Zugl.: Erlangen, Nürnberg, University, Diss., 2008.

The ability to accurately represent polymer melts at various levels of coarse graining is of great interest because of the wide range of time and length scales over which relevant process take place. Schemes for developing effective interaction potentials for coarse-grained representations that incorporate microscopic level system information are generally numerical and thus suffer from issues of transferability because they are state dependent and must be recalculated for different system and thermodynamic parameters. Numerically derived potentials are also known to suffer from representability problems, in that they may preserve structural correlations in the coarse-grained representation but many often fail to preserve thermodynamic averages of the coarse-grained representation. In this dissertation, analytical forms of the structural correlations and effective pair potentials for a family of highly coarse-grained representations of polymer melts are derived. It is shown that these effective potentials, when used in mesoscale simulations of the coarse-grained representation, generate consistent equilibrium structure and thermodynamic averages with low level representations and therefore with physical systems. Furthermore, analysis of the effective pair potential forms shows that a small long range tail feature that scales beyond the physical range of the polymer as the fourth root of the number of monomers making up the coarse-grained unit dominates thermodynamic averages at high levels of coarse graining. Because structural correlations are extremely insensitive to this feature, it can be shown that effective interaction potentials derived from optimization of structural correlations would require unrealistically high precision measurements of structural correlations to obtain thermodynamically consistent potentials, explaining the problems of numerical coarse-graining schemes. This dissertation includes previously published and unpublished co-authored material.

Coarse-graining and multi-scale approaches are rapidly becoming important tools for computer simulations of large complex molecular systems. Such theoretical models are powerful tools because they allow one to probe the essential features of a complex, many-bodied system on length and time scales over which emergent phenomena may occur. Because of the computational advantages and fundamental insight made available through coarse-grained methods, a vast array of various phenomenological potentials to describe coarse-grained interactions have been developed; nonetheless, the ability of these potentials to provide quantitative information about several different properties of the same system is not evident. On a theoretical level, it is not well-understood how small correlations in the long-range structure propagate through the coarse-graining procedure into the effective potential and lead to incorrect thermodynamics. Taking an alternative approach, this dissertation will discuss an analytical coarse-graining method for synthetic polymer chains of specific chemical structure, where a group of atoms on a polymer chain are represented by a variable number of soft interacting effective sites. The approach is based in liquid-state theory, providing a theoretical framework to address questions of thermodynamic consistency. It will be shown that the proposed method of coarse-graining maintains thermodynamic consistency for a variety of polymer models. In a multi-scale modeling scheme simulations of the same system represented by several different levels of detail may be joined to provide a complete description of the system at all length and time scales of interest. This dissertation includes previously published and unpublished co-authored material.

Dans le noyau des cellules eucaryotes, l’ADN s’enroule autour d’histones pour former des nucléosomes, lesquels s’arrangent à leur tour en une fibre compacte et dynamique appelée chromatine. Les propriétés physiques de cette fibre aux différentes échelles, depuis la double-hélice de l’ADN jusqu’aux chromosomes micrométriques, sont essentielles aux mécanismes complexes de l’expression des gènes et sa régulation. La présente thèse est une contribution audéveloppement de modèles physiques capables de relier les différentes échelles, et d’interpréter et d’intégrer des données provenant d’une large gamme d’approches expérimentales et numériques. En premier lieu, nous utilisons des simulations de dynamique moléculaire d’oligomères d’ADN pour étudier l’ADN double-hélical à différentes températures. Nous estimons la contribution séquence-dépendante de l’entropie à l’élasticité de l’ADN, en lien avec des expériencesrécentes sur la longueur de persistence de l’ADN. En second lieu, nous modélisons les interactions ADN-histones au sein du Nucleosome Core Particle. Nous utilisons la nanomécanique de l’ADN afin d’extraire un champ de force d’un ensemble de structures cristallographiques du nucléosome et de données de dynamique moléculaire. En troisième lieu, nous étudions la partie plus molle du nucléosome, l’ADN linker entre les core particles, qui s’associe transitoirement à l’histone H1 pour former un “stem”. Nous combinons des informations structurales existantes avec des données expérimentales à deux résolutions différentes (DNA footprinting et électro-microscopie) afin de développer un modèle de stem à l’échelle nanométrique. / In the nucleus of eukaryotic cells, DNA wraps around histone proteins to form nucleosomes, which in turn associate in a compact and dynamic fiber called chromatin. The physical properties of this fiber at different lengthscales, from the DNA double-helix to micrometer-sized chromosomes, are essential to the complex mechanisms of gene expression and its regulation. The present thesis is a contribution to the development of physical models, which are able to link different scales and to interpret and integrate data from a wide range of experimental and computational approaches. In the first part, we use Molecular Dynamics simulations of DNA oligomers to study doublehelical DNA at different temperatures. We estimate the sequence-dependent contribution of entropy to DNA elasticity, in relation with recent experiments on DNA persistence length. In the second part, we model the DNA-histone interactions within the nucleosome core particle,using DNA nanomechanics to extract a force field from a set of crystallographic nucleosome structures and Molecular Dynamics snapshots. In the third part, we consider the softer part of the nucleosome, the linker DNA between coreparticles which transiently associates with the histone H1 to form a “stem”.We combine existing structural knowledge with experimental data at two different resolutions (DNA footprints and electro-micrographs) to develop a nanoscale model of the stem.

La simulation des matériaux demande une compréhension de leur comportement à de nombreuses échelles de temps et d’espace. Ces différentes échelles requièrent des méthodes de simulations différentes, qui se basent sur des approximations différentes et donnent accès à différentes propriétés. La simulation multiéchelle est une approche qui regroupe l’utilisation de ces différentes méthodes, ainsi que des relations qui les unissent. Des développements plus récents ont permis la mise au point de méthodes mésoscopiques, comblant le trou entre les simulations atomistiques (< 10 nm) et les milieux continus (>mm). La dynamique de particules dissipatives (DPD) est une telle méthode, qui présente de nombreux avantages théoriques et pratiques en comparaison avec d’autres méthodes mésoscopiques. La DPD est une méthode modélisant la matière par des particules molles, s’inspirant de l’équation de Langevin. La dynamique des particules est gérée par trois forces : une force conservative, une force dissipative et une force aléatoire. La force conservative naît des interactions effectives moyennes à l’échelle méso, alors que la force dissipative et la force aléatoire sont d’origine statistique. Différentes formulations et contributions à la force conservative sont présentées, permettant notamment la simulation de polymères enchevêtrés et de systèmes chargés. Les contraintes auxquelles les forces statistiques sont soumises, ainsi que leurs impacts sur les dynamiques, sont ensuite discutés. La présentation de la DPD se termine par des considérations sur les effets numériques particuliers à la DPD. La puissance de la DPD est démontrée par la simulation de polymères arborescents. Les polymères arborescents sont des macromolécules hyperbranchées obtenues par une séquence de réactions de greffage de chaînes polymères. La structure qu’adoptent ces molécules n’est pas connue avec certitude. Des expériences ont permis aux chercheurs de proposer un modèle en loi de puissance pour le profil de densité radiale. Or, cette propriété n’est accessible qu’indirectement aux méthodes expérimentales, alors qu’elle peut être obtenue directement des travaux de simulation. La masse énorme de ces composés, ainsi que leur topologie complexe, impossible à réduire à un modèle plus simple, empêche toute simulation par des méthodes microscopiques traditionnelles. L’utilisation de méthodes mésoscopiques s’impose donc. Les polymères arborescents de génération 2 (d’une masse de l’ordre de 3,2×103 kDa) en solution (5 %) peuvent être simulés explicitement grâce à la DPD, et ce, en un temps acceptable. Les propriétés du solvant peuvent être ajustées, notamment leur qualité et leur masse moléculaire. Le profil de densité radiale moyen simulé correspond plutôt bien au modèle en loi de puissance proposé. L’analyse des données expérimentale suppose une symétrie sphérique des molécules individuelles qui s’avère être erronée. L’anisotropie des macromolécules est étudiée et s’avère être hautement variable. Des fonctions de distribution radiale ainsi que les patrons de diffusion de neutrons associés ont été obtenus. Ces derniers pourront être comparés directement aux résultats expérimentaux lorsque ces derniers seront disponibles. L’utilisation de la DPD est riche en possibilités. Elle est facilement étendue à diverses classes de matériaux. Par sa nature dynamique et ses propriétés, la DPD donne accès à certaines classes de phénomènes inaccessibles aux autres méthodes de simulation mésoscopique. Notamment, la DPD permet naturellement la simulation dans l’état stationnaire, tel que démontré par la simulation de la structure du Nafion c sous cisaillement. De plus, le comportement hydrodynamique devrait permettre la simulation à l’échelle mésoscopique de la transition vitreuse ou à tout le moins, d’une transition lui ressemblant. De plus, la DPD peut être étendue afin d’effectuer la simulation dans d’autres ensembles thermodynamiques, qui donnent accès à d’autres propriétés d’intérêt pour les matériaux (conductivité thermique, propriétés mécaniques). Les versions actuelles de la DPD, bien que versatiles, ne permettent pas encore de reproduire quantitativement les propriétés des matériaux. Différents succès, obstacles et pistes de réflexion sont présentés. Le perfectionnement de la DPD fournit à la fois un prétexte et un banc d’essai de choix pour tenter de comprendre les questions fondamentales suscitées par le coarse-graining et l’échelle méso en elle-même.

Zugl.: Freiburg (Breisgau), Univ., Diss., 2009

A theoretical formalism to reconstruct structural and dynamical properties of polymer liquids from their coarse-grained description is developed. This formalism relies on established earlier analytical coarse-graining of polymers derived from the first principles of liquid theory. The polymer chain is represented at a mesoscale level as a soft particle. Coarse-grained computer simulations provide input data to the reconstruction formalism and allow one to achieve the most gain in computational efficiency. The structure of polymer systems is reconstructed by combining global information from mesoscale simulations and local information from small united-atom simulations. The obtained monomer total correlation function is tested for a number of systems including polyethylene melts of different degrees of polymerization as well as melts with different local chemical structure. The agreement with full united-atom simulations is quantitative, and the procedure remains advantageous in computational time. The dynamics in mesoscale simulations is artificially accelerated due to the coarse-graining procedure and needs to be rescaled. The proposed formalism addresses two rescalings of the dynamics. First, the internal degrees of freedom averaged out during coarse-graining procedure are reintroduced in "a posteriori" manner, rescaling the simulation time. The second rescaling takes into account the change in friction when switching from a monomer level description to mesoscopic. Both friction coefficients for monomer and soft particle are calculated analytically and their ratio provides the rescaling factor for the diffusion coefficient. The formalism is extensively tested against the united-atom molecular dynamic simulations and experimental data. The reconstructed diffusive dynamics of the center-of-mass for polyethylene and polybutadiene melts of increasing degrees of polymerization show a quantitative agreement, supporting the foundation of the approach. Finally, from the center-of-mass diffusion the monomer friction coefficient is obtained and used as an input into Cooperative Dynamics theory. The dynamics of polymer chains at any length scale of interest is described through a Langevin equation. In summary, the proposed formalism reconstructs the structure and dynamics of polymer melts enhancing computational efficiency of molecular dynamic simulations. This dissertation includes previously published and unpublished co-authored material.

Isoporous membranes manufactured from diblock copolymer are successfully produced at laboratory scale under controlled conditions. Because of the complex phenomena involved, membrane preparation requires trial and error methodologies to find the optimal conditions, leading to a considerable demand of resources. Experimental insights demonstrate that the self-assembly of the block copolymers in solution has an effect on the final membrane structure. Nevertheless, the complete understanding of these multi-scale phenomena is elusive. Herein we use the coarse-grained method Dissipative Particle Dynamics to study the self-assembly of block copolymers that are used for the preparation of the membranes. To simulate representative time and length scales, we introduce a framework for model reduction of polymer chain representations for dissipative particle dynamics, which preserves the properties governing the phase equilibria. We reduce the number of degrees of freedom by accounting for the correlation between beads in fine-grained models via power laws and the consistent scaling of the simulation parameters. The coarse-graining models are consistent with the experimental evidence, showing a morphological transition of the aggregates as the polymer concentration and solvent affinity change. We show that hexagonal packing of the micelles can occur in solution within different windows of polymer concentration depending on the solvent affinity. However, the shape and size dispersion of the micelles determine the characteristic arrangement. We describe the order of crew-cut micelles using a rigid-sphere approximation and propose different phase parameters that characterize the emergence of monodisperse-spherical micelles in solution. Additionally, we investigate the effect of blending asymmetric diblock copolymers (AB/AC) over the properties of the membranes. We observe that the co-assembly mechanism localizes the AC molecules at the interface of A and B domains, and induces the swelling of the B-rich domains. The B-C interactions control the curvature of the assemblies in these blends. Finally, we study the self-assembly triblock copolymers used for membranes fabrication. We show that the polymer concentration, the block-copolymer composition, and the swelling of the micelle are responsible for the formation of elongated micelles in the casting solution. The formation of nanoporous membranes arises from the network-like packing of those micelles.

This thesis consists of two papers considering different aspects of stochastic process modelling and the minimisation of computational cost. In the first paper, we analyse statistical signal properties and develop a Gaussian pro- cess model for scenarios with a moving receiver in a scattering environment, as in Clarke’s model, with the generalisation that noise is introduced through scatterers randomly flip- ping on and off as a function of time. The Gaussian process model is developed by extracting mean and covariance properties from the Multipath Fading Channel model (MFC) through coarse graining. That is, we verify that under certain assumptions, signal realisations of the MFC model converge to a Gaussian process and thereafter compute the Gaussian process’ covariance matrix, which is needed to construct Gaussian process signal realisations. The obtained Gaussian process model is under certain assumptions less computationally costly, containing more channel information and having very similar signal properties to its corresponding MFC model. We also study the problem of fitting our model’s flip rate and scatterer density to measured signal data. The second paper generalises a multilevel Forward Euler Monte Carlo method intro- duced by Giles [1] for the approximation of expected values depending on the solution to an Ito stochastic differential equation. Giles work [1] proposed and analysed a Forward Euler Multilevel Monte Carlo method based on realsiations on a hierarchy of uniform time discretisations and a coarse graining based control variates idea to reduce the computa- tional effort required by a standard single level Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretisations generated by adaptive algorithms developed by Moon et al. [3, 2]. These adaptive algorithms apply either deterministic time steps or stochastic time steps and are based on a posteriori error expansions first developed by Szepessy et al. [4]. Under sufficient regularity conditions, our numerical results, which include one case with singular drift and one with stopped dif- fusion, exhibit savings in the computational cost to achieve an accuracy of O(T ol), from O(T ol−3 ) to O (log (T ol) /T ol)2 . We also include an analysis of a simplified version of the adaptive algorithm for which we prove similar accuracy and computational cost results.

Coarse-grained (CG) molecular dynamics (MD) simulations have seen a wide range of applications from biomolecules, polymers to graphene and metals. In CG MD simulations, atomistic groups are represented by beads, which reduces the degrees of freedom in the systems and allows larger timesteps. Thus, large time and length scales could be achieved in CG MD simulations with inexpensive computational cost. The representative example of large time- and length-scale phenomena is the conformation transitions of single polymer chains as well as polymer chains in their architectures, self-assembly of biomaterials, etc. Polymers exist in many aspects of our life, for example, plastic packages, automobile parts, and even medical devices. However, the large chemical and structural diversity of polymers poses a challenge to the existing CG MD models due to their limited accuracy and transferabilities. In this regard, this dissertation has developed CG models of polymers on the basis of accurate and transferable hydrocarbon models, which are important components of the polymer backbone. CG hydrocarbon models were created with 2:1 and 3:1 mapping schemes and their force-field (FF) parameters were optimized by using particle swarm optimization (PSO). The newly developed CG hydrocarbon models could reproduce their experimental properties including density, enthalpy of vaporization, surface tension and self-diffusion coefficients very well. The cross interaction parameters between CG hydrocarbon and water models were also optimized by the PSO to repeat the experimental properties of Gibbs free energies and interfacial tensions. With the hydrocarbon models as the backbone, poly(acrylic acid) (PAA) and polystyrene (PS) models were constructed. Their side chains were represented by one COOH (carboxylic acid) and three BZ beads, respectively. Before testing the PAA and PS models, their monomer models, propionic acid and ethylbenzene, were created and validated, to confirm that the cross interactions between hydrocarbon and COOH beads, and between hydrocarbon and BZ beads could be accurately predicted by the Lorentz-Berthelot (LB) combining rules. Then the experimental properties, density of polymers at 300 K and glass transition temperatures, and the conformations of their all-atom models in solvent mixtures of water and dimethylformamide (DMF) were reproduced by the CG models. The CG PAA and PS models were further used to build the bottlebrush copolymers of PAA-PS and to predict the structures of PAA-PA in different compositions of binary solvents water/DMF. Although CG models are useful in understanding the phenomena at large time- or length- scales, atomistic information is lost. Backmapping is usually involved in reconstructing atomistic models from their CG models. Here, four machine learning (ML) algorithms, artificial neural networks (ANN), k-nearest neighbor (kNN), gaussian process regression (GPR), and random forest (RF) were developed to improve the accuracy of the backmapped all-atom structures. These optimized four ML models showed R2 scores of more than 0.99 when testing the backmapping against four representative molecules: furan, benzene, naphthalene, graphene. / Doctor of Philosophy / Polymers have a wide range of applications from packaging, foams, coating to pipes, tanks and even medical devices and biosensors. To improve the properties of these materials it is important to understand their structure and features responsible for controlling their properties at the molecular-level. Molecular dynamic (MD) simulations are a powerful tool to study their structures and properties at microscopic level. However, studying the molecular-level conformations of polymers and their architectures usually requires large time- or length-scales, which is challenging for the all-atom MD simulations because of the high computational cost. Coarse-grained (CG) MD simulations can be used to study these soft-materials as they represent atomistic groups with beads, enabling the reduction of the system sizes drastically, and allowing the use of large timesteps in MD simulations. In MD simulations, force-fields (FF) that describe the intramolecular and intermolecular interactions determine the performance of simulations. Here, we firstly optimized the FF parameters for hydrocarbons. With the optimized CG hydrocarbon models, two representative CG polymer models, poly(acrylic acid) (PAA) and polystyrene (PS) were built by using hydrocarbons as the backbones of polymers. Furthermore, the PAA and PS chains were grafted on a linear hydrocarbon backbone to form a bottlebrush copolymer. Although CG MD models are useful in studying the complex process of polymers, the atomic detailed information is lost. To reconstruct accurate atomistic structures, backmapping by using machine learning (ML) algorithms was performed. The performance of the ML models was better than that of the existing backmapping packages built in Visual Molecular Dynamics (VMD).