A polymer brush is formed by densely grafting the chain ends of polymers onto a surface. This tethering of the long macromolecules has considerable influence on the surface properties, which can be additionally modified by changing the environmental conditions. In this context it is of special interest to understand and control the behavior of the grafted layer and to create surfaces that display a desired response to external stimulation. The present work studies densely grafted polymer brushes and the effects that such an environment imposes on an individual chain molecule in the grafted layer. For this purpose we developed a new self-consistent field approach to describe mixtures of heterogeneous chains comprised of differently sized hard spheres. Applying this method to the case of polymer brushes we consider a fraction of grafted molecules to be different from the majority brush chains. The modification of these chains includes a variation in the degree of polymerization, a different solvent selectivity behavior and a variable size of the free end-monomer. Due to the computational efficiency of the present approach, as compared for example to direct simulation methods, we can study the conformations of the modified 'guest' chains systematically in dependence of the relevant parameters. With respect to brush profile and the distribution of the free chain ends the new method shows very good quantitative agreement with corresponding simulation results. We also confirm the observation that these 'guest' chains can undergo a conformational transition depending on the type of modification and the solvent quality. For the cases studied in the present work we analyze the conditions to achieve a most sensitive behavior of this conformational switching. In addition, an analytical model is proposed to describe this effect. We compare its predictions to the numerical results and find good agreement.

This thesis presents a means of enhancing the iterative calculation techniques used in electronic structure calculations, particularly Kohn-Sham DFT. Based on the subspace iteration method of the FEAST eigenvalue solving algorithm, this nonlinear FEAST algorithm (NLFEAST) improves the convergence rate of traditional iterative methods and dramatically improves their robustness. A description of the algorithm is given, along with the results of numerical experiments that demonstrate its effectiveness and offer insight into the factors that determine how well it performs.

The phase behavior of chiral block copolymers (BCPs*), namely, BCPs with at least one of the constituent block is formed by chiral monomers, is studied both experimentally and theoretically. Specifically, the formation of a unique morphology with helical sense, the H* phase, where the chiral block forms nanohelices hexagonally embedded in the matrix of achiral block, is investigated. Such unique morphology was first observed in the cast film of polystyrene-b-poly(L-lactide) (PS-b-PLLA) from a neutral solvent dichloromethane at room temperature with all the nanohelices being left-handed, which would switch to right-handed if the PLLA block changes to PDLA. Further studies revealed that such morphology only forms when the chiral PLLA block possesses certain volume fraction (from 0.32 to 0.36), and the molecular weight exceeds certain critical value (around 20,000 to 25,000 g/mol). Achiral phases such as lamellae, gyroid, cylinder, and sphere will form if the above criteria are not satisfied. Even though the unique H* phase has been extensively studied and utilized for many applications, many fundamental and important questions remain unanswered for such BCP* system. Specifically, how does the molecular level chirality transfer from the several-angstrom scale of the lactide monomer to the tens-of-nanometer size scale of the H* domain morphology? Why is the chirality transfer not automatic for this BCP* system? Is H* phase a thermodynamic stable or metastable phase? Are there other novel phases other than the H* phase that could form within the BCP* system? We aimed at providing answers to the abovementioned questions regarding the formation of chiral H* phase, which is no longer limited to the PS-b-PLLA/PDLA system. We divided our studies into both experimental and theoretical parts. In the experiments, we studied the effect of solvent casting conditions, including solvent removal rate and polymer-solvent interactions, on the formation of the H* phase in PS-b-PLLA/PDLA BCPs*. In addition, we monitored the morphological evolution during solvent casting using time-resolved x-ray scattering technique. We found that good solubility towards both PS and PLLA/PDLA blocks are required for the formation of the H* phase, and microphase separation has to happen prior to crystallization of chiral block. Most importantly, we found that crystalline ordering is not necessary for the H* phase formation. This result led us to propose melt-state twisted molecular packing as the underlying driving force for such helical phase to form, and began our work on the theory for BCPs*. First we built the theoretical tool by incorporating the orientational segmental interactions into the self-consistent field theory (SCFT) for BCPs. As a demonstration, we constructed the phase diagrams for one-dimensional (1D) and two-dimensional (2D) phases, for achiral BCPs with different orientational stiffness. We found that orientational stiffness could serve as another parameter to introduce asymmetry into BCP systems, in addition to conformational and architectural asymmetry. This model was further applied to study the phase behavior of BCPs*, and two phase diagrams were constructed. Another chiral phase, wavy lamellae (L* phase), was observed for BCPs*. The H* phase was found to be a thermodynamic stable phase, as long as the segregation strength ����and chiral strength ��! exceed certain critical values. Energetically favorable cholesteric texture was observed for the chiral segment packing inside the H* phase, which is believed to drive such unusual morphology to form. A simple geometrical argument based on bending of cylindrical microdomain and twisted packing of the bended microdomain can be given to explain the nonlinear chiral sensitivity of BCP* morphology, which further explains the non-automatic feature of chirality transfer in such system.

<p>The phase behavior of AB diblock copolymers mixed with C homopolymers (AB/C), in which A and C are capable of forming hydrogen-bonds, is examined using self-consistent field theory. The study focuses on the modeling of hydrogen-bonding in polymers. Specifically, we examine two models for the formation of hydrogen-bonds between polymer chains. The first commonly used model assumes a large attractive interaction parameter between the A/C monomers. This model reproduces correct phase transition sequences as compared with experiments, but it fails to correctly describe the change of lamellar spacing induced by the addition of the C homopolymers. The second model is based on the fact that hydrogen-bonding leads to A/C complexation. We show that the interpolymer complexation model predicts correctly the order-order phase transition sequences and the decrease of lamellar spacing for strong hydrogen-bonding. Our analysis demonstrates that hydrogen-bonding of polymers should be modeled by interpolymer complexation.</p> / Master of Science (MSc)

<p>The pi-striped, <em>d</em>-wave superconducting (SC) state, which is a type of pair density wave wherein the SC order is spatially modulated, has recently been shown to generate the key ingredients for quantum oscillations consistent with experimental observations (Zelli <em>et al.</em>, 2011, 2012). This was accomplished with a phenomenological approach using non-self-consistent Bogoliubov-de Gennes (BdG) theory. The objective of this thesis is to explore two aspects of this approach: the addition of a charge density wave (CDW) order to the previous non-self-consistent calculations, and an attempt at stabilizing the pi-striped state in fully self-consistent BdG theory. It was found that the CDW order had a minimal effect on the Fermi surface characteristics of the pi-striped state, but that a sufficiently strong CDW degrades the Landau levels which are essential for the formation of quantum oscillations. The self-consistent mean-field calculations were unable to stabilize the pi-striped state under a range of modifications to the Hamiltonian. Free energy calculations with the modulated SC order treated as a parameter demonstrate that the pi-striped state is always less energetically favourable than the normal state for the scenarios which were considered. The results of this study constitute a basis for future, more comprehensive studies, using the BdG approach, of the stability of possible pi-striped SC phases.</p> / Master of Science (MSc)

Die Ladungsinjektion (-extraktion) an einer Schnittstelle spielt in der organischen Elektronik eine entscheidende Rolle, da sie die Leistung des Bauelements stark beeinflusst. Eine der effizientesten Methoden zur Optimierung der Energiebarrieren für die Injektion ist die Modifikation der Austrittsarbeit der Elektroden. In dieser Dissertation untersuchen wir die Modifikation der Austrittsarbeit von Au(111) durch dithiol-terminiertes Polyethylenglykol (PEG(thiol)) sowie deren Abhängigkeit von der Anzahl der PEG-Wiederholungseinheiten. In beiden Fällen beobachten wir, dass die Austrittsarbeit des Au(111) durch eine Monoschicht PEG(thiol)-Moleküle reduziert wird. Unsere Berechnungen zeigen, dass diese Änderung der Austrittsarbeit hauptsächlich durch (i) die Ladungsumlagerung aufgrund der Chemisorption und (ii) das intrinsische Dipolmoment der PEG(thiol)-Monoschicht verursacht wird. Die Größe des letzteren Beitrags hängt spürbar von der Anzahl der Wiederholungseinheiten ab und bewirkt somit eine Variation in der Reduktion der Austrittsarbeit. Das oszillatorische Verhalten spiegelt einen ausgeprägten Odd-Even-Effekt wider. Dadurch kann die Austrittsarbeit der Metallelektrode unter Berücksichtigung des Odd-Even-Effekts gesteuert werden. Die Konvergenz der selbstkonsistenten Felditeration für unsere Systeme ist nicht garantiert. Um die Konvergenz zu verbessern, schlagen wir die Verwendung eines speziell auf die FP-LAPW-Methode zugeschnittenen Mischalgorithmus vor. In einem auf Ag(111) basierenden System zeigt sich, dass eine Struktur mit drei Leerstellen in der Substratschicht besonders stabil ist. Dabei ist eine kontinuierliche Abnahme der Austrittsarbeit des Ag(111) feststellbar. Ähnlich wie beim Au(111) manifestiert sich der Odd-Even-Effekt, der auf das Dipolmoment der Molekularschicht zurückzuführen ist. / Charge injection (extraction) at an interface plays a crucial role to organic electronics because this injection (extraction) heavily affects the device performance. One of the most efficient way to optimize energy barriers of the injection (extraction) is modifying the work function of electrodes. In this dissertation, we investigate the modification of work function of Au(111) and Ag(111) induced by the dithiol-terminated polyethylene glycol (PEG(thiol)) as well as a dependence of the work function change on different numbers of PEG repeat units. We find that the work function of the Au(111) is reduced by a monolayer of PEG(thiol) molecules. Overall, our calculations indicate that the work function change is mainly induced by (i) the charge rearrangement due to chemisorption and (ii) the intrinsic dipole moment of the PEG(thiol) monolayer. The magnitude of the latter contribution noticeably depends on the number of repeat units and, thus, causes a variation in the reduction of the work function. The oscillatory behavior reflects a pronounced odd-even effect. As a result, the work function of the metal electrode would be controlled by considering the odd-even effect. Unfortunately, the convergence of the self-consistent field iteration is not guaranteed for our investigated systems. To make the smooth convergence, a mixing algorithm, which is applicable to FP-LAPW method, is devised. We add the Kerker preconditioner as well as further improvements to Pulay’s direct inversion in the iterative subspace. Using this method, one can avoid charge sloshing and noise in the exchange-correlation potential. This method is also implemented in the exciting code. We find the decrease of the work function of the Ag(111) surface is always presented. Similar to the Au(111) case, the odd-even effect is revealed, arising from the dipole moment of the molecular layer.

Le béton se présente comme un matériau constitué de granulats, jouant le rôle d'inclusions, enchâssés dans une matrice correspondant à la pâte de ciment hydraté. A l'échelle de la pâte, l'hydratation du ciment génère un milieu multiphasique, constitué d'un squelette solide et de pores remplis ou partiellement remplis d'eau selon leur taille. Le composant principal du squelette solide est le gel de C-S-H, les autres composants étant de nature cristalline. La qualification de gel du composant C-S-H est liée à sa nanostructure dont la schématisation la plus admise consiste en une phase aqueuse adsorbée, en sandwich avec des feuillets solides de nature cristalline. Il est bien admis que la structure du C-S-H est à l'origine de son comportement viscoélastique et donc de celui du béton. Ce comportement viscoélastique peut s'expliquer par un réarrangement de sa nanostructure sous l'effet des contraintes mécaniques appliquées à l'échelle macroscopique. La modélisation macroscopique du fluage du béton ne permet pas d'expliquer la variabilité du fluage d'une formulation de béton à une autre. En effet, les paramètres des modèles macroscopiques ne peuvent être identifiés que par l'analyse de résultats expérimentaux obtenus par des essais réalisés sur des éprouvettes de béton. Ces paramètres ne sont valables que pour une formulation donnée. L'identification de ces paramètres conduit donc à des programmes expérimentaux très coûteux et ne fournit pas suffisamment d'informations sur la sensibilité des paramètres macroscopiques à la variabilité des caractéristiques mécaniques et morphologies des constituants. Dans ce travail, on suppose qu'il existe une échelle microscopique à laquelle les mécanismes moteurs du fluage ne sont pas impactés par la formulation du béton. A cette échelle, celle du C-S-H, les propriétés viscoélastiques peuvent être considérées avoir un caractère intrinsèque. L'influence de la formulation ne concerne alors que les concentrations des différents hydrates. Trois approches, analytiques, semi-analytiques et numériques sont alors proposées pour estimer, par une homogénéisation multi-échelle, les propriétés viscoélastiques macroscopiques du béton à partir des propriétés de ses constituants ainsi qu'à partir de sa microstructure. Ces approches sont basées sur l'extension des schémas d'homogénéisation élastique au cas viscoélastique au moyen du principe de correspondance qui utilise la transformée de Laplace-Carson. Les propriétés effectives sont alors déterminées directement dans l'espace de Carson. Par la suite, celles dans l'espace temporel sont obtenues par la transformée inverse. Les approches proposées apportent des solutions aussi bien dans un cadre général que sous certaines hypothèses restrictives : coefficient de Poisson viscoélastique microscopique ou macroscopique constant, module de compressibilité constant. Sur le plan théorique, deux schémas d'homogénéisation ont été étudiés : le schéma de Mori-Tanaka, basé sur le problème de l'inclusion d'Eshelby, et le schéma auto-cohérente généralisé basé sur la neutralité énergique de l'inclusion. Les résultats obtenus montrent que sous ces hypothèses restrictives, le spectre macroscopique se présente comme une famille de sous ensembles de temps caractéristiques bornés par les temps caractéristiques microscopiques. Par ailleurs, les propriétés thermodynamiques, de croissance monotone et de concavité, des fonctions de retard macroscopiques ne sont préservées par l'homogénéisation que sous certaines conditions de compatibilité des spectres microscopiques. Sur le plan pratique, les méthodes développées ont été appliquées pour construire la complaisance de fluage propre macroscopique du béton en connaissant les données communes de toutes sortes de bétons et celles correspondant à une formulation donnée. Les résultats expérimentaux disponibles sont alors exploités pour analyser le caractère intrinsèque des propriétés viscoélastiques à l'origine du fluage du béton / Concrete can be considered as a multiscale heterogeneous material in which elastic inclusions, i.e., aggregates, are embedded in a viscoelastic matrix which corresponds to the hardened cement paste. At the cement paste scale, the hydration process leads to a partially saturated porous multiphase medium whose solid skeleton is mainly constituted of the C-S-H gel, the other hydrates being crystalline solids. The gel-like properties of the C-S-H are essentially related to the existence of strongly adsorbed structural water in the interlayer nanospace. It is well admitted that this feature is the microscopic origin of the creep mechanism of C-S-H and therefore of concrete at the macroscale. This viscoelastic behavior can be explained by a rearrangement of the nanostructure of the C-S-H component due to a macroscopically applied loading. Therefore, the macroscopic modeling of concrete creep does not allow explaining the variability of creep with respect to the concrete mix. Indeed, the identi?cation of the viscoelastic parameters of macroscopic models requires performing creep tests at the concrete scale. Thus, the validity of the identi?ed parameters is limited to the concrete mix under consideration and the identi?cation process does not permit to carry out the influence of the microstructure and the mechanical constituent properties on the macroscopic creep. In this work, we assume that there exists a microscopic scale at which the driving creep mechanisms are not affected by the concrete mix. At this scale, the C-S-H one, the viscoelastic properties can be considered to be intrinsic. The concrete mix will essentially influence the volume fraction of the hydrates. Analytical, semi-analytical and numerical approaches are developed in order to derive, by multi-scale homogenization, the macroscopic viscoelastic properties of concrete on the basis of the knowledge of the microscopic properties, of the constituents together with the knowledge of the mix-dependent microstructure. These approaches consist in extending results of elastic homogenization schemes to viscoelasticity with the help of the correspondence principle using the Laplace-Carson transform. Therefore, the effective properties are obtained in a straightforward manner in the Carson transform space, which requires the transform inversion in order to determine the time evolution of these properties. The proposed models permit to answer to this requirement, both under some restrictive assumptions (constant Poisson's ratio at either microscopic or macroscopic scale, constant bulk microscopic modulus) and in a general way. At the theoretical level, two homogenization schemes are investigated : the Mori-Tanaka scheme based on the Eshelby solution and the Generalized Self Consistent scheme, based on the energetic neutrality condition of the inclusion. The obtained results show that under the aforementioned restrictive conditions, the macroscopic creep spectrum presents as a family of sets of retardation times which are bounded by two successive microscopic characteristic times. Furthermore, the monotonically increasing and concavity features of the macroscopic creep compliance, which derive from thermodynamic considerations, are not always preserved, except if some compatibility conditions are ful?lled by the microscopic spectrums. From the practical point of view, these methods developed are used to establish the complaisance creep function of concrete from the knowledge of the common data of all types of concrete, as well as the other parameters that characterize a given formulation. Hence, by a back-analysis of creep tests obtained on cement paste or on concrete, the intrinsic basic creep properties of the gel C-S-H are estimated

Une bonne compréhension des interactions entre les ondes à la fréquence cyclotronique ionique (FCI) (40-80MHz) et le plasma de bord est nécessaire pour injecter de fortes puissances dans un plasma de fusion en continu. Les objectifs de cette thèse étaient de modéliser séparément, avec Comsol Multiphysics, mais de façon compatible le couplage d'ondes et la formation de gaines radiofréquences (RF), qui rétroagissent sur le couplage, pour aboutir à terme à une modélisation auto-cohérente. Modéliser le couplage de l'onde rapide nécessite une description détaillée de l'antenne émettrice (2D ou 3D) et du plasma environnant par une approche pleine onde en plasma froid. L'absorption des ondes sortant du domaine de simulation est émulée par des couches parfaitement adaptées, rendues compatibles avec un tenseur diélectrique plasma. Les tendances expérimentales des résistances de couplage des antennes de Tore Supra sont qualitativement reproduites mais l'efficacité de couplage est surestimée. Parallèlement une description novatrice auto-cohérente, incluant les effets des gaines RF, de la propagation de l'onde lente et de la polarisation DC (Direct Current) du bord d'un plasma magnétisé a été développée avec le minimum d'ingrédients physiques. Dans le cas des antennes Tore Supra, le couplage du code avec TOPICA a permis d'expliciter qualitativement certaines observations inattendues sur un écran de Faraday dont le schéma électrique visait à minimiser les gaines RF. Un transport de courants DC dans la SOL est apparu nécessaire pour expliquer les structures radiales des mesures. Les barreaux coupés sont les éléments de l'antenne responsable de l'augmentation du potentiel plasma / A correct understanding of the interactions between the edge plasma and the ion cyclotron (IC) waves (40-80MHz) is needed to inject reliably large amount of power required for self-sustainable fusion plasmas. These thesis objectives were to model separately, with Comsol Multiphysics, but in compatible approaches the wave coupling and the radio-frequency (RF) sheath formation to anticipate development of a single code combining both. Modelling of fast wave coupling requires a detailed description of the antenna (2D or 3D) and of the plasma environment by a full wave approach for a cold plasma. Absorption of outgoing waves is emulated by perfectly matched layers, rendered compatible with a plasma dielectric tensor. Experimental trends for the coupling resistance of the antennas of Tore Supra are qualitatively reproduced but the coupling efficiency is overestimated. In parallel a novel self-consistent description, including RF sheaths, of the interplay between the cold wave propagation and DC biasing of the magnetized edge plasma of a tokamak was developed with the minimum set of physics ingredients. For Tore Supra antenna cases, the code coupled with TOPICA allowed to unveil qualitatively some unexpected observations on the latest design of Tore Supra Faraday screens whose electrical design was supposed to minimize RF sheaths. From simulations, a DC (Direct Current) current transport appears necessary to explain the radial structures of measurements. Cantilevered bars have been identified as the design element in the antenna structure enhancing the plasma potential

Dans la modélisation de la matière dense, et partiellement ionisée, une question importante concerne le traitement des électrons libres. Vis-à-vis des électrons liés, la nature délocalisée et non discrète de ces électrons est responsable d’une différence de traitement, qui est souvent effectuée dans les modélisations des propriétés radiatives des plasmas. Cependant, afin d’éviter les incohérences dans le calcul des spectres d’absorption, tous les électrons devraient, en principe, être décrits dans un même formalisme.Nous utilisons deux modèles variationnels d’atome-moyen : un modèle semi-classique, et un modèle quantique, qui permettent cette égalité de traitement pour tous les électrons. Nous calculons la section-efficace de photo-extinction, en appliquant le cadre de la théorie de la réponse linéaire dynamique à chacun de ces modèles d’atome dans un plasma. Pour cette étude, nous développons et utilisons une approche auto-cohérente, de type random-phase-approximation (RPA), qui, en allant au-delà de la réponse des électrons indépendants, permet d’évaluer les effets collectifs, par l’introduction de la polarisation dynamique. Cette approche s’inscrit dans le formalisme de la théorie de la fonctionnelle de la densité dépendant du temps (TDDFT), appliquée au cas d’un système atomique immergé dans un plasma.Pour les deux modèles, semi-classique et quantique, nous dérivons, et vérifions dans nos calculs, une nouvelle règle de somme, qui permet d’évaluer le dipôle atomique à partir d’un volume fini dans le plasma. Cette règle de somme s’avère être un outil de premier ordre pour le calcul des propriétés radiatives des atomes dans les plasmas denses. / In modeling dense and partially ionized matter, the treatment of the free electrons remains an important issue. Compared to bound electrons, the delocalized and non-discrete nature of these electrons is responsible to treat them differently, which is usually adopted in the modelings of radiative properties of plasmas. However, in order to avoid inconsistencies in the calculation of absorption spectra, all the electrons should be described in the same formalism.We use two variational average-atom models: a semi-classical and a quantum model, which allow this common treatment for all the electrons. We calculate the photo-extinction cross-section, by applying the framework of the linear dynamical response theory to each of these models of an atom in a plasma. For this study, we develop and use a self-consistent approach, of random-phase-approximation (RPA) type, which, while going beyond the independent electron response, permits to evaluate the collective effects by the introduction of the dynamical polarization. This approach uses the formalism of the time dependent density functional theory (TDDFT), applied in the case of an atomic system immersed in a plasma.For both models, semi-classical and quantum, we derive and verify in our calculations, a new sum rule, which allows the evaluation of the atomic dipole from a finite volume in the plasma. This sum rule turns out to be a crucial device in the calculation of radiative properties of atoms in dense plasmas.

Le formalisme des fonctions de Green hors-équilibre (NEGF pour « Non-equilibrium Green’s function) a suscité au cours des dernières décennies un engouement fort pour étudier les propriétés du transport quantique des nanostructures et des nano-dispositifs dans lesquels les interactions inélastiques, comme la diffusion des électrons-phonons, jouent un rôle significatif. L'incorporation d'interactions inélastiques dans le cadre du NEGF s’effectue généralement dans l'approximation auto-cohérente de Born (SCBA pour « Self-consistent Born approximation) qui représente une approche itérative plus exigeante en ressources numériques. Nous proposons dans ce travail de thèse une méthode efficace alternative dite LOA pour (« Lowest Order Approximation. Son principal avantage est de réduire considérablement le temps de calcul et de décrire physiquement la diffusion électron-phonon. Cette approche devrait considérablement étendre l'accessibilité de l'utilisation de codes atomistiques de transport quantique pour étudier des systèmes 3D réalistes sans faire à des ressources numériques importantes. / Non-equilibrium Green’s function (NEGF) formalism during recent decades has attracted numerous interests for studying quantum transport properties of nanostructures and nano-devices in which inelastic interactions like electron-phonon scattering have a significant impact. Incorporation of inelastic interactions in NEGF framework is usually performed within the self-consistent Born approximation (SCBA) which induces a numerically demanding iterative scheme. As an alternative technique, we propose an efficient method, the so-called Lowest Order Approximation (LOA) coupled with the Pade approximants. Its main advantage is to significantly reduce the computational time, and to describe the electron-phonon scattering physically. This approach should then considerably extend the accessibility of using atomistic quantum transport codes to study three-dimensional (3D) realistic systems without requiring numerous numerical resources.