O fenômeno da nucleação é um processo intrinsecamente irreversível. A Teoria Entrópica da Nucleação (TEN) aborda-o analisando um processo reversível equivalente no qual há liberação de calor latente (variação da entalpia), concomitante a um rearranjo estrutural descrito pela variação da entropia antes e depois de certa quantidade de material ter nucleado. Para visualizar a dinâmica e facilitar a análise foi escolhido um processo isobárico. O diagrama de Mollier modificado para evidenciar a região metaestável ajudou a desenvolver uma expressão para o cálculo do tamanho do núcleo crítico, mediante a teoria da flutuação de Landau. Para analisar o sistema na região metaestável, obteve-se a função entropia, S(H,P0), em que aspectos físicos e geométricos (como o princípio de estabilidade termodinâmica) foram determinantes. Cálculos do núcleo crítico em relação à temperatura mostraram concordância qualitativa com o trabalho de Dillmann-Meier. Porém, entende-se que a função do núcleo crítico está incompleta. Para lidar com aglomerados e núcleos em uma abordagem termodinâmica, um ensemble a pressão constante é o mais apropriado, cuja variável conjugada é o volume. Com base em uma teoria das flutuações isotérmicas em um fluido ideal (Koper-Reiss), desenvolveu-se a teoria das flutuações não-isotérmicas (Mokross), aplicável a um fluido não-ideal metaestável mantido a pressão e temperatura constantes. Os parâmetros termodinâmicos do elemento de volume que flutua mudam e diferem daqueles do banho, e evolvem acordando com a equação de estado S=S(H,P). / The phenomenon of nucleation is an intrinsically irreversible process. The nucleation is explored by the Entropic Nucleation Theory (ENT), in which, the irreversible process is replaced by an equivalent one, although now, the process is reversible in which there is a change in the enthalpy, and also an structural rearrangement coded in the change of de entropy. To study the dynamics and perform the analysis an isobaric process was chosen. The metastable region was used to develop an expression for the calculation of size of the critical nucleus, having in mind the Landau´s fluctuation theory. This region was obtained with the help of the modified Mollier diagram. The physical and geometric features of the system were crucial to obtain the entropy function, S(H,P0), used to analyze the metastable region. Calculations of the critical nucleus, with respect to the temperature, were in qualitative agreement with Dillmann-Meier work. Although, the function for the critical nucleus is incomplete. To handle with clusters and nucleus in a thermodynamic framework, a constant pressure assemble is preferable having the volume as the conjugated variable. With the help of the isothermal fluctuation theory, in an ideal fluid (Koper-Reiss), the non-isothermal fluctuation theory (Mokross) was developed, and used to study a non-ideal metastable fluid kept at constant pressure and temperature. The thermodynamics parameters of the fluctuating volume element change, differing from those of the bath, and the state equation, S=S(H,P) gives its evolution.

O fenômeno da nucleação é um processo intrinsecamente irreversível. A Teoria Entrópica da Nucleação (TEN) aborda-o analisando um processo reversível equivalente no qual há liberação de calor latente (variação da entalpia), concomitante a um rearranjo estrutural descrito pela variação da entropia antes e depois de certa quantidade de material ter nucleado. Para visualizar a dinâmica e facilitar a análise foi escolhido um processo isobárico. O diagrama de Mollier modificado para evidenciar a região metaestável ajudou a desenvolver uma expressão para o cálculo do tamanho do núcleo crítico, mediante a teoria da flutuação de Landau. Para analisar o sistema na região metaestável, obteve-se a função entropia, S(H,P0), em que aspectos físicos e geométricos (como o princípio de estabilidade termodinâmica) foram determinantes. Cálculos do núcleo crítico em relação à temperatura mostraram concordância qualitativa com o trabalho de Dillmann-Meier. Porém, entende-se que a função do núcleo crítico está incompleta. Para lidar com aglomerados e núcleos em uma abordagem termodinâmica, um ensemble a pressão constante é o mais apropriado, cuja variável conjugada é o volume. Com base em uma teoria das flutuações isotérmicas em um fluido ideal (Koper-Reiss), desenvolveu-se a teoria das flutuações não-isotérmicas (Mokross), aplicável a um fluido não-ideal metaestável mantido a pressão e temperatura constantes. Os parâmetros termodinâmicos do elemento de volume que flutua mudam e diferem daqueles do banho, e evolvem acordando com a equação de estado S=S(H,P). / The phenomenon of nucleation is an intrinsically irreversible process. The nucleation is explored by the Entropic Nucleation Theory (ENT), in which, the irreversible process is replaced by an equivalent one, although now, the process is reversible in which there is a change in the enthalpy, and also an structural rearrangement coded in the change of de entropy. To study the dynamics and perform the analysis an isobaric process was chosen. The metastable region was used to develop an expression for the calculation of size of the critical nucleus, having in mind the Landau´s fluctuation theory. This region was obtained with the help of the modified Mollier diagram. The physical and geometric features of the system were crucial to obtain the entropy function, S(H,P0), used to analyze the metastable region. Calculations of the critical nucleus, with respect to the temperature, were in qualitative agreement with Dillmann-Meier work. Although, the function for the critical nucleus is incomplete. To handle with clusters and nucleus in a thermodynamic framework, a constant pressure assemble is preferable having the volume as the conjugated variable. With the help of the isothermal fluctuation theory, in an ideal fluid (Koper-Reiss), the non-isothermal fluctuation theory (Mokross) was developed, and used to study a non-ideal metastable fluid kept at constant pressure and temperature. The thermodynamics parameters of the fluctuating volume element change, differing from those of the bath, and the state equation, S=S(H,P) gives its evolution.

No description available.

This dissertation is a collection of works that investigate non-prototypical sources leading to new particle formation in the atmosphere. Particles play a major role in atmospheric chemistry. For example, particles are a component of smog and are commonly found in high concentrations under conditions of atmospheric inversions. In order to reconcile the difference between measured and modeled particle concentrations new mechanisms from non-prototypical sources for particle formation need to be determined. Formation of particles has frequently been modeled using classical nucleation theory (CNT). The first step in CNT is the nucleation step where molecular clusters form. In a second step, these clusters grow into particles through coagulation or condensation. First, this research aims to improve the modeling of equilibrium constants for the formation of peroxy radical-water complexes. Failure of the harmonic approximation in the partition function for describing the low frequency vibrational modes of the complexes was explored. Instead the dissociative hydrogen bond mode using a Lennard-Jones 6-3 potential and the other low frequency vibrational modes using one- and two-fold hindered rotors was modeled. It was determined that the contribution of the two-fold hindered rotors is more important than the long-range dipole-dipole potentials and of vibration-rotation coupling. In related work, the hydroperoxy radical was investigated as a non-prototypical source of particles using high level ab initio calculations. The results indicate that the addition of an amine to the dimer increased the overall stability of complex through the increased number and strength of the hydrogen bonds. When compared to prototypical systems, sulfuric acid and methane sulfonic acid, the strength of the complex was found to be similar to the peroxy radical system. Finally, carboxylic acids, formic acid and acetic acid, were investigated as a source for new particle formation using computational and experimental techniques. Using a slow flow reactor cell particle formation was enhanced by the addition of trimethylamine. High level ab initio calculations indicate like the peroxy radicals, carboxylic acids may act as a molecular cluster in particle formation

The knowledge of solid-state second phase heterogeneous nucleation process is limited due to the experimental difficulty, such as tiny length scale, short time period, and high temperature condition. In recent years, some significant breakthroughs in nucleation studies have been achieved by aid of computational techniques. In this study, we apply molecular dynamics (MD) simulations to perform with heterogeneous nucleation occurring at grain boundaries (GB) during the austenite (FCC) phase to ferrite (BCC) phase transformation in a pure Fe polycrystalline system. A neighbor vector analysis (NVA) method has been introduced and it is shown how the NVA can be used to determine the misorientation of grain or interphase boundaries, which allow a further investigation of the boundary structure correlated to interfacial energy and mobility during the nucleation and early grain growth stage. Meanwhile, benefited from the MD technique, the bulk energy, grain boundary energy, and interfacial energy can be individually captured during the simulations, which allow a detail analyze of the shape, critical size and nucleation energy of specific nuclei, through the classical nucleation theory (CNT) and according to a faceted-spherical cap geometric model (FSC). In addition, we also compared the results from the classical approach with a new algorithm that combination of the multi-phase field model (MPFM) and the nudged elastic band (NEB) method to demonstrate the CNT in the solid-state conduction. Finally, we extend our simulation method to a more complex triple GB junction nucleation event, and investigate the non-classical barrier-free nucleation behaviors. The results support the critical informations to clarify the initial state of austenite to ferrite transition, and improve our knowledge of the heterogeneous nucleation process, which help to bridge the gap between the experimental measurements and the theoretical calculations. The simulation method also provided a new approach for studying the complicate heterogeneous nucleation phenomenon in solid-state for a wide variety of polycrystalline material systems. / Thesis / Doctor of Philosophy (PhD)

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.

Additive manufacturing (AM), also known as 3D-printing, has made it possible to produce components made of bulk metallic glass (BMG) which have remarkable properties compared to parts made of conventional alloys. A metallic glass is a metastable noncrystalline alloy that form if a melt is quenched with a sufficient cooling rate. Research on systems with low critical cooling rates have made the maximum dimensions of these alloys to grow to what is called BMG's. The high local cooling rate obtained during AM makes it in principle possible to bypass the dimension restrictions that otherwise have been present when creating these alloys but the procedure is complex. It is believed that oxygen impurities in the powder feedstock material used during AM of Zr-based alloys makes it favourable for nucleation of stable crystalline phases at lower activation energies which hinders fully glass features to develop. The purpose of this thesis is to investigate how the limiting solute concentration in the bulk of the AM produced alloy AMZ4 (Zr59.3Cu28.8Al10.4Nb1.5(at\%)) impact the nucleation. Using a numerical model based on classical nucleation theory (CNT) that couples the interfacial and long range fluxes makes it possible to study how impurities impact the nucleation event. However, missing oxygen dependent data makes this a study on how limiting solute impact the nucleation in AMZ4. The numerical model is validated against earlier work and the results obtained from the simulations on AMZ4 shows a strong connection between the nucleation event and the limiting solute concentration. Further investigations on phase separation energies and the production of concentration dependent time-temperature-transformation (TTT) diagrams are needed to fully describe the connection to oxygen concentration. Nevertheless, the implemented model captures important features that the classical model cannot describe which needs to be taken into account when describing the nucleation in AMZ4. / Friformsframställning (eng. additive manufacturing (AM)), också känt som 3D-printing, har gjort det möjligt att producera komponenter gjorda av bulkmetallglas (eng. bulk metallic glass (BMG)) vilka har anmärkningsvärda egenskaper jämfört med delar gjord av konventionella legeringar. Ett metalliskt glas är en metastabil icke kristallin legering som skapas om en smälta släcks med en tillräcklig kylhastighet. Forsking på system med låga kritiska kylhastigheter har gjort att de maximala dimensionerna av dessa legeringar har ökat till vad som kallas BMG's. Den höga lokala kylhastigheten som erhålls under AM gör att  dimensionsrestriktionerna principiellt kan kringgås vilka annars är närvarande vid skapandet dessa legeringar men proceduren är komplex. Det är trott att orenheter av syre i pulver-råvarumaterialet som används vid AM av Zr-baserade legeringar gör det fördelaktigt för kärnbildning av stabila kristallina faser vid lägre aktiveringsenergier vilket hindrar fulla glas egenskaper från att utvecklas. Syftet med denna uppsats är att undersöka hur den begränsande lösningen påverkar kärnbildningsförloppet i den AM producerade legeringen AMZ4 (Zr59.3Cu28.8Al10.4Nb1.5(at\%)). En numerisk modell baserad  på klassisk kärnbildningsteori (eng. classical nucleation theory (CNT)) som kopplar gränsskikt- och långdistans-flödet gör det möjligt att studera hur orenheter påverkar kärnbildningsförloppet. Syreberoende data gör dock detta till en studie om hur den begränsande lösningen påverkar kärnbildningen i AMZ4. Den numeriska modellen valideras mot tidigare arbeten och resultaten från simuleringarna av AMZ4 visar ett starkt samband mellan kärnbildningsförloppet och den begränsade lösningskoncentrationen. Vidare studier rörande fas-separeringsenergier och framställningen av koncentrationsberoende tid-temperature-transformation (eng. time-temperature-transformation (TTT)) diagram behövs för att till fullo beskriva kopplingen till syrekoncentrationen. Den implementerade modellen fångar dock viktiga egenskaper som den klassiska modellen inte kan beskriva vilka måste tas hänsyn till när kärnbildning i AMZ4 ska beskrivas.

The crystallization and melting behaviors of an ethylene/1-hexene copolymer and series of narrow molecular weight linear polyethylene and poly(ethylene oxide) fractions were studied using a combination of ultra-fast and conventional differential scanning calorimetry, optical microscopy, small angle X-ray scattering, and wide angle X-ray diffraction. In the case of linear polyethylene and poly(ethylene oxide), the zero-entropy production melting temperatures of initial lamellae of isothermally crystallized fractions were analyzed in the context of the non-linear Hoffman-Weeks method. Using the Huggins equation, limiting equilibrium melting temperatures of 141.4 ± 0.8oC and 81.4 ± 1.0oC were estimated for linear polyethylene and poly(ethylene oxide), respectively. The former and the latter are about 4oC lower and 12.5oC higher than these predicted by Flory/Vrij and Buckley/Kovacs, respectively. Accuracy of the non-linear Hoffman-Weeks method was also examined using initial lamellar thickness literature data for a linear polyethylene fraction at different crystallization temperatures. The equilibrium melting temperature obtained by the Gibbs-Thomson approach and the C2 value extracted from the initial lamellar thickness vs. reciprocal of undercooling plot were similar within the limits of experimental error to those obtained here through the non-linear Hoffman-Weeks method. In the next step, the Lauritzen-Hoffman (LH) secondary nucleation theory was modified to account for the effect of stem length fluctuations, tilt angle of the crystallized stems, and temperature dependence of the lateral surface free energy. Analysis of spherulite growth rate and wide angle X-ray diffraction data for 26 linear polyethylene and 5 poly(ethylene oxide) fractions revealed that the undercooling at the regime I/II transition, the equilibrium fold surface free energy, the strength of the stem length fluctuations and the substrate length at the regime I/II transition are independent of chain length. The value of the equilibrium fold surface free energy derived from crystal growth rate data using the modified Lauritzen-Hoffman theory matches that calculated from lamellar thickness and melting data through the Gibbs-Thomson equation for both linear polyethylene and poly(ethylene oxide). Larger spherulitic growth rates for linear polyethylene than for poly(ethylene oxide) at low undercooling is explained by the higher secondary nucleation constant of poly(ethylene oxide). While the apparent friction coefficient of a crystallizing linear polyethylene chain is 2 to 8 times higher than that of a chain undergoing reptation in the melt state, the apparent friction coefficient of a crystallizing poly(ethylene oxide) chain is about two orders of magnitude lower. This observation suggests that segmental mobility on the crystal phase plays a significant role in the crystal growth process. In case of the statistical ethylene/1-hexene copolymer, the fold surface free energies of the copolymer lamellae at the time of crystallization and melting increase with increasing undercooling, approaching the same magnitude at high undercooling. As a result of this temperature dependence, the experimental melting vs. crystallization temperature plot is parallel to the Tm = Tc line and the corresponding Gibbs-Thomson plot is non-linear. This behavior is attributed to the fact that longer ethylene sequences form a chain-folded structure with lower concentration of branch points on the lamellar surface at lower undercooling, while shorter ethylene sequences form lamellar structures at higher undercooling exhibiting a higher concentration of branch points on the lamellar surface. Branch points limit the ability of lamellar structures to relax their kinetic stem-length fluctuations during heating prior to melting. / Ph. D. / Morphology of semi-crystalline polymers is strongly affected by their crystallization conditions. Thermodynamic and kinetic models allow us to understand the crystallization mechanism of a semi-crystalline polymer and relate its crystallization conditions to the final morphology. In this research, we studied the molar mass dependence of the crystallization and melting behaviors of narrow molecular weight distribution linear polyethylene (LPE) and poly(ethylene oxide) (PEO) fractions using a modified Lauritzen-Hoffman (LH) secondary nucleation theory. We have shown that the equilibrium melting temperature of LPE and PEO fractions found from the non-linear Hoffman-Weeks method are within the experimental uncertainty identical with these measured directly for extended chain crystals or derived from a Gibbs-Thomson analysis. The value of the equilibrium fold surface free energy derived from crystal growth rate data using the modified LH theory matches that calculated from lamellar thickness and melting data through the Gibbs-Thomson equation for both LPE and PEO. We reported that the higher segmental mobility of PEO in the crystalline phase leads to significantly lower apparent chain friction coefficients during crystal growth compared to LPE. We also studied the role of short-chain branching in the crystal growth kinetics of ethylene/1-hexene copolymers. We observed that the fold surface free energies during crystallization and during melting are both function of the undercooling while the ratio of the former to the latter decreases with increasing undercooling. We proposed that this behavior may be related to the concentration of short-chain branches at the surface of the lamellae, where higher concentration leads to lower relaxation.

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.