Un fondu de polymères est un liquide complexe constitué de chaînes macromoléculaires. Ces chaînes présentent la particularité d'offrir une distribution de temps caractéristiques extrêmement importante. L'ensemble de ces différentes échelles représente donc un défi pour la simulation numérique de polymères longs et sont bien au-delà des capacités des ordinateurs actuels. Un thème actuel de recherche porte donc sur le développement de modèles mésoscopiques (modèle gros grains). La construction d'un tel modèle consiste à éliminer les degrés de liberté rapide en regroupant un certain nombre d'atomes en un monomère. Ce monomère est représenté par une sphère molle évoluant dans un bain thermique créé par les degrés de liberté rapides éliminés au cours du processus de nivellement. La dynamique des particules créées est donc stochastique. La dynamique particulaire dissipative qui intègre ces idées est une combinaison de dynamique moléculaire, de Lattice Gas Automata ainsi que de dynamique Brownienne. Le champ de force DPD est constitué d'une interaction molle et d'un thermostat (force dissipative et bruit) et les paramètres de ce champ de force sont généralement calibrés sur des données expérimentales (compressibilité et diffusion). Cette approche est difficilement applicable aux mélanges de polymères. Pour surmonter cette difficulté, l'intégralité du champ de force DPD est construit à partir d'une dynamique moléculaire pour des corps purs ainsi que pour des mélanges. Nous montrons également que pour calculer correctement la force dissipative, la dynamique moléculaire doit être altérée en contraignant la position des monomères. Les coefficients de transport sont calculés par DPD et comparés à ceux obtenus par dynamique moléculaire. Ce travail s'achève par une étude de la transferabilité du champ de force du monomère vers toute une chaîne de polymères. / A molten polymer is a complex liquid consisting of macromolecular chains. These chains have many different time scales. All these scales present a real challenge to numerical simulations and exceed the computational capabilities of today's computers. A current topic of research therefore focuses on the development of mesoscopic models. The main idea behind coarse-graining is to eliminate fast degrees of freedom grouping atoms or molecules into clusters (or monomers). This monomer is represented by a soft sphere operating in a thermal bath generated by the fast degrees of freedom eliminated during the coarse-graining. Particle dynamics is therfore stochastic. Dissipative particle dyna-mics, which includes these ideas, is a combination of molecular dynamics, Lattice Gas Automata and Brownian dynamics. DPD force field consist of a soft interaction and a thermostat (dissipative and random force) and parameters of DPD interaction are generally optimized to match some macroscopic properties like compressibility or self-diffusion coefficient. This approach is difficult to apply to polymer melt. To overcome this problem, we apply an operational procedure available in the literature to the cons-truction of conservative and dissipative forces of DPD force field for pure substances and mixtures. We also show that in order to calculate the dissipative forces, the underlying molecular dynamics must be altered by constraining the position of the mo-nomers. Transport coefficients are calculated by DPD and compared with those obtained by molecular dynamics. This work concludes with a study of the transferability of the force field of the monomer to a chain of polymers.

La prédiction des microstructures représente un enjeu majeur pour l'étude des processus de vieillissement des alliages métalliques, en particulier sous irradiation. Les résultats des calculs ab initio de structure électronique peuvent être utilisés pour paramétrer les méthodes cinétiques de Monte Carlo Atomique et permettent ainsi de simuler quantitativement la diffusion des atomes et l'évolution de la microstructure qui en résulte. Cette méthode est cependant limitée par le temps de calcul qu'elle exige. Les simulations mésoscopiques évitent cet écueil, mais souffrent généralement de ne pouvoir être paramétrées sur les résultats obtenus aux échelles inférieures, limitant ainsi leur pouvoir de prédiction. Dans ce travail, une méthode de simulation appelée Monte Carlo cellulaire cinétique a été développée pour relier les échelles atomiques et mésoscopiques tout en conservant la nature discrète des atomes. Une procédure de paramétrisation basée sur les simulations Monte Carlo à l'échelle atomique a été établie. Elle permet de reproduire quantitativement les propriétés macroscopiques d'équilibre des alliages indépendamment de la taille des cellules utilisées. Une application à l'alliage fer-cuivre est présentée. Afin de décrire les propriétés cinétiques à ces échelles, un outil générique de calcul de la matrice d'Onsager dans les alliages a été mis en place. Il est fondé sur la theorie du Champ Moyen Auto-Cohérent. Les résultats obtenus sur des cinétiques de diffusion et de précipitation dans un alliage modèle sont présentés et validés par une comparaison systématique avec des simulations Monte Carlo à l'échelle atomique. / Predicting microstructural evolution is a decisive step in the study of aging processes in alloys, especially under irradiation. The results of ab initio calculations of electronic structures can be used to parameterize kinetic methods such as Atomic Kinetic Monte Carlo simulations that allow reproducing quantitatively atomic diffusion and the resulting microstructure. Their use is however limited by their computational cost. Mesoscopic simulations are less concerned by such limitation, but suffer from the lack of reliable parameterization method to use data from simulations at lower scales that leads to a limited prediction capacity. A simulation method called Cellular Kinetic Monte Carlo is developed in this work to bridge the gap scales between atomic and mesoscopic scale simulation of diffusion. A crystal is there modeled as a. This method is based on a description of the crystal as a lattice of cells described by the discrete number of solute atoms they represents. The properties are then obtained by a controlled coarse-graining procedure based on Atomic Kinetic Monte Carlo simulations. It allows reproducing quantitatively macroscopic equilibrium for all cell sizes and has been applied to the Iron-Copper alloy. In order to describe kinetic properties at these scales, a generic computational tool has been developed to compute the Onsager matrix of alloys, based on the Self Consistent Mean field method. Diffusion and precipitation simulations have been done and the results are presented and assessed by a systematic comparison with Atomic Kinetic Monte Carlo simulations.

abstract: Polyurea is a highly versatile material used in coatings and armor systems to protect against extreme conditions such as ballistic impact, cavitation erosion, and blast loading. However, the relationships between microstructurally-dependent deformation mechanisms and the mechanical properties of polyurea are not yet fully understood, especially under extreme conditions. In this work, multi-scale coarse-grained models are developed to probe molecular dynamics across the wide range of time and length scales that these fundamental deformation mechanisms operate. In the first of these models, a high-resolution coarse-grained model of polyurea is developed, where similar to united-atom models, hydrogen atoms are modeled implicitly. This model was trained using a modified iterative Boltzmann inversion method that dramatically reduces the number of iterations required. Coarse-grained simulations using this model demonstrate that multiblock systems evolve to form a more interconnected hard phase, compared to the more interrupted hard phase composed of distinct ribbon-shaped domains found in diblock systems. Next, a reactive coarse-grained model is developed to simulate the influence of the difference in time scales for step-growth polymerization and phase segregation in polyurea. Analysis of the simulated cured polyurea systems reveals that more rapid reaction rates produce a smaller diameter ligaments in the gyroidal hard phase as well as increased covalent bonding connecting the hard domain ligaments as evidenced by a larger fraction of bridging segments and larger mean radius of gyration of the copolymer chains. The effect that these processing-induced structural variations have on the mechanical properties of the polymer was tested by simulating uniaxial compression, which revealed that the higher degree of hard domain connectivity leads to a 20% increase in the flow stress. A hierarchical multiresolution framework is proposed to fully link coarse-grained molecular simulations across a broader range of time scales, in which a family of coarse-grained models are developed. The models are connected using an incremental reverse–mapping scheme allowing for long time scale dynamics simulated at a highly coarsened resolution to be passed all the way to an atomistic representation. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2020

Die vorliegende Arbeit behandelt die Modellierung von Fließprozessen in Grundwasserleitern. Grundlage dafür ist die Grundwassergleichung, welche diese Prozesse mathematisch beschreibt. Die wichtigste hydraulische Eigenschaft von Untergründen ist hierbei die hydraulische Leitfähigkeit, welche die Fließgeschwindigkeit des Grundwassers angibt. Da man die Verteilung der Leitfähigkeit in einem betrachten Wasserleiter aber durch das Fehlen von Informationen nicht vollständig bestimmen kann, ist man auf vereinfachende Modelle und Versuchsszenarien angewiesen. In der Vergangenheit haben sich zur Untersuchung von Böden sogenannte Pumpversuche etabliert, wobei ein Brunnen gebohrt wird, welcher den Grundwasserleiter vollständig durchteuft und an dem mit konstanter Rate Wasser aus dem Boden gepumpt wird. Parallel beobachtet man an einem oder mehreren Referenzbrunnen die sich verändernde hydraulische Druckhöhe. Aus diesen Daten möchte man Informationen über den betrachteten Boden gewinnen. Dazu braucht es gewisse Modellfunktionen, welche für fest definierte Standardsituationen das Grundwasserverhalten beschreiben. Eine Möglichkeit, Böden zu klassifizieren ist es, die heterogene Struktur der Leitfähigkeit durch log-normal verteilte Zufallsgrößen zu modellieren. Dabei beschränkt man sich auf den Mittelwert, die Varianz und die Korrelationslänge dieser Verteilungen. Das hier zugrunde liegende Coarse-Graining-Modell generiert zu diesen Parametern eine effektive Leitfähigkeitsverteilung, welche nur vom radialen Abstand zum Pumpbrunnen abhängt. Damit wird die Grundwassergleichung zu einer radialsymmetrischen parabolischen Differentialgleichung. Zu dieser Differentialgleichung wurde in der vorliegenden Arbeit ein Lösungsalgorithmus entwickelt und implementiert sowie anschließend gegen verschiedene Parametereingaben getestet.

No description available.

The present thesis is on the error estimates of different energy based quasicontinuum (QC) methods, which are a class of computational methods for the coupling of atomistic and continuum models for micro- or nano-scale materials. The thesis consists of two parts. The first part considers the a priori error estimates of three energy based QC methods. The second part deals with the a posteriori error estimates of a specific energy based QC method which was recently developed. In the first part, we develop a unified framework for the a priori error estimates and present a new and simpler proof based on negative-norm estimates, which essentially extends previous results. In the second part, we establish the a posteriori error estimates for the newly developed energy based QC method for an energy norm and for the total energy. The analysis is based on a posteriori residual and stability estimates. Adaptive mesh refinement algorithms based on these error estimators are formulated. In both parts, numerical experiments are presented to illustrate the results of our analysis and indicate the optimal convergence rates. The thesis is accompanied by a thorough introduction to the development of the QC methods and its numerical analysis, as well as an outlook of the future work in the conclusion.

Despite numerous advances in experimental methodologies capable of addressing the various phenomenon occurring on metal surfaces, atomic scale resolution of the microscopic dynamics remains elusive for most systems. Computational models of the processes may serve as an alternative tool to fill this void. To this end, parallel molecular dynamics simulations of self-diffusion on metal surfaces have been developed and employed to address microscopic details of the system. However these simulations are not without their limitations and prove to be computationally impractical for a variety of chemically relevant systems, particularly for diffusive events occurring in the low temperature regime. To circumvent this difficulty, a corresponding coarse-grained representation of the surface is also developed resulting in a reduction of the required computational effort by several orders of magnitude, and this description becomes all the more advantageous with increasing system size and complexity. This representation provides a convenient framework to address fundamental aspects of diffusion in nonequilibrium environments and an interesting mechanism for directing diffusive motion along the surface is explored. In the ensuing discussion, additional topics including transition state theory in noisy systems and the construction of a checking function for protein structure validation are outlined. For decades the former has served as a cornerstone for estimates of chemical reaction rates. However, in complex environments transition state theory most always provides only an upper bound for the true rate. An alternative approach is described that may alleviate some of the difficulties associated with this problem. Finally, one of the grand challenges facing the computational sciences is to develop methods capable of reconstructing protein structure based solely on readily-available sequence information. Herein a checking function is developed that may prove useful for addressing whether a particular proposed structure is a viable possibility.

La prévision de l'évolution des déchets radioactifs lors d'un stockage en couche géologique argileuse profonde nécessite une bonne compréhension du transport de l'eau et des ions dans l'argile. Leur diffusion dans ce milieu poreux et chargé est décrite par des paramètres empiriques, comme le coefficient de distribution (Kd) qui rend compte des interactions avec les surfaces minérales. Notre travail a porté sur la pertinence de ce concept et sa définition à partir de processus microscopiques. <br /><br />Nous avons d'abord modélisé la contribution ionique aux propriétés diélectriques des argiles, et proposé une détermination de Kd par spectroscopie diélectrique. <br /><br />Nous avons ensuite calculé par simulations microscopiques (Monte-Carlo et dynamique moléculaire) les enthalpies libres et enthalpies d'échange ionique pour les ions alcalins, qui contrôlent Kd et ses variations avec la température T. Les résultats pour le césium sont en bon accord avec des mesures de microcalorimétrie et de Kd en fonction de T. <br /><br />Après avoir contribué au développement d'une nouvelle méthode de simulation sur réseau (Lattice Fokker-Planck), nous l'avons utilisée pour établir un lien explicite entre la dynamique microscopique des ions et le modèle de diffusion-réaction qui sous-tend la notion de Kd. <br /><br />Enfin, nous avons étudié par simulation de dynamique moléculaire la cinétique d'échange d'eau et d'ions entre les particules d'argile (porosité interfoliaire) et la porosité extra-particulaire. Les résultats confirment les hypothèses généralement admises selon lesquelles l'eau et les cations peuvent explorer toute la porosité, tandis que les anions sont exclus des espaces interfoliaires.

The Flory ideality hypothesis states that flexible polymer chains in a melt assume the shape of three-dimensional random walks leading to so called Gaussian coils. The basis of this hypothesis is that any local conformational information decays exponentially along the chain backbone and thus has no influence on the long range conformation. Additionally it is argued that the excluded volume shielding of neigbor chains cancels out any swelling effects. Neutron scattering (NS) experiments dating back 30 years confirm the postulated Gaussian coil shape of polymers. This leads to a pillar of polymer theory: Any flexible polymer can be described as a three-dimensional random walk. Advances in simulation technics and computing power have opened the door to the possibility of studing very long chains. This allowed for a closer look at the chain structure of polymer melts and revealed deviations from ideality. This deviation is very slight and thus great care must be taken to distinguish it from noise. So far the deviation from the Gaussian coil structure was only studied for coarse-grained models. The scope of this thesis is to explore if these deviations are also measurable in atomistically realistic simulations and modern day NS experiments.

LTA-type zeolites with narrow window apertures coinciding with the approximate size of small gaseous molecules such as CO2 and N2 are interesting candidates for adsorbents with swing adsorption technologies due to their molecular sieving capabilities and otherwise attractive properties. These sieving capabilities are dependent on the energy barriers of diffusion between the zeolite pores, which can be fine-tuned by altering the framework composition. An ab initio level of theory is necessary to accurately describe specific gas-zeolite interaction and diffusion properties, while it is desirable to predict the macroscopic scale diffusion for industrial applications. Hence, a multiscale modeling approach is necessary to describe the molecular sieving phenomena exhaustively. In this thesis, we use several different modeling methods on different length and time scales to describe the diffusion driven uptake and separation of CO2 and N2 in Zeolite NaKA. A combination of classical force field based modeling methods are used to show the importance of taking into account both thermodynamic, as well as, kinetic effects when modeling gas uptake in narrow pore zeolites where the gas diffusion is to some extent hindered. For a more detailed investigation of the gas molecules’ pore-to-pore dynamics in the material, we present a procedure to compute the free energy barriers of diffusion using spatially constrained ab initio Molecular Dynamics. With this procedure, we seek to identify diffusion rate determining local properties of the Zeolite NaKA pores, including the Na+-to-K+ exchange at different ion sites and the presence of additional CO2 molecules in the pores. This energy barrier information is then used as input for the Kinetic Monte Carlo method, allowing us to simulate and compare these and other effects on the diffusion driven uptake using a realistic powder particle model on macroscopic timescales. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.</p>