Polymer surfaces on small length- and short time-scales

The behaviour of a polymer depends strongly on the length- and time scale as well as on the temperature rnat which it is probed. In this work, I describe investigations of polymer surfaces using scanning probe rnmicroscopy with heatable probes. With these probes, surfaces can be heated within seconds down to rnmicroseconds. I introduce experiments for the local and fast determination of glass transition and melting rntemperatures. I developed a method which allows the determination of glass transition and melting rntemperatures on films with thicknesses below 100 nm: A background measurement on the substrate was rnperformed. The resulting curve was subtracted from the measurement on the polymer film. The rndifferential measurement on polystyrene films with thicknesses between 35 nm and 160 nm showed rncharacteristic signals at 95 ± 1 °C, in accordance with the glass transition of polystyrene. Pressing heated rnprobes into polymer films causes plastic deformation. Nanometer sized deformations are currently rninvestigated in novel concepts for high density data storage. A suitable medium for such a storage system rnhas to be easily indentable on one hand, but on the other hand it also has to be very stable towards rnsurface induced wear. For developing such a medium I investigated a new approach: A comparably soft rnmaterial, namely polystyrene, was protected with a thin but very hard layer made of plasma polymerized rnnorbornene. The resulting bilayered media were tested for surface stability and deformability. I showed rnthat the bilayered material combines the deformability of polystyrene with the surface stability of the rnplasma polymer, and that the material therefore is a very good storage medium. In addition we rninvestigated the glass transition temperature of polystyrene at timescales of 10 µs and found it to be rnapprox. 220 °C. The increase of this characteristic temperature of the polymer results from the short time rnat which the polymer was probed and reflects the well-known time-temperature superposition principle. rnHeatable probes were also used for the characterization of silverazide filled nanocapsules. The use of rnheatable probes allowed determining the decomposition temperature of the capsules from few rnnanograms of material. The measured decomposition temperatures ranged from 180 °C to 225 °C, in rnaccordance with literature values. The investigation of small amounts of sample was necessary due to the rnlimited availability of the material. Furthermore, investigating larger amounts of the capsules using rnconventional thermal gravimetric analysis could lead to contamination or even damage of the instrument. rnBesides the analysis of material parameters I used the heatable probes for the local thermal rndecomposition of pentacene precursor material in order to form nanoscale conductive structures. Here, rnthe thickness of the precursor layer was important for complete thermal decomposition. rnAnother aspect of my work was the investigation of redox active polymers - Poly-10-(4-vinylbenzyl)-10H-rnphenothiazine (PVBPT)- for data storage. Data is stored by changing the local conductivity of the material rnby applying a voltage between tip and surface. The generated structures were stable for more than 16 h. It rnwas shown that the presence of water is essential for succesfull patterning.

Climate signatures in corals of the tropical-temperate transition zone (Late Miocene, Crete/Greece)

The present study describes a Late Miocene (early Tortonian - early Messinian) transitional carbonate system that combines elements of tropical and cool-water carbonate systems (Irakleion Basin, island of Crete, Greece). As documented by stratal geometries, the submarine topography of the basin was controlled by tilting blocks. Coral reefs formed by Porites and Tarbellastrea occurred in a narrow clastic coastal belt along a „central Cretan landmass“, and steep escarpments formed by faulting. Extensive covers of level-bottom communities existed in a low-energy environment on the gentle dip-slope ramps of the blocks that show the widest geographical distribution within the basin. Consistent patterns of landward and basinward shift of coastal onlap in all outcrop studies reveal an overriding control of 3rd and 4th order sea level changes on sediment dynamics and facies distributions over block movements. An increasingly dry climate and the complex submarine topography of the fault block mosaic kept sediment and nutrient discharge at a minimum. The skeletal limestone facies therefore reflects oligotrophic conditions and a sea surface temperature (SST) near the lower threshold temperature of coral reefs in a climatic position transitional between the tropical coral reef belt and the temperate zone. Stable isotope records (δ18O, δ13C) from massiv, exceptionally preserved Late Miocene aragonite coral skeletons reflect seasonal changes in sea surface temperature and symbiont autotrophy. Spectral analysis of a 69 years coral δ18O record reveals significant variance at interannual time scales (5-6 years) that matches the present-day eastern Mediterranean climate variability controlled by the Arctic Oscillation/North Atlantic Oscillation (AO/NAO), the Northern Hemisphere’s dominant mode of atmospheric variability. Supported by simulations with a complex atmospheric general circulation model coupled to a mixed-layer ocean model, it is suggested, that climate dynamics in the eastern Mediterranean and central Europe reflect atmospheric variability related to the Icelandic Low 10 million years ago. Usually, Miocene corals are transformed in calcite spar in geological time and isotope values are reset by diagenetic alteration. It is demonstrated that the relicts of growth bands represent an intriguing source of information for the growth conditions of fossil corals. Recrystallized growth bands were measured systematically in massive Porites from Crete. The Late Miocene corals were growing slowly with 2-4 mm/yr, compatible with present-day Porites from high latitude reefs, a relationship that fits the position of Crete at the margin of the Miocene tropical reef belt. Over Late Miocene time (Tortonian - early Messinian) growth rates remained remarkably constant, and if the modern growth temperature relationship for massive Porites applies to the Neogene, minimum (winter) SST did not exceed 19-21°C.

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

Pinning-Effekte kolumnarer Schwerionenspuren in Kuprat-Supraleiter-Dünnschichten

In this work the flux line dynamics in High-Temperature Superconductor (HTSC) thin films in the presence of columnar defects was studied using electronic transport measurements. The columnar defects which are correlated pinning centers for vortices were generated by irradiation with swift heavy ions at the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt. In the first part, the vortex dynamics is discussed within the framework of the Bose-glass model. This approach describes the continuous transition from a vortex liquid to a Bose-glass phase which is characterized by the localization of the flux lines at the columnar defects. The critical behavior of the characteristic length and time scales for temperatures in the vicinity of this phase transition were probed by scaling properties of experimentally obtained current-voltage characteristics. In contrast to the predicted universal properties of the critical behavior the scaling analysis shows a strong dependence of the dynamic critical exponent on the experimentally accessible electric field range. In addition, the predicted divergence of the activation energy in the limit of low current densities was experimentally not confirmed.The dynamic behavior of flux lines in spatially resolved irradiation geometries is reported in the second part. Weak pinning channels with widths between 10 µm and 100 µm were generated in a strong pinning environment with the use of metal masks and the GSI microprobe, respectively. Measurements of the anisotropic transport properties of these structures show a striking resemblance to the results in YBCO single crystals with unidirected twin boundaries which were interpreted as a guided vortex motion effect. The use of two additional test bridges allowed to determine in parallel the resistivities of the irradiated and unirradiated parts as well as the respective current-voltage characteristics. These measurements provided the input parameters for a numerical simulation of the potential distribution in the spatially resolved irradiation geometry. The results are interpreted within a model that describes the hydrodynamic interaction between a Bose-glass phase and a vortex liquid. The interface between weakly pinned flux lines in the unirradiated channels and strongly pinned vortices leads to a nonuniform vortex velocity profile and therefore a variation of the local electric field. The length scale of these interactions was estimated for the first time in measuring the local variation of the electric field profile in a Bose-glass contact.Finally, a method for the determination of the true temperature in HTSC thin films at high dissipation levels is described. In this regime of electronic transport the occurrence of a flux flow instability is accompanied by heating effects in the vortex system. The heat propagation properties of the film/substrate system are deduced from the time dependent voltage response to a short high current density pulse of rectangular shape. The influence of heavy ion irradiation on the heat resistance at the film/substrate interface is studied.

Relaxationsuntersuchungen in unterkühlten und glasig erstarrten Polyalkoholen mittels dielektrischer und NMR Spektroskopie

Es wurde eine homologe Reihe von Polyalkoholen mit der allgemeinen Summenformel CNHN+2(OH)N (N=3-6) hinsichtlich ihrer Glaseigenschaften ober- und unterhalb der Glasübergangstemperatur TG untersucht. Dabei kamen die dielektrische und magnetische Resonanzspektroskopie (NMR) zum Einsatz. Es ergab sich oberhalb TG eine systematische Zunahme aller untersuchten dynamischen Parameter wie Fragilität, Breite der angenommenen Korrelationszeitenverteilungen und der Sprungwinkel der primären Glasrelaxation mit zunehmendem N. Dies kann insgesamt als eine Abnahme des Netzwerkcharakters, der durch Wasserstoffbrückenbindungen bedingt ist, bei zunehmender Kettenlänge interpretiert werden. Unterhalb TG entwickelt sich mit zunehmendem N die Sekundärrelaxation von einem 'Wing Szenario' zu einem ausgeprägten Johari - Goldstein (JG) - Prozess. Ein Sprungmodell, welches eine eingeschränkte Reorientierung auf einem Konusrand beschreibt, erzeugt mit Hilfe der parametrisierten dielektrischen Verlustspektren Sprungwinkel, die mit denen aus aktuellen ²H - NMR spektroskopischen Untersuchungen vergleichbar sind. Durch den Vergleich unterschiedlich deuterierter Derivate von Glyzerin (N=3) und Sorbitol (N=6) wurde gefolgert, dass auch unterhalb TG der Netzwerkcharakter mit zunehmender Kettenlänge abnimmt.Aufgrund der hier durchgeführten Untersuchungen konnte eine Zeitskala für einen Johari - Goldstein - Prozess im Modellglasbildner Glyzerin extrapoliert werden. Eine Deutung des Wings als Hochfrequenzausläufer des JG - Prozesses ist dadurch möglich.Der JG - Prozess kann somit als universeller Glasprozess interpretiert werden, der in verschiedenen Glasbildnern in unterschiedlicher Ausprägung auftritt.

Untersuchungen zur Verfestigungskinetik in Suspensionen kolloidaler Partikel

Kolloidale Suspensionen, bei denen man die kolloidalen Teilchen als "Makroatome" in einem Kontinuum aus Lösungsmittelmolekülen auffaßt, stellen ein geeignetes Modellsystem zur Untersuchung von Verfestigungsvorgängen dar. Auf Grund der typischen beteiligten Längen- und Zeitskalen können Phasenübergänge bequem mit optischen Verfahren studiert werden. In der vorliegenden Arbeit wurde die Kinetik der Kristallisation in drei kolloidalen Systemen unterschiedlicher Teilchen-Teilchen-Wechselwirkung mit Lichtstreu- und mikroskopischen Methoden untersucht. Zur Untersuchung von Suspensionen aus sterisch stabilisierten PMMA-Teilchen, die in guter Näherung wie harte Kugeln wechselwirken, wurde ein neuartiges Laserlichtstreuexperiment aufgebaut, das die gleichzeitige Detektion von Bragg- und Kleinwinkelstreuung an einer Probe erlaubt. Damit konnte der zeitliche Verlauf der Kristallisation verfolgt sowie u.a. Nukleationsraten und erstmals auch Wachstumsgeschwindigkeiten bestimmt werden; diese wurden mit klassischer Nukleationstheorie sowie Wilson-Frenkel-Wachstum verglichen. In beiden Fällen konnte sehr gute Übereinstimmung mit der Theorie festgestellt werden. In Systemen geladener Partikel wurden mit Bragg-Mikroskopie die Wachstumsgeschwindigkeiten heterogener, an der Wand der Probenzelle aufwachsender Kristalle untersucht. Die Anpassung eines Wilson-Frenkel-Wachstumsgesetzes gelingt auch hier, wenn man die dazu eingeführte reskalierte Energiedichte auf den Schmelzpunkt bezieht. Geeignete Reskalierung der Daten erlaubt den Vergleich mit den Hartkugelsystemen. Zum ersten Mal wurde die Kristallisationskinetik in zwei verschiedenen kolloidalen binären Mischungen bestimmt und ausgewertet: In Beimischungen einer nichtkristallisierenden Teilchensorte zu einer kristallisierenden Suspension konnten die Daten mit einem modifizierten Wilson-Frenkel-Gesetz beschrieben werden, während in Mischungen aus zwei kristallisierenden Partikelsystemen eine unerwartet hohe Abnahme der Wachstumsgeschwindigkeiten beobachtet wurde. Kolloidale Suspensionen hartkugelähnlicher Mikrogel-Partikel konnten mit Hilfe des Lichtstreuaufbaues ebenfalls zum ersten Mal untersucht werden. Es wurde eine ähnliche Kristallisationskinetik wie in den PMMA-Systemen gefunden, jedoch auch einige wichtige Unterschiede, die insbesondere den Streumechanismus im Kleinwinkelbereich betrafen. Hier wurden verschiedene Interpretationsvorschläge diskutiert.

The swelling behaviour of polyelectrolyte networks

Being basic ingredients of numerous daily-life products with significant industrial importance as well as basic building blocks for biomaterials, charged hydrogels continue to pose a series of unanswered challenges for scientists even after decades of practical applications and intensive research efforts. Despite a rather simple internal structure it is mainly the unique combination of short- and long-range forces which render scientific investigations of their characteristic properties to be quite difficult. Hence early on computer simulations were used to link analytical theory and empirical experiments, bridging the gap between the simplifying assumptions of the models and the complexity of real world measurements. Due to the immense numerical effort, even for high performance supercomputers, system sizes and time scales were rather restricted until recently, whereas it only now has become possible to also simulate a network of charged macromolecules. This is the topic of the presented thesis which investigates one of the fundamental and at the same time highly fascinating phenomenon of polymer research: The swelling behaviour of polyelectrolyte networks. For this an extensible simulation package for the research on soft matter systems, ESPResSo for short, was created which puts a particular emphasis on mesoscopic bead-spring-models of complex systems. Highly efficient algorithms and a consistent parallelization reduced the necessary computation time for solving equations of motion even in case of long-ranged electrostatics and large number of particles, allowing to tackle even expensive calculations and applications. Nevertheless, the program has a modular and simple structure, enabling a continuous process of adding new potentials, interactions, degrees of freedom, ensembles, and integrators, while staying easily accessible for newcomers due to a Tcl-script steering level controlling the C-implemented simulation core. Numerous analysis routines provide means to investigate system properties and observables on-the-fly. Even though analytical theories agreed on the modeling of networks in the past years, our numerical MD-simulations show that even in case of simple model systems fundamental theoretical assumptions no longer apply except for a small parameter regime, prohibiting correct predictions of observables. Applying a "microscopic" analysis of the isolated contributions of individual system components, one of the particular strengths of computer simulations, it was then possible to describe the behaviour of charged polymer networks at swelling equilibrium in good solvent and close to the Theta-point by introducing appropriate model modifications. This became possible by enhancing known simple scaling arguments with components deemed crucial in our detailed study, through which a generalized model could be constructed. Herewith an agreement of the final system volume of swollen polyelectrolyte gels with results of computer simulations could be shown successfully over the entire investigated range of parameters, for different network sizes, charge fractions, and interaction strengths. In addition, the "cell under tension" was presented as a self-regulating approach for predicting the amount of swelling based on the used system parameters only. Without the need for measured observables as input, minimizing the free energy alone already allows to determine the the equilibrium behaviour. In poor solvent the shape of the network chains changes considerably, as now their hydrophobicity counteracts the repulsion of like-wise charged monomers and pursues collapsing the polyelectrolytes. Depending on the chosen parameters a fragile balance emerges, giving rise to fascinating geometrical structures such as the so-called pear-necklaces. This behaviour, known from single chain polyelectrolytes under similar environmental conditions and also theoretically predicted, could be detected for the first time for networks as well. An analysis of the total structure factors confirmed first evidences for the existence of such structures found in experimental results.

Stochastische Modelle für nichtlineare Antwortfunktionen in ungeordneten Systemen

In dieser Arbeit werden nichtlineare Experimente zur Untersuchung der Dynamik in amorphen Festkörpern im Rahmen von Modellrechnungen diskutiert. Die Experimente beschäftigen sich mit der Frage nach dynamischen Heterogenitäten, worunter man das Vorliegen dynamischer Prozesse auf unterschiedlichen Zeitskalen versteht. Ist es möglich, gezielt 'langsame' oder 'schnelle' Dynamik in der Probe nachzuweisen, so ist die Existenz von dynamischen Heterogenitäten gezeigt. Ziel der Experimente sind deshalb sogenannte frequenzselektive Anregungen des Systems. In den beiden diskutierten Experimenten, zum einen nichtresonantes Lochbrennen, zum anderen ein ähnliches Experiment, das auf dem dynamischen Kerreffekt beruht, werden nichtlineare Antwortfunktionen gemessen. Um eine Probe in frequenzselektiver Weise anzuregen, werden zunächst einer oder mehrere Zyklen eines oszillierenden elektrischen Feldes an die Probe angelegt. Die Experimente werden zunächst im Terahertz-Bereich untersucht. Auf dieser Zeitskala findet man phonon-ähnliche kollektive Schwingungen in Gläsern. Diese Schwingungen werden durch (anharmonische) Brownsche Oszillatoren beschrieben. Der zentrale Befund der Modellrechnungen ist, daß eine frequenzselektive Anregung im Terahertz-Bereich möglich ist. Ein Nachweis dynamischer Heterogenitäten im Terahertz-Bereich ist somit durch beide Experimente möglich. Anschliessend wird das vorgestellte Kerreffekt-Experiment im Bereich wesentlich kleinerer Frequenzen diskutiert. Die langsame Reorientierungsdynamik in unterkühlten Flüssigkeiten wird dabei durch ein Rotationsdiffusionsmodell beschrieben. Es werden zum einen ein heterogenes und zum anderen ein homogenes Szenario zugrundegelegt. Es stellt sich heraus, daß wie beim Lochbrennen eine Unterscheidung durch das Experiment möglich ist. Das Kerreffekt-Experiment wird somit als eine relativ einfache Alternative zur Technik des nichtresonanten Lochbrennens vorgeschlagen.

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.

Untersuchung der Struktur und Assemblierung des Lichtsammelkomplexes II höherer Pflanzen mittels elektronenparamagnetischer Resonanz (EPR)

Der Haupt-Lichtsammelkomplex (LHCII) des Photosyntheseapparates höherer Pflanzen gehört zu den häufigsten Membranproteinen der Erde. Seine Kristallstruktur ist bekannt. Das Apoprotein kann rekombinant in Escherichia coli überexprimiert und somit molekularbiologisch vielfältig verändert werden. In Detergenzlösung besitzt das denaturierte Protein die erstaunliche Fähigkeit, sich spontan zu funktionalen Protein-Pigment-Komplexen zu organisieren, welche strukturell nahezu identisch sind mit nativem LHCII. Der Faltungsprozess findet in vitro im Zeitbereich von Sekunden bis Minuten statt und ist abhängig von der Bindung der Cofaktoren Chlorophyll a und b sowie verschiedenen Carotinoiden.rn Diese Eigenschaften machen LHCII besonders geeignet für Strukturuntersuchungen mittels der elektronenparamagnetischen Resonanz (EPR)-Spektrokopie. Diese setzt eine punktspezifische Spinmarkierung des LHCII voraus, die in dieser Arbeit zunächst optimiert wurde. Einschließlich der Beiträge Anderer stand eine breite Auswahl von über 40 spinmarkierten Mutanten des LHCII bereit, einen N-terminalen „Cys walk“ eingeschlossen. Weder der hierfür notwendige Austausch einzelner Aminosäuren noch die Anknüpfung des Spinmarkers beeinträchtigten die Funktion des LHCII. Zudem konnte ein Protokoll zur Präparation heterogen spinmarkierter LHCII-Trimere entwickelt werden, also von Trimeren, die jeweils nur ein Monomer mit einer Spinmarkierung enthalten.rn Spinmarkierte Proben des Detergenz-solubilisierten LHCII wurden unter Verwendung verschiedener EPR-Techniken strukturell analysiert. Als besonders aussagekräftig erwies sich die Messung der Wasserzugänglichkeit einzelner Aminosäurepositionen anhand der Electron Spin Echo Envelope Modulation (ESEEM). In Kombination mit der etablierten Double Electron-Electron Resonance (DEER)-Technik zur Detektion von Abständen zwischen zwei Spinmarkern wurde der membranständige Kernbereich des LHCII in Lösung eingehend untersucht und strukturell der Kristallstruktur für sehr ähnlich befunden. Die Vermessung kristallographisch nicht erfasster Bereiche nahe dem N-Terminus offenbarte die schon früher detektierte Strukturdynamik der Domäne in Abhängigkeit des Oligomerisierungsgrades. Der neue, noch zu vervollständigende Datensatz aus Abstandsverteilungen und ESEEM-Wasserzugänglichkeiten monomerer wie trimerer Proben sollte in naher Zukunft die sehr genaue Modellierung der N-terminalen Domäne des LHCII ermöglichen.rn In einem weiteren Abschnitt der Arbeit wurde die Faltung des LHCII-Apoproteins bei der LHCII-Assemblierung in vitro untersucht. Vorausgegangene fluoreszenzspektroskopi-sche Arbeiten hatten gezeigt, dass die Bindung von Chlorophyll a und b in aufeinanderfolgenden Schritten im Zeitbereich von weniger als einer Minute bzw. mehreren Minuten erfolgten. Sowohl die Wasserzugänglichkeit einzelner Aminosäurepositionen als auch Spin-Spin-Abstände änderten sich in ähnlichen Zeitbereichen. Die Daten deuten darauf hin, dass die Ausbildung der mittleren Transmembran-Helix mit der schnelleren Chlorophyll-a-Bindung einhergeht, während sich die Superhelix aus den beiden anderen Transmembranhelices erst im langsameren Schritt, zusammen mit der Chlorophyll-b-Bindung, ausbildet.rn

Simulations of charge transport in organic compounds

To aid the design of organic semiconductors, we study the charge transport properties of organic liquid crystals, i.e. hexabenzocoronene and carbazole macrocycle, and single crystals, i.e. rubrene, indolocarbazole and benzothiophene derivatives (BTBT, BBBT). The aim is to find structure-property relationships linking the chemical structure as well as the morphology with the bulk charge carrier mobility of the compounds. To this end, molecular dynamics (MD) simulations are performed yielding realistic equilibrated morphologies. Partial charges and molecular orbitals are calculated based on single molecules in vacuum using quantum chemical methods. The molecular orbitals are then mapped onto the molecular positions and orientations, which allows calculation of the transfer integrals between nearest neighbors using the molecular orbital overlap method. Thus we obtain realistic transfer integral distributions and their autocorrelations. In case of organic crystals the differences between two descriptions of charge transport, namely semi-classical dynamics (SCD) in the small polaron limit and kinetic Monte Carlo (KMC) based on Marcus rates, are studied. The liquid crystals are investigated solely in the hopping limit. To simulate the charge dynamics using KMC, the centers of mass of the molecules are mapped onto lattice sites and the transfer integrals are used to compute the hopping rates. In the small polaron limit, where the electronic wave function is spread over a limited number of neighboring molecules, the Schroedinger equation is solved numerically using a semi-classical approach. The results are compared for the different compounds and methods and, where available, with experimental data. The carbazole macrocycles form columnar structures arranged on a hexagonal lattice with side chains facing inwards, so columns can closely approach each other allowing inter-columnar and thus three-dimensional transport. When taking only intra-columnar transport into account, the mobility is orders of magnitude lower than in the three-dimensional case. BTBT is a promising material for solution-processed organic field-effect transistors. We are able to show that, on the time-scales of charge transport, static disorder due to slow side chain motions is the main factor determining the mobility. The resulting broad transfer integral distributions modify the connectivity of the system but sufficiently many fast percolation paths remain for the charges. Rubrene, indolocarbazole and BBBT are examples of crystals without significant static disorder. The high mobility of rubrene is explained by two main features: first, the shifted cofacial alignment of its molecules, and second, the high center of mass vibrational frequency. In comparsion to SCD, only KMC based on Marcus rates is capable of describing neighbors with low coupling and of taking static disorder into account three-dimensionally. Thus it is the method of choice for crystalline systems dominated by static disorder. However, it is inappropriate for the case of strong coupling and underestimates the mobility of well-ordered crystals. SCD, despite its one-dimensionality, is valuable for crystals with strong coupling and little disorder. It also allows correct treatment of dynamical effects, such as intermolecular vibrations of the molecules. Rate equations are incapable of this, because simulations are performed on static snapshots. We have thus shown strengths and weaknesses of two state of the art models used to study charge transport in organic compounds, partially developed a program to compute and visualize transfer integral distributions and other charge transport properties, and found structure-mobility relations for several promising organic semiconductors.

Coarse-graining methods and polymer dynamics

This thesis studies molecular dynamics simulations on two levels of resolution: the detailed level of atomistic simulations, where the motion of explicit atoms in a many-particle system is considered, and the coarse-grained level, where the motion of superatoms composed of up to 10 atoms is modeled. While atomistic models are capable of describing material specific effects on small scales, the time and length scales they can cover are limited due to their computational costs. Polymer systems are typically characterized by effects on a broad range of length and time scales. Therefore it is often impossible to atomistically simulate processes, which determine macroscopic properties in polymer systems. Coarse-grained (CG) simulations extend the range of accessible time and length scales by three to four orders of magnitude. However, no standardized coarse-graining procedure has been established yet. Following the ideas of structure-based coarse-graining, a coarse-grained model for polystyrene is presented. Structure-based methods parameterize CG models to reproduce static properties of atomistic melts such as radial distribution functions between superatoms or other probability distributions for coarse-grained degrees of freedom. Two enhancements of the coarse-graining methodology are suggested. Correlations between local degrees of freedom are implicitly taken into account by additional potentials acting between neighboring superatoms in the polymer chain. This improves the reproduction of local chain conformations and allows the study of different tacticities of polystyrene. It also gives better control of the chain stiffness, which agrees perfectly with the atomistic model, and leads to a reproduction of experimental results for overall chain dimensions, such as the characteristic ratio, for all different tacticities. The second new aspect is the computationally cheap development of nonbonded CG potentials based on the sampling of pairs of oligomers in vacuum. Static properties of polymer melts are obtained as predictions of the CG model in contrast to other structure-based CG models, which are iteratively refined to reproduce reference melt structures. The dynamics of simulations at the two levels of resolution are compared. The time scales of dynamical processes in atomistic and coarse-grained simulations can be connected by a time scaling factor, which depends on several specific system properties as molecular weight, density, temperature, and other components in mixtures. In this thesis the influence of molecular weight in systems of oligomers and the situation in two-component mixtures is studied. For a system of small additives in a melt of long polymer chains the temperature dependence of the additive diffusion is predicted and compared to experiments.

Quantifying and modeling financial market fluctuations

Die Entstehung eines Marktpreises für einen Vermögenswert kann als Superposition der einzelnen Aktionen der Marktteilnehmer aufgefasst werden, die damit kumulativ Angebot und Nachfrage erzeugen. Dies ist in der statistischen Physik mit der Entstehung makroskopischer Eigenschaften vergleichbar, die von mikroskopischen Wechselwirkungen zwischen den beteiligten Systemkomponenten hervorgerufen werden. Die Verteilung der Preisänderungen an Finanzmärkten unterscheidet sich deutlich von einer Gaußverteilung. Dies führt zu empirischen Besonderheiten des Preisprozesses, zu denen neben dem Skalierungsverhalten nicht-triviale Korrelationsfunktionen und zeitlich gehäufte Volatilität zählen. In der vorliegenden Arbeit liegt der Fokus auf der Analyse von Finanzmarktzeitreihen und den darin enthaltenen Korrelationen. Es wird ein neues Verfahren zur Quantifizierung von Muster-basierten komplexen Korrelationen einer Zeitreihe entwickelt. Mit dieser Methodik werden signifikante Anzeichen dafür gefunden, dass sich typische Verhaltensmuster von Finanzmarktteilnehmern auf kurzen Zeitskalen manifestieren, dass also die Reaktion auf einen gegebenen Preisverlauf nicht rein zufällig ist, sondern vielmehr ähnliche Preisverläufe auch ähnliche Reaktionen hervorrufen. Ausgehend von der Untersuchung der komplexen Korrelationen in Finanzmarktzeitreihen wird die Frage behandelt, welche Eigenschaften sich beim Wechsel von einem positiven Trend zu einem negativen Trend verändern. Eine empirische Quantifizierung mittels Reskalierung liefert das Resultat, dass unabhängig von der betrachteten Zeitskala neue Preisextrema mit einem Anstieg des Transaktionsvolumens und einer Reduktion der Zeitintervalle zwischen Transaktionen einhergehen. Diese Abhängigkeiten weisen Charakteristika auf, die man auch in anderen komplexen Systemen in der Natur und speziell in physikalischen Systemen vorfindet. Über 9 Größenordnungen in der Zeit sind diese Eigenschaften auch unabhängig vom analysierten Markt - Trends, die nur für Sekunden bestehen, zeigen die gleiche Charakteristik wie Trends auf Zeitskalen von Monaten. Dies eröffnet die Möglichkeit, mehr über Finanzmarktblasen und deren Zusammenbrüche zu lernen, da Trends auf kleinen Zeitskalen viel häufiger auftreten. Zusätzlich wird eine Monte Carlo-basierte Simulation des Finanzmarktes analysiert und erweitert, um die empirischen Eigenschaften zu reproduzieren und Einblicke in deren Ursachen zu erhalten, die zum einen in der Finanzmarktmikrostruktur und andererseits in der Risikoaversion der Handelsteilnehmer zu suchen sind. Für die rechenzeitintensiven Verfahren kann mittels Parallelisierung auf einer Graphikkartenarchitektur eine deutliche Rechenzeitreduktion erreicht werden. Um das weite Spektrum an Einsatzbereichen von Graphikkarten zu aufzuzeigen, wird auch ein Standardmodell der statistischen Physik - das Ising-Modell - auf die Graphikkarte mit signifikanten Laufzeitvorteilen portiert. Teilresultate der Arbeit sind publiziert in [PGPS07, PPS08, Pre11, PVPS09b, PVPS09a, PS09, PS10a, SBF+10, BVP10, Pre10, PS10b, PSS10, SBF+11, PB10].

Patterns in and kinetics of phase separation in binary mixtures

This work focused mainly on two aspects of kinetics of phase separation in binary mixtures. In the first part, we studied the interplay of hydrodynamics and the phase separation of binary mixtures. A considerably flat container (a laterally extended geometry), at an aspect ratio of 14:1 (diameter: height) was chosen, so that any hydrodynamic instabilities, if they arise, could be tracked. Two binary mixtures were studied. One was a mixture of methanol and hexane, doped with 5% ethanol, which phase separated under cooling. The second was a mixture of butoxyethanol and water, doped with 2% decane, which phase separated under heating. The dopants were added to bring down the phase transition temperature around room temperature.rnrnAlthough much work has been done already on classical hydrodynamic instabilities, not much has been done in the understanding of the coupling between phase separation and hydrodynamic instabilities. This work aimed at understanding the influence of phase separation in initiating any hydrodynamic instability, and also vice versa. Another aim was to understand the influence of the applied temperature protocol on the emergence of patterns characteristic to hydrodynamic instabilities. rnrnOn slowly cooling the system continuously, at specific cooling rates, patterns were observed in the first mixture, at the start of phase separation. They resembled the patterns observed in classical Rayleigh-Bénard instability, which arises when a liquid continuously is heated from below. To suppress this classical convection, the cooling setup was tuned such that the lower side of the sample always remained cooler by a few millikelvins, relative to the top. We found that the nature of patterns changed with different cooling rates, with stable patterns appearing for a specific cooling rate (1K/h). On the basis of the cooling protocol, we estimated a modified Rayleigh number for our system. We found that the estimated modified Rayleigh number is near the critical value for instability, for cooling rates between 0.5K/h and 1K/h. This is consistent with our experimental findings. rnrnThe origin of the patterns, in spite of the lower side being relatively colder with respect to the top, points to two possible reasons. 1) During phase separation droplets of either phases are formed, which releases a latent heat. Our microcalorimetry measurements show that the rise in temperature during the first phase separation is in the order of 10-20millikelvins, which in some cases is enough to reverse the applied temperature bias. Thus phase separation in itself initiates a hydrodynamic instability. 2) The second reason comes from the cooling protocol itself. The sample was cooled from above and below. At sufficiently high cooling rates, there are situations where the interior of the sample is relatively hotter than both top and bottom of the sample. This is sufficient to create an instability within the cell. Our experiments at higher cooling rates (5K/h and above) show complex patterns, which hints that there is enough convection even before phase separation occurs. Infact, theoretical work done by Dr.Hayase show that patterns could arise in a system without latent heat, with symmetrical cooling from top and bottom. The simulations also show that the patterns do not span the entire height of the sample cell. This is again consistent with the cell sizes measured in our experiment.rnrnThe second mixture also showed patterns at specific heating rates, when it was continuously heated inducing phase separation. In this case though, the sample was turbid for a long time until patterns appeared. A meniscus was most probably formed before the patterns emerged. We attribute the reason of patterns in this case to Marangoni convection, which is present in systems with an interface, where local differences in surface tension give rise to an instability. Our estimates for the Rayleigh number also show a significantly lower number than that's required for RB-type instability.rnrnIn the first part of the work, therefore, we identify two different kinds of hydrodynamic instabilities in two different mixtures. Both are observed during, or after the first phase separation. Our patterns compare with the classical convection patterns, but here the origins are from phase separation and the cooling protocol.rnrnIn the second part of the work, we focused on the kinetics of phase separation in a polymer solution (polystyrene and methylcyclohexane), which is cooled continuously far down into the two phase region. Oscillations in turbidity, denoting material exchange between the phases are seen. Three processes contribute to the phase separation: Nucleation of droplets, their growth and coalescence, and their subsequent sedimentation. Experiments in low molecular binary mixtures had led to models of oscillation [43] which considered sedimentation time scales much faster than the time scales of nucleation and growth. The size and shape of the sample therefore did not matter in such situations. The oscillations in turbidity were volume-dominated. The present work aimed at understanding the influence of sedimentation time scales for polymer mixtures. Three heights of the sample with same composition were studied side by side. We found that periods increased with the sample height, thus showing that sedimentation time determines the period of oscillations in the polymer solutions. We experimented with different cooling rates and different compositions of the mixture, and we found that periods are still determined by the sample height, and therefore by sedimentation time. rnrnWe also see that turbidity emerges in two ways; either from the interface, or throughout the sample. We suggest that oscillations starting from the interface are due to satellite droplets that are formed on droplet coalescence at the interface. These satellite droplets are then advected to the top of the sample, and they grow, coalesce and sediment. This type of an oscillation wouldn't require the system to pass the energy barrier required for homogenous nucleation throughout the sample. This mechanism would work best in sample where the droplets could be effectively advected throughout the sample. In our experiments, we see more interface dominated oscillations in the smaller cells and lower cooling rates, where droplet advection is favourable. In larger samples and higher cooling rates, we mostly see that the whole sample becomes turbid homogenously, which requires the system to pass the energy barrier for homogenous nucleation.rnrnOscillations, in principle, occur since the system needs to pass an energy barrier for nucleation. The height of the barrier decreases with increasing supersaturation, which in turn is from the temperature ramp applied. This gives rise to a period where the system is clear, in between the turbid periods. At certain specific cooling rates, the system can follow a path such that the start of a turbid period coincides with the vanishing of the last turbid period, thus eliminating the clear periods. This means suppressions of oscillations altogether. In fact we experimentally present a case where, at a certain cooling rate, oscillations indeed vanish. rnrnThus we find through this work that the kinetics of phase separation in polymer solution is different from that of a low molecular system; sedimentation time scales become relevant, and therefore so does the shape and size of the sample. The role of interface in initiating turbid periods also become much more prominent in this system compared to that in low molecular mixtures.rnrnIn summary, some fundamental properties in the kinetics of phase separation in binary mixtures were studied. While the first part of the work described the close interplay of the first phase separation with hydrodynamic instabilities, the second part investigated the nature and determining factors of oscillations, when the system was cooled deep into the two phase region. Both cases show how the geometry of the cell can affect the kinetics of phase separation. This study leads to further fundamental understandings of the factors contributing to the kinetics of phase separation, and to the understandings of what can be controlled and tuned in practical cases. rn