order. This differs from other work where simpler measures of structure, classifying phases into either liquid or crystal, are used. The results indicate that the liquid/crystal interface of a hard sphere system is very narrow and no readily observable structures were found that extended past the width of the equilibrium interface. The second section of the thesis is a theoretical study of growth kinetics in hard sphere systems using density functional theory. The kinetics in a fixed volume are examined with a single conserved order parameter. The work is extended incorporating both conserved particle and non-conserved structure dynamics. The kinetics of growth are examined and it is shown that the small initial crystals are quickly isolated from the higher pressure of the surrounding system through the development of a depletion zone.

The primary focus of this work is to develop an understanding of crystallisation in hard sphere systems. The thesis is presented in two parts. The first section is an investigation of the liquid/crystal interface at equilibrium using molecular dynamical simulations. The objective is to understand how the interface might bridge between the disordered and ordered states in liquid/crystal environments. Topological measures of structure are used to investigate whether any precursor structures are present in the liquid phase, close to the interface, that would allow transition from disorder to order. This differs from other work where simpler measures of structure, classifying phases into either liquid or crystal, are used. The results indicate that the liquid/crystal interface of a hard sphere system is very narrow and no readily observable structures were found that extended past the width of the equilibrium interface. The second section of the thesis is a theoretical study of growth kinetics in hard sphere systems using density functional theory. The kinetics in a fixed volume are examined with a single conserved order parameter. The work is extended incorporating both conserved particle and non-conserved structure dynamics. The kinetics of growth are examined and it is shown that the small initial crystals are quickly isolated from the higher pressure of the surrounding system through the development of a depletion zone.

No description available.

This works examines the question whether a vapour-liquid phase transition exists in systems of particles with purely dipolar interactions, a topic which has been the subject of a longstanding debate. Monte Carlo simulation results for two modi operandi to tackle this issue are presented. One approach examines the phase behaviour of fluids of charged hard dumbbells (CHD), each made up of two oppositely charged hard spheres with diameters σ and separation d. In the limit d/σ → 0, and with the temperature scaled accordingly, the system corresponds to dipolar hard spheres (DHS) while for larger values of d ionic interactions are dominant. The crossover between ionic and dipolar regimes is examined and a linear variation of the critical temperature T*c in dipolar reduced units as a function of d is observed, giving rise to an extrapolated T*cDHS ≈ 0:15. The second approach focuses on the dipolar Yukawa hard sphere (DYHS)fluid, which is given by a dipolar hard sphere and an attractive isotropic interaction Y of the Yukawa tail form. In this case, the DHS limit is obtained for Y → 0. It is found that T*c depends linearly on the isotropic interaction strength Y over a wide range, coinciding with the results for the CHD model and extrapolating to a similar value of T*c;DHS. However, with the use of specially adapted biased Monte Carlo techniques which are highly efficient, it is shown that the linear variation of T*c is violated for very small values of the Yukawa interaction strength, almost two orders of magnitude smaller than the characteristic dipolar interaction energy. It is found that phase separation is not observable beyond a critical value of the Yukawa energy parameter, even though in thermodynamic and structural terms, the DYHS and DHS systems are very similar. It is suggested that either some very subtle physics distinguishes the DYHS and DHS systems, or the observation of a phase transition in DHSs is precluded by finite-size effects. In the context of phase separation in highly correlated fluids, new flat-histogram Monte Carlo simulation techniques based on the Wang-Landau algorithm are evaluated and shown to be useful tools. This work presents a general and unifying framework for deriving Monte Carlo acceptance rules which facilitate flat histogram sampling. The framework yields uniform sampling rules for thermodynamic states given either by the mechanically extensive variables appearing in the Hamiltonian or, equivalently, uniformly sample the thermodynamic fields which are conjugate to these mechanical variables.

No description available.

Homogeneous crystal nucleation in binary hard sphere mixtures is an active area of research for last two decades. Although Classical nucleation theory (CNT) gives a qualitative picture, it fails at high super saturations because of the following reasons. CNT assumes that the cluster formed is spherical in shape, its properties can be modeled using the bulk properties of the stable solid phase and the interfacial free energy γ between the nucleus and the surrounding metastable fluid is equal to the planar surface tension between two phases at coexistence. These assumptions get increasingly tenuous at higher degrees of super saturations where the critical nucleus formed is microscopic in size leading to breakdown in the predictions of CNT. In addition direct experimental observation of critical nucleus is very difficult because, 1. Critical nucleus is microscopic in size, consisting of few hundreds of particles. 2. Formation of critical cluster is very rare (typically of the order of 101– 106nuclei/cm3/s) 3. Its life time is very short (it either rapidly grows to form a solid phase or melts back to fluid) In these circumstances molecular simulations are an attractive tool to study the crystal nucleation, because in these simulations microscopic size critical nucleus properties can be calculated. However, brute force molecular dynamic (MD) simulation techniques to study the homogeneous crystal nucleation is currently not feasible due to long times involved. Hence, an indirect approach is needed. In this work, Monte Carlo Abstract v (MC) molecular simulation techniques are used to calculate free energy barrier height during the crystal nucleation. Phase behavior of Binary hard sphere mixtures with varying ratios of smaller diameter to larger diameter (α) is very similar to that of binary organic liquids. By studying the crystal nucleation in hard sphere system, the physics behind the nucleation for binary organic liquids can be understood. This is the key motivation to study the homogeneous crystal nucleation in binary hard sphere mixtures using MC simulations. Simulations were done using umbrella sampling in combination with local bond order analysis for the identification of crystal nuclei and to compute shape and height of nucleation barrier. Parallel tempering scheme of Geyer and Thomson was utilized to sample phase space more efficiently. Parallel tempering technique was implemented using Message passing interface (MPI) libraries. By using all the above Monte-Carlo simulation techniques, nucleation barrier was calculated during crystallization of binary hard sphere mixtures under the moderate degrees of super cooling in Isothermal-Isobaric semi grand ensembles. Crystal nucleation in binary hard sphere mixtures has been studied for size ratios α = 0.85, 0.42 and 0.43. For α=0.85, phase diagram contains eutectic point. In this system, the effect of eutectic composition on the nucleation barrier height was observed, by calculating nucleation barriers at various fluid mixture compositions keeping Laplace pressure constant. It is observed that as the fluid mixture composition move towards the eutectic point, free energy barrier height, surface tension and critical cluster sizes are increased and the nucleation rate is drastically decreased by a factor of 10-31. Thus the difficulty of homogenous crystal nucleation increases near the eutectic point. For α=0.42 and 0.43 in the hard sphere system, compound solids such as AB and AB2 solids are stable respectively. In these systems crystal nucleation study was done to observe the compound solid formation. It is observed that in these systems crystallization kinetics are very slow and more advanced simulation techniques need to be developed in order to study crystal nucleation.

Rheological properties of idealised models which exhibit all the non-Newtonian flow phenomenology commonly seen in dense suspensions are investigated by particulate-dynamics computer-simulations. The objectives of these investigations are: (i) to establish the origins of various aspects of dense suspension rheology such as shear-thinning, shear thickening and dilatancy; (ii) to elucidate the different regions of a typical dense suspension rheogram by examining underlying structures and shear induced anisotropies in kinetic energy, diffusivity and pressure; (iii) to investigate the scaling of the simplest idealised model suspension; i.e. the hard-sphere model in Newtonian media and its relationship to the isokinetic flow curves obtained through non-equilibrium molecular dynamics (NEMD) simulations; (iv) to preliminarily determine the effect of perturbations present in all real colloidal suspensions, namely particle size polydispersity and a slight 'softness' of the interparticle potential. Non-equilibrium isokinetic simulations have been performed upon ;systems of particles interacting through the classical hard-sphere potential and a perturbation thereof, in which the hard-core is surrounded by a 'slightly soft' repulsive skin. The decision to base the present work upon isokinetic studies was made in order to obtain a better under- standing of suspension rheology by making a direct connection with previous NEMD studies of thermal systemst(93). These studies have shown that the non-linear behaviour exhibited by these systems under shear is atttributable to a shear-induced perturbation of the equilibrium phase behaviour. The present study shows this behaviour to correspond to the high shear region of the generalised suspension flow curve.

Colloidal crystals of \(1.55 \mu m\) diameter silica particles were grown on {100} and flat templates by sedimentation and centrifugation. The particles interact as hard spheres. The vacancies and divacancies in these crystals are not in equilibrium, since no movement of single vacancies is observed. The lack of mobility is consistent with the extrapolation of earlier simulations at lower densities. The volume of relaxation of the vacancy has a plausible value for these densities as the volume of formation is approaching the volume in a close-packed crystal. The volume of relaxation for the divacancy is smaller than that of two vacancies, so that the association of two vacancies into a divacancy requires extra volume, and hence extra entropy. The mean square displacement of the nearest neighbors of the vacancies is an order of magnitude larger than that of the nearest neighbors of particles. The mobility of the divacancies is consistent with the extrapolation of older simulations and is similar to that associated with the annihilation of the vacancy-interstitial pair. The volume of motion of the divacancies is \(\Delta V_m = 0.19V_o (V_o\): close-packed volume) and the entropy of motion is \(\Delta S_m = 0.49k_BT\). Dislocation-twin boundary interactions can be observed by introducing strain via a misfit template. The dislocations formed are Shockley partials. When a dislocation goes through the boundary, two more dislocations are created: a reflected dislocation and one left at the boundary, both with the same magnitude Burgers vector. The dislocations relieve a total of about a third of the misfit strain. The remaining strain is sufficiently large to move the dislocation up to the boundary and close to sufficient to move the dislocation through the boundary. A small amount to extra strain energy is needed to cause nucleation of the two additional dislocations after a waiting time. / Engineering and Applied Sciences

An improved crystallisation spectrometer has been designed, built and tested. It is to be used by others to gain new knowledge about the solidification of matter by study of the crystallisation of hard sphere colloid samples that are an established model for the behaviour of some aspects of atoms. In this crystallisation spectrometer, expanded and collimated green laser light is Bragg scattered from the colloidal crystals as they form, and the diffracted light is focused by a liquid filled hollow glass hemispherical lens onto low cost CCD array detectors that are rotated about the optical axis to average the intensities around the whole Debye-Scherrer cone of scattered light. The temperature of the sample is controlled to +/-0.1„a, and because of the ability to change the refractive index of the sample particles with temperature, this is utilised to control the amount of scattering from the sample Also, this spectrometer uniquely exploits the refractive index match of the colloidal particles, the solvent, the bath liquid, and the glass used for both the sample bottle and the hollow glass hemisphere. A unique facility has been incorporated to permit tumbling of the sample prior to the measurement commencing to shear-melt any pre-existing crystals. This ensures that the sample is completely fluid and is at the correct temperature at the start of the measurement. The instrument is assembled on an optical table and is computer controlled. Results presented show that this new spectrometer with its use of the whole Debye-Scherrer cone of Bragg scattered light and other enhancements gives insight into the crystallisation process more than one order of magnitude of time earlier than previous light scattering experiments, providing new knowledge about the crystallisation process.

Rheological properties of idealised models which exhibit all the non-Newtonian flow phenomenology commonly seen in dense suspensions are investigated by particulate-dynamics computer-simulations. The objectives of these investigations are: (i) to establish the origins of various aspects of dense suspension rheology such as shear-thinning, shear thickening and dilatancy; (ii) to elucidate the different regions of a typical dense suspension rheogram by examining underlying structures and shear induced anisotropies in kinetic energy, diffusivity and pressure; (iii) to investigate the scaling of the simplest idealised model suspension; i.e. the hard-sphere model in Newtonian media and its relationship to the isokinetic flow curves obtained through non-equilibrium molecular dynamics (NEMD) simulations; (iv) to preliminarily determine the effect of perturbations present in all real colloidal suspensions, namely particle size polydispersity and a slight 'softness' of the interparticle potential. Non-equilibrium isokinetic simulations have been performed upon ;systems of particles interacting through the classical hard-sphere potential and a perturbation thereof, in which the hard-core is surrounded by a 'slightly soft' repulsive skin. The decision to base the present work upon isokinetic studies was made in order to obtain a better under- standing of suspension rheology by making a direct connection with previous NEMD studies of thermal systemst(93). These studies have shown that the non-linear behaviour exhibited by these systems under shear is atttributable to a shear-induced perturbation of the equilibrium phase behaviour. The present study shows this behaviour to correspond to the high shear region of the generalised suspension flow curve. / Science and Engineering Research Council and Unilever Research