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.

No / There is considerable interest, both fundamental and technological, in understanding how additives and impurities influence nucleation, and in being able to modulate nucleation in a predictable way using designer auxiliary molecules. Notable applications involving auxiliaries include the control of nucleation in proteins, inhibition of urinary stone formation, inhibition of ice formation in living tissues during cryoprotection, prevention of blockages in oil and gas pipelines due to wax precipitation, and gas hydrate formation. Despite the immense interest, our understanding of how these molecules exert their effect is still rudimentary, partially because the molecular level processes involved are inaccessible to experiment. We have investigated mechanisms of action of nucleation additives and have derived explicit rules for designing additive molecules for modulating crystal nucleation. The mechanisms of action and the design features have been derived using molecular simulation of simple model systems. Our studies reveal that an effective nucleation inhibitor should have a strong interaction with the solute and have a structure that is able to disrupt the periodicity characterizing the emerging nucleus. Disruption can be achieved by steric effects resulting from structural differences between the additive and solute molecules, the additive possessing extensive degrees of freedom, or via a strong energetic interaction with the solute. Additive molecules that have an amphiphilic character and end up at the solute/solvent interface can inhibit, retard or promote nucleation depending on their specific structure and interactions with the solute and solvent and the given supersaturation, and these specific features and the link with the supersaturation will be discussed. These findings will help to rationalize the mechanisms of action of known nucleation inhibitors and modulators. They will also serve as a framework for rationally identifying or designing additive molecules for either inhibiting or promoting nucleation in specific systems.

<p> A brief review of the theoretical and experimental aspects of liquid droplet nucleation from vapours and of crystal nucleation from aqueous solution is presented. In order to study the nucleation and crystal growth of several analytically important metal chelates, methods were developed to measure the size distribution of crystals growing in a supersaturated solution. These methods involved rapid mixing techniques followed by measurement of the size distribution of the precipitated particles using a Coulter counter and multichannel analyser. The size distributions were dumped from the analyser onto magnetic tape and recovered using computer methods. The mixing and counting techniques were calibrated and tested using barium sulphate and spheres of known size distribution. </p> <p> From the size distributions obtained for the metal chelates, conclusions were made regarding the nucleation step, and the parameters important in the classical Volmer-Weber-Becker-Doring theory of nucleation were calculated. The validity of the values were evaluated and comparisons made with values obtained by other workers. </p> <p> The laws controlling the crystal growth of the metal chelates and their importance in elucidating the type of nucleation process were also investigated. </p> / Thesis / Doctor of Philosophy (PhD)

no / There is considerable interest, both fundamental and technological, in understanding how additives and impurities influence crystal nucleation, and in the modulation of nucleation in a predictable way by using designer additives. An appropriate additive can promote, retard, or inhibit crystal nucleation and growth, assist in the selective crystallization of a particular enantiomer or polymorphic form, or enable crystals of a desired habit to be obtained.[1¿3] Applications involving additives include the control of the nucleation of proteins,[4] the inhibition of urinary-stone formation[5] and of ice formation in living tissues during cryoprotection,[6] their use as antifreeze agents in Antarctic fish,[7,8] the prevention of blockages in oil and gas pipelines as a result of wax precipitation[9] and gas-hydrate formation,[10] crystal-twin formation,[11] and as a possible basis for the antimalarial activity of some drugs.[12]We report herein the mode of action and explicit (apparently intuitive) rules for designing additive molecules for the modulation of crystal nucleation. The mode of action and the design features have been derived from molecular-dynamics simulations involving simple models.[13] These findings will help to rationalize how known nucleation inhibitors and modulators exert their effect and aid in the identification or design of new additives for the inhibition or promotion of nucleation in specific systems.

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This thesis has made two significant contributions to the field of reactive crystallisation. First, new data from batch cooling crystallisation and semi-batch reactive crystallisation experiments of mono-ammonium phosphate (MAP) were obtained to describe the key factors that influence crystal nucleation and growth rates, crystal size distribution (CSD), and crystal shape. The second contribution is the development of a numerical scheme for solving the population balance equations, which can be used to describe the evolution of CSD during the crystallisation process. This scheme combines the finite difference method with a wavelet method, and is the first reported application of this approach for crystallisation modelling and simulation. / Experiments into the batch cooling crystallisation of MAP were conducted both with and without seed crystals. The effects of key factors such as cooling rate, initial level of supersaturation and seeding technique, including seed concentration and seed size, on the real time supersaturation, final CSD, crystal yield and crystal shape were investigated. It was found that a seed concentration of 20-30% effectively suppressed nucleation. The growth and nucleation rate were estimated by using an isothermal seeded batch approach and their parameters were calculated by non-linear optimisation techniques. / The second series of experiments involved the semi-batch reactive crystallisation of MAP. Both single-feed and dual-feed systems were investigated. In the single-feed arrangement, an ammonia solution was fed into a charge of phosphoric acid. In the dual-feed system, phosphoric acid and ammonia solution were fed into a charge of saturated MAP solution. The molar ratio of the reactants, initial supersaturation, presence or absence of seed crystals, initial MAP concentration, reactants’ flow rate, feeding time and stirring speed were varied, and the effects upon the real time supersaturation, final CSD, crystal yield, crystal shape and solution temperature were measured. X-ray diffraction analysis showed that MAP can be produced in both the single-feed and dual-feed arrangements. For the single feed system, the N/P mole ratio controlled the degree of reaction and the CSD of the product. Di-ammonium phosphate (DAP) was not be observed in the single-feed system due to its high solubility. In the dual-feed system, a seeded solution with slow feed addition, moderate stirring speed and a low initial supersaturation provided the most favourable conditions for generating a desirable supersaturation profile, and thus obtaining a product with good CSD and crystal shape. / A comparative numerical study was undertaken in order to evaluate the existing numerical schemes for solving the population balance equations (PBE) that describe crystallisation. Several analytical solutions to the PBE were used to benchmark the following numerical schemes: Upwind Finite Difference, Biased Upwind Finite Difference, Orthogonal Collocation with Finite Elements, and Wavelet Orthogonal Collocation. The Wavelet Finite Difference (WFD) method has been applied here for the first time for solving PBE problems. The WFD scheme was adapted to solve the batch cooling and the semi-batch reactive crystallisation models, and the solutions were validated against experimental data that we obtained. / In summary, the experimental data provide an improved understanding of MAPreaction and crystallisation mechanisms. The adaptability of the WFD method has beendemonstrated validating the two crystallisation systems, and this should help extendthe application of wavelet-based solutions beyond crystallisation processes and intomore diverse areas of chemical engineering.

The main objectives of the present project were to increase the understanding of small intestinal precipitation of poorly soluble pharmaceutical drugs, investigate occurrence of crystalline small intestinal precipitation and effects of precipitation on absorption. The aim was to create and evaluate methods of predicting crystalline small intestinal drug precipitation using in vivo, in vitro and in silico models. In vivo small intestinal precipitation from highly supersaturated solutions of two weakly basic model drugs, AZD0865 and mebendazole, was investigated in humans and canine models. Potential precipitation of AZD0865 was investigated by examining dose dependent increases in human maximum plasma concentration and total exposure, which turned out to be dose linear over the range investigated, indicating no significant in vivo precipitation. The small intestinal precipitation of mebendazole was investigated from drug concentrations and amount of solid drug present in dog jejunum as well as through the bioavailability after direct duodenal administration in dogs. It was concluded that mebendazole small intestinal precipitation was limited, and that intestinal supersaturation was measurable for up to 90 minutes. In vitro precipitation methods utilizing simulated or real fasted gastric and intestinal fluids were developed in order to simulate the in vivo precipitation rate. The methods overpredicted in vivo precipitation when absorption of drug was not simulated. An in vitro-in silico approach was therefore developed, where the in vitro method was used for determining the interfacial tension (γ), necessary for describing crystallization in Classical Nucleation Theory (CNT). CNT was evaluated using a third model drug, bicalutamide, and could successfully describe different parts of the crystallization process of the drug. CNT was then integrated into an in silico absorption model. The in vivo precipitation results of AZD0865 and mebendazole were well predicted by the model, but only by allowing the fundamental constant γ to vary with concentration. Thus, the in vitro-in silico approach could be used for small intestinal precipitation prediction if the in vitro concentration closely matched in vivo small intestinal concentrations.

Semicrystalline polymers are an important class of materials for their prevalence in today's markets and their desirable properties. These properties depend on the early stages of the polymer crystallization process where a crystal nucleates from the polymer melt. This nucleation process is conventionally understood via an extension of Classical Nucleation Theory to polymers (CNTP). However, recent experimental and simulation evidence points to nucleation mechanisms that do not agree with the predictions of CNTP. Specifically, these experiments suggest a previously unrecognized role of nematic phases in mediating the melt"“crystal transtion. To explain these observations, several new theories of nucleation alternate to CNTP have emerged in the literature, all of which suggest specific modifications to the free energy landscape (FEL) near-equilibrium. To address these theoretical controversies, this dissertation aimed to study the equilibrium phase behavior of polymers via Monte Carlo (MC) simulations. Simulating equilibrium phase behavior of polymer melts is not a trivial task due to the large free energy barriers involved. Throughout this research, we employed a combination of strategies to speed up these molecular simulations. First, we employed a domain decomposition to divide the simulation box into multiple independent simulations that execute independent MC trajectories in parallel. The novel GPU-accelerated MC algorithm successfully and accurately simulated the phase behavior of bead spring chains. Additionally, it sped up MC simulations of Lennard Jones chains by up to 10 times. In its current form, the GPU-accelerated algorithm did not achieve significant speedups to improve outcomes of simulating large polymer melts with detailed potentials. We recommended various strategies to improving the current algorithm. This reality motivated the use of biased MC simulations to study the phase behavior of polymers more expediently without the need for GPU acceleration. Specifically, the latter part of the Dissertation employed Wang Landau MC (WLMC) simulations to build phase diagrams and expanded ensemble density of states (EXEDOS) simulations to construct FELs. Phase diagrams from WLMC simulations divided volume-temperature space into melt, nematic and crystal phases. Then, FELs from EXEDOS simulations at equilibrium provided direct access to the relative stability and minimum free energy paths between coexistant states. By employing a two-dimensional EXEDOS sampling in both crystal and nematic order for hard bead semiflexible oligomers with a stepwise bending stiffness, we built FELs that show that the crystalline transition cooperatively and simultaneously formed crystal and nematic order. This nucleation mechanism was not in agreement with predictions from CNTP or newer theoretical formulations. To investigate the sensitivity of the phase behavior to the employed polymer model, we then employed WLMC simulations to build phase diagrams for a number of different polymer models to ascertain their impact on the resulting nucleation mechanism. We found that the phase behavior was sensitive to the form of the bending stiffness potential used. Chains with a stepwise bending stiffness yielded the previously mentioned cooperative and simultaneous crystal and nematic ordering. In contrast, chains with a harmonic bending stiffness potential crystallized via a two-step nucleation process, first forming a nematic phase that nucleates the crystal. The latter nucleation mechanism was in line with predictions from new theories of nucleation that incorporate the nematic phase as a precursor. Furthermore, we found that it is important to correct for excluded volume differences when comparing chains with soft and hard beads or chains with differing bending stiffnesses.

This work entails efforts to understand effects of solvent choice on paracetamol crystallization. Various techniques have been developed and implemented to study aforementioned. A clear-cut, direct evidence of two-step nucleation mechanism is demonstrated using a bench top Raman spectrometer and a novel method named as OSANO. / Polymorphismus ist die Eigenschaft vieler anorganischer und insbesondere organischer Moleküle, in mehr als einer Struktur zu kristallisieren. Es ist wichtig, die Faktoren zu verstehen, die den Polymorphismus beeinflussen, da er viele physikochemische Eigenschaften wie Stabilität und Löslichkeit beeinflusst. Nahezu 80 % der vermarkteten Medikamente weisen Polymorphismus auf. In dieser Arbeit wurde der Einfluss der Wahl des organischen Lösungsmittels auf den Polymorphismus von Paracetamol untersucht und verschiedene Methoden entwickelt und angewandt, um den Einfluss genauer zu verstehen. Es wurde festgestellt, dass Ethanol viel stärker auf Paracetamol-Kristallisation als Methanol wirkt. Nichtgleichgewichts-Molekulardynamiksimulationen mit periodischer, simulierter Abkühlung (Simulated Annealing) wurden verwendet, um Vorläufer der metastabilen Zwischenprodukte im Kristallisationsprozess zu untersuchen. Es wurde festgestellt, dass die Strukturen der Bausteine der Paracetamol-Kristalle durch geometrische Wechselwirkungen zwischen Lösungsmittel und Paracetamol bestimmt werden. Die statistisch häufigsten Bausteine in der Selbstassemblierung definieren die finale Kristallstruktur. Ein speziell angefertigter akustischer Levitator hat die Proben zuverlässig gehalten, wodurch die Untersuchung des Einflusses von Lösungsmitteln ermöglicht, heterogene Keimbildung abgeschwächt und andere Umgebungsfaktoren stabilisiert wurden. Die Kristallisation wurde in diesem Aufbau mit zeitaufgelöster In-situ-Raman-Spektroskopie verfolgt und mit einer neuen Zielfunktion basierenden Methode der nichtnegativen Matrixfaktorisierung (NMF) analysiert. Orthogonale Zeitrafferfotografie wurde in Verbindung mit NMF verwendet, um eindeutige und genaue Faktoren zu erhalten, die sich auf die Spektren und Konzentrationen verschiedener Anteile der Paracetamol-Kristallisation beziehen, die als latente Komponenten in den unbehandelten Daten vorhanden sind. / Polymorphism is the property exhibited by many inorganic and organic molecules to crystallize in more than one crystal structure. There is a strong need for understanding the influencing factors on polymorphism, as it is responsible for differences in many physicochemical properties such as stability and solubility. Nearly 80 % of marketed drugs exhibit polymorphism. In this work, we took the model system of paracetamol to investigate the influence of solvent choice on its polymorphism. Different methods were developed and employed to understand the influence of small organic solvents on the crystallization of paracetamol. Non-equilibrium molecular dynamics simulations with periodic simulated annealing were used as a tool to probe the nature of precursors of the metastable intermediates occurring in the crystallization process. Using this method, it was found that the structures of the building blocks of crystals of paracetamol is governed by solvent-solute interactions. In situ Raman spectroscopy was used with a custom-made acoustic levitator to follow crystallization. This set-up is a reliable method for investigating solvent influence, attenuating heterogeneous nucleation and stabilizing other environmental factors. It was established that as a solvent, ethanol is much stronger than methanol in its effect of driving paracetamol solutions to their crystal form. The time-resolved Raman spectroscopy crystallization data was processed using a newly developed objective function based non-negative matrix factorization method (NMF). An orthogonal time-lapse photography was used in conjunction with NMF to get unique and accurate factors that pertain to the spectra and concentrations of different moieties of paracetamol crystallization existing as latent components in the untreated data.