Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the "lab-on-a-chip" paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results.

Crystal phases and glassy dynamics in monodisperse hard ellipsoids

We have performed Monte Carlo and molecular dynamics simulations of suspensions of monodisperse, hard ellipsoids of revolution. Hard-particle models play a key role in statistical mechanics. They are conceptually and computationally simple, and they offer insight into systems in which particle shape is important, including atomic, molecular, colloidal, and granular systems. In the high density phase diagram of prolate hard ellipsoids we have found a new crystal, which is more stable than the stretched FCC structure proposed previously . The new phase, SM2, has a simple monoclinic unit cell containing a basis of two ellipsoids with unequal orientations. The angle of inclination is very soft for length-to-width (aspect) ratio l/w=3, while the other angles are not. A symmetric state of the unit cell exists, related to the densest-known packings of ellipsoids; it is not always the stable one. Our results remove the stretched FCC structure for aspect ratio l/w=3 from the phase diagram of hard, uni-axial ellipsoids. We provide evidence that this holds between aspect ratios 3 and 6, and possibly beyond. Finally, ellipsoids in SM2 at l/w=1.55 exhibit end-over-end flipping, warranting studies of the cross-over to where this dynamics is not possible. Secondly, we studied the dynamics of nearly spherical ellipsoids. In equilibrium, they show a first-order transition from an isotropic phase to a rotator phase, where positions are crystalline but orientations are free. When over-compressing the isotropic phase into the rotator regime, we observed super-Arrhenius slowing down of diffusion and relaxation, and signatures of the cage effect. These features of glassy dynamics are sufficiently strong that asymptotic scaling laws of the Mode-Coupling Theory of the glass transition (MCT) could be tested, and were found to apply. We found strong coupling of positional and orientational degrees of freedom, leading to a common value for the MCT glass-transition volume fraction. Flipping modes were not slowed down significantly. We demonstrated that the results are independent of simulation method, as predicted by MCT. Further, we determined that even intra-cage motion is cooperative. We confirmed the presence of dynamical heterogeneities associated with the cage effect. The transit between cages was seen to occur on short time scales, compared to the time spent in cages; but the transit was shown not to involve displacements distinguishable in character from intra-cage motion. The presence of glassy dynamics was predicted by molecular MCT (MMCT). However, as MMCT disregards crystallization, a test by simulation was required. Glassy dynamics is unusual in monodisperse systems. Crystallization typically intervenes unless polydispersity, network-forming bonds or other asymmetries are introduced. We argue that particle anisometry acts as a sufficient source of disorder to prevent crystallization. This sheds new light on the question of which ingredients are required for glass formation.

Single polymers at surfaces: adsorption and detachment

This thesis is concerned with the adsorption and detachment of polymers at planar, rigid surfaces. We have carried out a systematic investigation of adsorption of polymers using analytical techniques as well as Monte Carlo simulations with a coarse grained off-lattice bead spring model. The investigation was carried out in three stages. In the first stage the adsorption of a single multiblock AB copolymer on a solid surface was investigated by means of simulations and scaling analysis. It was shown that the problem could be mapped onto an effective homopolymer problem. Our main result was the phase diagram of regular multiblock copolymers which shows an increase in the critical adsorption potential of the substrate with decreasing size of blocks. We also considered the adsorption of random copolymers which was found to be well described within the annealed disorder approximation. In the next phase, we studied the adsorption kinetics of a single polymer on a flat, structureless surface in the regime of strong physisorption. The idea of a ’stem-flower’ polymer conformation and the mechanism of ’zipping’ during the adsorption process were used to derive a Fokker-Planck equation with reflecting boundary conditions for the time dependent probability distribution function (PDF) of the number of adsorbed monomers. The numerical solution of the time-dependent PDF obtained from a discrete set of coupled differential equations were shown to be in perfect agreement with Monte Carlo simulation results. Finally we studied force induced desorption of a polymer chain adsorbed on an attractive surface. We approached the problem within the framework of two different statistical ensembles; (i) by keeping the pulling force fixed while measuring the position of the polymer chain end, and (ii) by measuring the force necessary to keep the chain end at fixed distance above the adsorbing plane. In the first case we treated the problem within the framework of the Grand Canonical Ensemble approach and derived analytic expressions for the various conformational building blocks, characterizing the structure of an adsorbed linear polymer chain, subject to pulling force of fixed strength. The main result was the phase diagram of a polymer chain under pulling. We demonstrated a novel first order phase transformation which is dichotomic i.e. phase coexistence is not possible. In the second case, we carried out our study in the “fixed height” statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain end is kept fixed at height h over the solid plane at different adsorption strength ε. The phase diagram in the h − ε plane was calculated both analytically and by Monte Carlo simulations. We demonstrated that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than the force, f, is used as an independent control parameter.

Exploring physical processes related to past climate proxies: lake sediments and stable water isotopes

Proxy data are essential for the investigation of climate variability on time scales larger than the historical meteorological observation period. The potential value of a proxy depends on our ability to understand and quantify the physical processes that relate the corresponding climate parameter and the signal in the proxy archive. These processes can be explored under present-day conditions. In this thesis, both statistical and physical models are applied for their analysis, focusing on two specific types of proxies, lake sediment data and stable water isotopes.rnIn the first part of this work, the basis is established for statistically calibrating new proxies from lake sediments in western Germany. A comprehensive meteorological and hydrological data set is compiled and statistically analyzed. In this way, meteorological times series are identified that can be applied for the calibration of various climate proxies. A particular focus is laid on the investigation of extreme weather events, which have rarely been the objective of paleoclimate reconstructions so far. Subsequently, a concrete example of a proxy calibration is presented. Maxima in the quartz grain concentration from a lake sediment core are compared to recent windstorms. The latter are identified from the meteorological data with the help of a newly developed windstorm index, combining local measurements and reanalysis data. The statistical significance of the correlation between extreme windstorms and signals in the sediment is verified with the help of a Monte Carlo method. This correlation is fundamental for employing lake sediment data as a new proxy to reconstruct windstorm records of the geological past.rnThe second part of this thesis deals with the analysis and simulation of stable water isotopes in atmospheric vapor on daily time scales. In this way, a better understanding of the physical processes determining these isotope ratios can be obtained, which is an important prerequisite for the interpretation of isotope data from ice cores and the reconstruction of past temperature. In particular, the focus here is on the deuterium excess and its relation to the environmental conditions during evaporation of water from the ocean. As a basis for the diagnostic analysis and for evaluating the simulations, isotope measurements from Rehovot (Israel) are used, provided by the Weizmann Institute of Science. First, a Lagrangian moisture source diagnostic is employed in order to establish quantitative linkages between the measurements and the evaporation conditions of the vapor (and thus to calibrate the isotope signal). A strong negative correlation between relative humidity in the source regions and measured deuterium excess is found. On the contrary, sea surface temperature in the evaporation regions does not correlate well with deuterium excess. Although requiring confirmation by isotope data from different regions and longer time scales, this weak correlation might be of major importance for the reconstruction of moisture source temperatures from ice core data. Second, the Lagrangian source diagnostic is combined with a Craig-Gordon fractionation parameterization for the identified evaporation events in order to simulate the isotope ratios at Rehovot. In this way, the Craig-Gordon model can be directly evaluated with atmospheric isotope data, and better constraints for uncertain model parameters can be obtained. A comparison of the simulated deuterium excess with the measurements reveals that a much better agreement can be achieved using a wind speed independent formulation of the non-equilibrium fractionation factor instead of the classical parameterization introduced by Merlivat and Jouzel, which is widely applied in isotope GCMs. Finally, the first steps of the implementation of water isotope physics in the limited-area COSMO model are described, and an approach is outlined that allows to compare simulated isotope ratios to measurements in an event-based manner by using a water tagging technique. The good agreement between model results from several case studies and measurements at Rehovot demonstrates the applicability of the approach. Because the model can be run with high, potentially cloud-resolving spatial resolution, and because it contains sophisticated parameterizations of many atmospheric processes, a complete implementation of isotope physics will allow detailed, process-oriented studies of the complex variability of stable isotopes in atmospheric waters in future research.rn

Realisierung der IceCube MonteCarlo-Produktion im WLCG und Untersuchung von Auswirkungen meteorologischer Parameter auf die Erzeugung atmosphärischer Myonen

Das am Südpol gelegene Neutrinoteleskop IceCube detektiert hochenergetische Neutrinos über die schwache Wechselwirkung geladener und neutraler Ströme. Die Analyse basiert auf einem Vergleich mit Monte-Carlo-Simulationen, deren Produktion global koordiniert wird. In Mainz ist es erstmalig gelungen, Simulationen innerhalb der Architektur des Worldwide LHC Computing Grid (WLCG) zu realisieren, was die Möglichkeit eröffnet, Monte-Carlo-Berechnungen auch auf andere deutsche Rechnerfarmen (CEs) mit IceCube-Berechtigung zu verteilen. Atmosphärische Myonen werden mit einer Rate von über 1000 Ereignissen pro Sekunde aufgezeichnet. Eine korrekte Interpretation dieses dominanten Signals, welches um einen Faktor von 10^6 reduziert werden muss um das eigentliche Neutrinosignal zu extrahieren, ist deswegen von großer Bedeutung. Eigene Simulationen mit der Software-Umgebung CORSIKA wurden durchgeführt um die von Energie und Einfallswinkel abhängige Entstehungshöhe atmosphärischer Myonen zu bestimmen. IceCube Myonraten wurden mit Wetterdaten des European Centre for Medium-Range Weather Forcasts (ECMWF) verglichen und Korrelationen zwischen jahreszeitlichen sowie kurzzeitigen Schwankungen der Atmosphärentemperatur und Myonraten konnten nachgewiesen werden. Zudem wurde eine Suche nach periodischen Effekten in der Atmosphäre, verursacht durch z.B. meteorologische Schwerewellen, mit Hilfe einer Fourieranalyse anhand der IceCube-Daten durchgeführt. Bislang konnte kein signifikanter Nachweis zur Existenz von Schwerewellen am Südpol erbracht werden.

Numerische und analytische Untersuchungen stark korrelierter fermionischer Mehrbandsysteme

In dieser Arbeit werden vier unterschiedliche, stark korrelierte, fermionische Mehrbandsysteme untersucht. Es handelt sich dabei um ein Mehrstörstellen-Anderson-Modell, zwei Hubbard-Modelle sowie ein Mehrbandsystem, wie es sich aus einer ab initio-Beschreibung für ein korreliertes Halbmetall ergibt.rnrnDie Betrachtung des Mehrstörstellen-Anderson-Modells konzentriert sich auf die Untersuchung des Einflusses der Austauschwechselwirkung und der nicht-lokalen Korrelationen zwischen zwei Störstellen in einem einfach-kubischen Gitter. Das zentrale Resultat ist die Abstandsabhängigkeit der Korrelationen der Störstellenelektronen, welche stark von der Gitterdimension und der relativen Position der Störstellen abhängen. Bemerkenswert ist hier die lange Reichweite der Korrelationen in der Diagonalrichtung des Gitters. Außerdem ergibt sich, dass eine antiferromagnetische Austauschwechselwirkung ein Singulett zwischen den Störstellenelektronen gegenüber den Kondo-Singuletts der einzelnen Störstellen favorisiert und so den Kondo-Effekt der einzelnen Störstellen behindert.rnrnEin Zweiband-Hubbard-Modell, das Jz-Modell, wird im Hinblick auf seine Mott-Phasen in Abhängigkeit von Dotierung und Kristallfeldaufspaltung auf dem Bethe-Gitter untersucht. Die Entartung der Bänder ist durch eine unterschiedliche Bandbreite aufgehoben. Wichtigstes Ergebnis sind die Phasendiagramme in Bezug auf Wechselwirkung, Gesamtfüllung und Kristallfeldparameter. Im Vergleich zu Einbandmodellen kommen im Jz-Modell sogenannte orbital-selektive Mott-Phasen hinzu, die, abhängig von Wechselwirkung, Gesamtfüllung und Kristallfeldparameter, einerseits metallischen und andererseits isolierenden Charakter haben. Ein neuer Aspekt ergibt sich durch den Kristallfeldparameter, der die ionischen Einteilchenniveaus relativ zueinander verschiebt, und für bestimmte Werte eine orbital-selektive Mott-Phase des breiten Bands ermöglicht. Im Vergleich mit analytischen Näherungslösungen und Einbandmodellen lassen sich generische Vielteilchen- und Korrelationseffekte von typischen Mehrband- und Einteilcheneffekten differenzieren.rnrnDas zweite untersuchte Hubbard-Modell beschreibt eine magneto-optische Falle mit einer endlichen Anzahl Gitterplätze, in welcher fermionische Atome platziert sind. Es wird eine z-antiferromagnetische Phase unter Berücksichtigung nicht-lokaler Vielteilchenkorrelationen erhalten, und dabei werden bekannte Ergebnisse einer effektiven Einteilchenbeschreibung verbessert.rnrnDas korrelierte Halbmetall wird im Rahmen einer Mehrbandrechnung im Hinblick auf Korrelationseffekte untersucht. Ausgangspunkt ist eine ab initio-Beschreibung durch die Dichtefunktionaltheorie (DFT), welche dann durch die Hinzunahme lokaler Korrelationen ergänzt wird. Die Vielteilcheneffekte werden an Hand einer einfachen Wechselwirkungsnäherung verdeutlicht, und für ein Wechselwirkungsmodell in sphärischer Symmetrie präzisiert. Es ergibt sich nur eine schwache Quasiteilchenrenormierung. Besonders für röntgenspektroskopische Experimente wird eine gute Übereinstimmung erzielt.rnrnDie numerischen Ergebnisse für das Jz-Modell basieren auf Quanten-Monte-Carlo-Simulationen im Rahmen der dynamischen Molekularfeldtheorie (DMFT). Für alle anderen Systeme wird ein Mehrband-Algorithmus entwickelt und implementiert, welcher explizit nicht-diagonale Mehrbandprozesse berücksichtigt.rnrn

Quantum dot-dye hybrid systems for energy transfer applications

In this thesis, we focus on the preparation of energy transfer-based quantum dot (QD)-dye hybrid systems. Two kinds of QD-dye hybrid systems have been successfully synthesized: QD-silica-dye and QD-dye hybrid systems.rn rnIn the QD-silica-dye hybrid system, multishell CdSe/CdS/ZnS QDs were adsorbed onto monodisperse Stöber silica particles with an outer silica shell of thickness 2 - 24 nm containing organic dye molecules (Texas Red). The thickness of this dye layer has a strong effect on the total sensitized acceptor emission, which is explained by the increase in the number of dye molecules homogeneously distributed within the silica shell, in combination with an enhanced surface adsorption of QDs with increasing dye amount. Our conclusions were underlined by comparison of the experimental results with Monte-Carlo simulations, and by control experiments confirming attractive interactions between QDs and Texas Red freely dissolved in solution. rnrnNew QD-dye hybrid system consisting of multishell QDs and organic perylene dyes have been synthesized. We developed a versatile approach to assemble extraordinarily stable QD-dye hybrids, which uses dicarboxylate anchors to bind rylene dyes to QD. This system yields a good basis to study the energy transfer between QD and dye because of its simple and compact design: there is no third kind of molecule linking QD and dye; no spacer; and the affinity of the functional group to the QD surface is strong. The FRET signal was measured for these complexes as a function of both dye to QD ratio and center-to-center distance between QD and dye by controlling number of covered ZnS layers. Data showed that fluorescence resonance energy transfer (FRET) was the dominant mechanism of the energy transfer in our QD-dye hybrid system. FRET efficiency can be controlled by not only adjusting the number of dyes on the QD surface or the QD to dye distance, but also properly choosing different dye and QD components. Due to the strong stability, our QD-dye complexes can also be easily transferred into water. Our approach can apply to not only dye molecules but also other organic molecules. As an example, the QDs have been complexed with calixarene molecules and the QD-calixarene complexes also have potential for QD-based energy transfer study. rn

Morphology and charge transport in conjugated polymers

To assist rational compound design of organic semiconductors, two problems need to be addressed. First, the material morphology has to be known at an atomistic level. Second, with the morphology at hand, an appropriate charge transport model needs to be developed in order to link charge carrier mobility to structure.rnrnThe former can be addressed by generating atomistic morphologies using molecular dynamics simulations. However, the accessible range of time- and length-scales is limited. To overcome these limitations, systematic coarse-graining methods can be used. In the first part of the thesis, the Versatile Object-oriented Toolkit for Coarse-graining Applications is introduced, which provides a platform for the implementation of coarse-graining methods. Tools to perform Boltzmann inversion, iterative Boltzmann inversion, inverse Monte Carlo, and force-matching are available and have been tested on a set of model systems (water, methanol, propane and a single hexane chain). Advantages and problems of each specific method are discussed.rnrnIn partially disordered systems, the second issue is closely connected to constructing appropriate diabatic states between which charge transfer occurs. In the second part of the thesis, the description initially used for small conjugated molecules is extended to conjugated polymers. Here, charge transport is modeled by introducing conjugated segments on which charge carriers are localized. Inter-chain transport is then treated within a high temperature non-adiabatic Marcus theory while an adiabatic rate expression is used for intra-chain transport. The charge dynamics is simulated using the kinetic Monte Carlo method.rnrnThe entire framework is finally employed to establish a relation between the morphology and the charge mobility of the neutral and doped states of polypyrrole, a conjugated polymer. It is shown that for short oligomers, charge carrier mobility is insensitive to the orientational molecular ordering and is determined by the threshold transfer integral which connects percolating clusters of molecules that form interconnected networks. The value of this transfer integral can be related to the radial distribution function. Hence, charge mobility is mainly determined by the local molecular packing and is independent of the global morphology, at least in such a non-crystalline state of a polymer.

A soft-tetramer model for diblock copolymer melts: structure formation and geometric characterization

The ability of block copolymers to spontaneously self-assemble into a variety of ordered nano-structures not only makes them a scientifically interesting system for the investigation of order-disorder phase transitions, but also offers a wide range of nano-technological applications. The architecture of a diblock is the most simple among the block copolymer systems, hence it is often used as a model system in both experiment and theory. We introduce a new soft-tetramer model for efficient computer simulations of diblock copolymer melts. The instantaneous non-spherical shape of polymer chains in molten state is incorporated by modeling each of the two blocks as two soft spheres. The interactions between the spheres are modeled in a way that the diblock melt tends to microphase separate with decreasing temperature. Using Monte Carlo simulations, we determine the equilibrium structures at variable values of the two relevant control parameters, the diblock composition and the incompatibility of unlike components. The simplicity of the model allows us to scan the control parameter space in a completeness that has not been reached in previous molecular simulations.The resulting phase diagram shows clear similarities with the phase diagram found in experiments. Moreover, we show that structural details of block copolymer chains can be reproduced by our simple model.We develop a novel method for the identification of the observed diblock copolymer mesophases that formalizes the usual approach of direct visual observation,using the characteristic geometry of the structures. A cluster analysis algorithm is used to determine clusters of each component of the diblock, and the number and shape of the clusters can be used to determine the mesophase.We also employ methods from integral geometry for the identification of mesophases and compare their usefulness to the cluster analysis approach.To probe the properties of our model in confinement, we perform molecular dynamics simulations of atomistic polyethylene melts confined between graphite surfaces. The results from these simulations are used as an input for an iterative coarse-graining procedure that yields a surface interaction potential for the soft-tetramer model. Using the interaction potential derived in that way, we perform an initial study on the behavior of the soft-tetramer model in confinement. Comparing with experimental studies, we find that our model can reflect basic features of confined diblock copolymer melts.

Between the scales: Water from different perspectives

In der vorliegenden Arbeit werden verschiedene Wassermodelle in sogenannten Multiskalen-Computersimulationen mit zwei Auflösungen untersucht, in atomistischer Auflösung und in einer vergröberten Auflösung, die als "coarse-grained" bezeichnet wird. In der atomistischen Auflösung wird ein Wassermolekül, entsprechend seiner chemischen Struktur, durch drei Atome beschrieben, im Gegensatz dazu wird ein Molekül in der coarse-grained Auflösung durch eine Kugel dargestellt.rnrnDie coarse-grained Modelle, die in dieser Arbeit vorgestellt werden, werden mit verschiedenen coarse-graining Methoden entwickelt. Hierbei kommen hauptsächlich die "iterative Boltzmann Inversion" und die "iterative Monte Carlo Inversion" zum Einsatz. Beides sind struktur-basierte Ansätze, die darauf abzielen bestimmte strukturelle Eigenschaften, wie etwa die Paarverteilungsfunktionen, des zugrundeliegenden atomistischen Systems zu reproduzieren. Zur automatisierten Anwendung dieser Methoden wurde das Softwarepaket "Versatile Object-oriented Toolkit for Coarse-Graining Applications" (VOTCA) entwickelt.rnrnEs wird untersucht, in welchem Maße coarse-grained Modelle mehrere Eigenschaftenrndes zugrundeliegenden atomistischen Modells gleichzeitig reproduzieren können, z.B. thermodynamische Eigenschaften wie Druck und Kompressibilität oder strukturelle Eigenschaften, die nicht zur Modellbildung verwendet wurden, z.B. das tetraedrische Packungsverhalten, welches für viele spezielle Eigenschaft von Wasser verantwortlich ist.rnrnMit Hilfe des "Adaptive Resolution Schemes" werden beide Auflösungen in einer Simulation kombiniert. Dabei profitiert man von den Vorteilen beider Modelle:rnVon der detaillierten Darstellung eines räumlich kleinen Bereichs in atomistischer Auflösung und von der rechnerischen Effizienz des coarse-grained Modells, die den Bereich simulierbarer Zeit- und Längenskalen vergrössert.rnrnIn diesen Simulationen kann der Einfluss des Wasserstoffbrückenbindungsnetzwerks auf die Hydration von Fullerenen untersucht werden. Es zeigt sich, dass die Struktur der Wassermoleküle an der Oberfläche hauptsächlich von der Art der Wechselwirkung zwischen dem Fulleren und Wasser und weniger von dem Wasserstoffbrückenbindungsnetzwerk dominiert wird.rn

Charge transport in amorphous organic semiconductors

Organic semiconductors with the unique combination of electronic and mechanical properties may offer cost-effective ways of realizing many electronic applications, e.g. large-area flexible displays, printed integrated circuits and plastic solar cells. In order to facilitate the rational compound design of organic semiconductors, it is essential to understand relevant physical properties e.g. charge transport. This, however, is not straightforward, since physical models operating on different time and length scales need to be combined. First, the material morphology has to be known at an atomistic scale. For this atomistic molecular dynamics simulations can be employed, provided that an atomistic force field is available. Otherwise it has to be developed based on the existing force fields and first principle calculations. However, atomistic simulations are typically limited to the nanometer length- and nanosecond time-scales. To overcome these limitations, systematic coarse-graining techniques can be used. In the first part of this thesis, it is demonstrated how a force field can be parameterized for a typical organic molecule. Then different coarse-graining approaches are introduced together with the analysis of their advantages and problems. When atomistic morphology is available, charge transport can be studied by combining the high-temperature Marcus theory with kinetic Monte Carlo simulations. The approach is applied to the hole transport in amorphous films of tris(8-hydroxyquinoline)aluminium (Alq3). First the influence of the force field parameters and the corresponding morphological changes on charge transport is studied. It is shown that the energetic disorder plays an important role for amorphous Alq3, defining charge carrier dynamics. Its spatial correlations govern the Poole-Frenkel behavior of the charge carrier mobility. It is found that hole transport is dispersive for system sizes accessible to simulations, meaning that calculated mobilities depend strongly on the system size. A method for extrapolating calculated mobilities to the infinite system size is proposed, allowing direct comparison of simulation results and time-of-flight experiments. The extracted value of the nondispersive hole mobility and its electric field dependence for amorphous Alq3 agree well with the experimental results.

Numerical study of homogeneous and heterogeneous crystal nucleation in colloidal systems

Im Rahmen dieser Arbeit wurden Computersimulationen von Keimbildungs- und Kris\-tallisationsprozessen in rnkolloidalen Systemen durchgef\"uhrt. rnEine Kombination von Monte-Carlo-Simulationsmethoden und der Forward-Flux-Sampling-Technik wurde rnimplementiert, um die homogene und heterogene Nukleation von Kristallen monodisperser Hart\-kugeln zu untersuchen. rnIm m\"a\ss{ig} unterk\"uhlten Bulk-Hartkugelsystem sagen wir die homogenen Nukleationsraten voraus und rnvergleichen die Resultate mit anderen theoretischen Ergebnissen und experimentellen Daten. rnWeiterhin analysieren wir die kristallinen Cluster in den Keimbildungs- und Wachstumszonen, rnwobei sich herausstellt, dass kristalline Cluster sich in unterschiedlichen Formen im System bilden. rnKleine Cluster sind eher l\"anglich in eine beliebige Richtung ausgedehnt, w\"ahrend gr\"o\ss{ere} rnCluster kompakter und von ellipsoidaler Gestalt sind. rn rnIm n\"achsten Teil untersuchen wir die heterogene Keimbildung an strukturierten bcc (100)-W\"anden. rnDie 2d-Analyse der kristallinen Schichten an der Wand zeigt, dass die Struktur der rnWand eine entscheidende Rolle in der Kristallisation von Hartkugelkolloiden spielt. rnWir sagen zudem die heterogenen Kristallbildungsraten bei verschiedenen \"Ubers\"attigungsgraden voraus. rnDurch Analyse der gr\"o\ss{ten} Cluster an der Wand sch\"atzen wir zus\"atzlich den Kontaktwinkel rnzwischen Kristallcluster und Wand ab. rnEs stellt sich heraus, dass wir in solchen Systemen weit von der Benetzungsregion rnentfernt sind und der Kristallisationsprozess durch heterogene Nukleation stattfindet. rn rnIm letzten Teil der Arbeit betrachten wir die Kristallisation von Lennard-Jones-Kolloidsystemen rnzwischen zwei ebenen W\"anden. rnUm die Erstarrungsprozesse f\"ur ein solches System zu untersuchen, haben wir eine Analyse des rnOrdnungsparameters f\"ur die Bindung-Ausrichtung in den Schichten durchgef\"urt. rnDie Ergebnisse zeigen, dass innerhalb einer Schicht keine hexatische Ordnung besteht, rnwelche auf einen Kosterlitz-Thouless-Schmelzvorgang hinweisen w\"urde. rnDie Hysterese in den Erhitzungs-Gefrier\-kurven zeigt dar\"uber hinaus, dass der Kristallisationsprozess rneinen aktivierten Prozess darstellt.

Tracking, b-tagging and measurement of the b-jet production cross section with the ATLAS detector

The Standard Model of elementary particle physics was developed to describe the fundamental particles which constitute matter and the interactions between them. The Large Hadron Collider (LHC) at CERN in Geneva was built to solve some of the remaining open questions in the Standard Model and to explore physics beyond it, by colliding two proton beams at world-record centre-of-mass energies. The ATLAS experiment is designed to reconstruct particles and their decay products originating from these collisions. The precise reconstruction of particle trajectories plays an important role in the identification of particle jets which originate from bottom quarks (b-tagging). This thesis describes the step-wise commissioning of the ATLAS track reconstruction and b-tagging software and one of the first measurements of the b-jet production cross section in pp collisions at sqrt(s)=7 TeV with the ATLAS detector. The performance of the track reconstruction software was studied in great detail, first using data from cosmic ray showers and then collisions at sqrt(s)=900 GeV and 7 TeV. The good understanding of the track reconstruction software allowed a very early deployment of the b-tagging algorithms. First studies of these algorithms and the measurement of the b-tagging efficiency in the data are presented. They agree well with predictions from Monte Carlo simulations. The b-jet production cross section was measured with the 2010 dataset recorded by the ATLAS detector, employing muons in jets to estimate the fraction of b-jets. The measurement is in good agreement with the Standard Model predictions.

Messung der Charmonium-Produktion und Energiekalibration für Elektronen mit dem Atlas-Experiment

Der Wirkungsquerschnitt der Charmoniumproduktion wurde unter Nutzung der Daten aus pp-Kollisionen bei s^{1/2}=7TeV, die im Jahr 2010 vom Atlas-Experiment am LHC aufgezeichnet wurden, gemessen. Um das notwendige Detektorverständnis zu verbessern, wurde eine Energiekalibration durchgeführt.rnrnrnUnter Nutzung von Elektronen aus Zerfällen des Charmoniums wurde die Energieskala der elektromagnetischen Kalorimeter bei niedrigen Energien untersucht. Nach Anwendung der Kalibration wurden für die Energiemessung im Vergleich mit in Monte-Carlo-Simulationen gemessenen Energien Abweichungen von weniger als 0,5% gefunden.rnrnrnMit einer integrierten Luminosität von 2,2pb^{-1} wurde eine erste Messung des inklusiven Wirkungsquerschnittes für den Prozess pp->J/psi(e^{+}e^{-})+X bei s^{1/2}=7TeV vorgenommen. Das geschah im zugänglichen Bereich für Transversalimpulse p_{T,ee}>7GeV und Rapiditäten |y_{ee}|<2,4. Es wurden differentielle Wirkungsquerschnitte für den Transversalimpuls p_{T,ee} und für die Rapidität |y_{ee}| bestimmt. Integration beider Verteilungen lieferte für den inklusiven Wirkungsquerschnitt sigma(pp-> J/psi X)BR(J/psi->e^{+}e^{-}) die Werte (85,1+/-1,9_{stat}+/-11,2_{syst}+/-2,9_{Lum})nb und (75,4+/-1,6_{stat}+/-11,9_{syst}+/-2,6_{Lum})nb, die innerhalb der Systematik kompatibel sind.rnrnrnVergleiche mit Messungen von Atlas und CMS für den Prozess pp->J/psi(mu^{+}mu^{-})+X zeigten gute Übereinstimmung. Zum Vergleich mit der Theorie wurden Vorhersagen mit verschiedenen Modellen in nächst-zu-führender und mit Anteilen in nächst-zu-nächst-zu-führender Ordnung kombiniert. Der Vergleich zeigt eine gute Übereinstimmung bei Berücksichtigung von Anteilen in nächst-zu-nächst-zu-führender Ordnung.

Developments for transactinide chemistry experiments behind the gas-filled separator TASCA

Topic of this thesis is the development of experiments behind the gas-filled separator TASCA(TransActinide Separator and Chemistry Apparatus) to study the chemical properties of the transactinide elements.rnIn the first part of the thesis, the electrodepositions of short-lived isotopes of ruthenium and osmium on gold electrodes were studied as model experiments for hassium. From literature it is known that the deposition potential of single atoms differs significantly from the potential predicted by the Nernst equation. This shift of the potential depends on the adsorption enthalpy of therndeposited element on the electrode material. If the adsorption on the electrode-material is favoured over the adsorption on a surface made of the same element as the deposited atom, the electrode potential is shifted to higher potentials. This phenomenon is called underpotential deposition.rnPossibilities to automatize an electro chemistry experiment behind the gas-filled separator were explored for later studies with transactinide elements.rnThe second part of this thesis is about the in-situ synthesis of transition-metal-carbonyl complexes with nuclear reaction products. Fission products of uranium-235 and californium-249 were produced at the TRIGA Mainz reactor and thermalized in a carbon-monoxide containing atmosphere. The formed volatile metal-carbonyl complexes could be transported in a gas-stream.rnFurthermore, short-lived isotopes of tungsten, rhenium, osmium, and iridium were synthesised at the linear accelerator UNILAC at GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt. The recoiling fusion products were separated from the primary beam and the transfer products in the gas-filled separator TASCA. The fusion products were stopped in the focal plane of TASCA in a recoil transfer chamber. This chamber contained a carbon-monoxide – helium gas mixture. The formed metal-carbonyl complexes could be transported in a gas stream to various experimental setups. All synthesised carbonyl complexes were identified by nuclear decay spectroscopy. Some complexes were studied with isothermal chromatography or thermochromatography methods. The chromatograms were compared with Monte Carlo Simulations to determine the adsorption enthalpyrnon silicon dioxide and on gold. These simulations based on existing codes, that were modified for the different geometries of the chromatography channels. All observed adsorption enthalpies (on silcon oxide as well as on gold) are typical for physisorption. Additionally, the thermalstability of some of the carbonyl complexes was studied. This showed that at temperatures above 200 °C therncomplexes start to decompose.rnIt was demonstrated that carbonyl-complex chemistry is a suitable method to study rutherfordium, dubnium, seaborgium, bohrium, hassium, and meitnerium. Until now, only very simple, thermally stable compounds have been synthesized in the gas-phase chemistry of the transactindes. With the synthesis of transactinide-carbonyl complexes a new compound class would be discovered. Transactinide chemistry would reach the border between inorganic and metallorganic chemistry.rnFurthermore, the in-situ synthesised carbonyl complexes would allow nuclear spectroscopy studies under low background conditions making use of chemically prepared samples.