Der Renormierungsgruppen-Fluß der konform-reduzierten Quantengravitation

Wir analysieren die Rolle von "Hintergrundunabhängigkeit" im Zugang der effektiven Mittelwertwirkung zur Quantengravitation. Wenn der nicht-störungstheoretische Renormierungsgruppen-(RG)-Fluß "hintergrundunabhängig" ist, muß die Vergröberung durch eine nicht spezifizierte, variable Metrik definiert werden. Die Forderung nach "Hintergrundunabhängigkeit" in der Quantengravitation führt dazu, daß die funktionale RG-Gleichung von zusätzlichen Feldern abhängt; dadurch unterscheidet sich der RG-Fluß in der Quantengravitation deutlich von dem RG-Fluß einer gewöhnlichen Quantentheorie, deren Moden-Cutoff von einer starren Metrik abhängt. Beispielsweise kann in der "hintergrundunabhängigen" Theorie ein Nicht-Gauß'scher Fixpunkt existieren, obwohl die entsprechende gewöhnliche Quantentheorie keinen solchen entwickelt. Wir untersuchen die Bedeutung dieses universellen, rein kinematischen Effektes, indem wir den RG-Fluß der Quanten-Einstein-Gravitation (QEG) in einem "konform-reduzierten" Zusammenhang untersuchen, in dem wir nur den konformen Faktor der Metrik quantisieren. Alle anderen Freiheitsgrade der Metrik werden vernachlässigt. Die konforme Reduktion der Einstein-Hilbert-Trunkierung zeigt exakt dieselben qualitativen Eigenschaften wie in der vollen Einstein-Hilbert-Trunkierung. Insbesondere besitzt sie einen Nicht-Gauß'schen Fixpunkt, der notwendig ist, damit die Gravitation asymptotisch sicher ist. Ohne diese zusätzlichen Feldabhängigkeiten ist der RG-Fluß dieser Trunkierung der einer gewöhnlichen $phi^4$-Theorie. Die lokale Potentialnäherung für den konformen Faktor verallgemeinert den RG-Fluß in der Quantengravitation auf einen unendlich-dimensionalen Theorienraum. Auch hier finden wir sowohl einen Gauß'schen als auch einen Nicht-Gauß'schen Fixpunkt, was weitere Hinweise dafür liefert, daß die Quantengravitation asymptotisch sicher ist. Das Analogon der Metrik-Invarianten, die proportional zur dritten Potenz der Krümmung ist und die die störungstheoretische Renormierbarkeit zerstört, ist unproblematisch für die asymptotische Sicherheit der konform-reduzierten Theorie. Wir berechnen die Skalenfelder und -imensionen der beiden Fixpunkte explizit und diskutieren mögliche Einflüsse auf die Vorhersagekraft der Theorie. Da der RG-Fluß von der Topologie der zugrundeliegenden Raumzeit abhängt, diskutieren wir sowohl den flachen Raum als auch die Sphäre. Wir lösen die Flußgleichung für das Potential numerisch und erhalten Beispiele für RG-Trajektorien, die innerhalb der Ultraviolett-kritischen Mannigfaltigkeit des Nicht-Gauß'schen Fixpunktes liegen. Die Quantentheorien, die durch einige solcher Trajektorien definiert sind, zeigen einen Phasenübergang von der bekannten (Niederenergie-) Phase der Gravitation mit spontan gebrochener Diffeomorphismus-Invarianz zu einer neuen Phase von ungebrochener Diffeomorphismus-Invarianz. Diese Hochenergie-Phase ist durch einen verschwindenden Metrik-Erwartungswert charakterisiert.

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

Microstructure of epitaxial thin films of the ferromagnetic shape memory alloy Ni 2 MnGa

Gegenstand dieser Arbeit ist die Präparation und die ausführliche Charakterisierung epitaktischer Dünnschicht-Proben der Heusler Verbindung Ni2MnGa. Diese intermetallische Verbindung zeigt einen magnetischen Formgedächtnis-Effekt (MFG), der sowohl im Bezug auf mögliche Anwendungen, als auch im Kontext der Grundlagenforschung äußerst interessant ist. In Einkristallen nahe der Stöchiometrie Ni2MnGa wurden riesige magnetfeldinduzierte Dehnungen von bis zu 10 % nachgewiesen. Der zugrundeliegende Mechanismus basiert auf einer Umverteilung von kristallographischen Zwillings-Varianten, die eine tetragonale oder orthorhombische Symmetrie besitzen. Unter dem Einfluss des Magnetfeldes bewegen sich die Zwillingsgrenzen durch den Kristall, was eine makroskopische Formänderung mit sich bringt. Die somit erzeugten reversiblen Längenänderungen können mit hoher Frequenz geschaltet werden, was Ni2MnGa zu einem vielversprechenden Aktuatorwerkstoff macht. rnDa der Effekt auf einem intrinsischen Prozess beruht, eignen sich Bauteile aus MFG Legierungen zur Integration in Mikrosystemen (z.B. im Bereich der Mikrofluidik). rnrnBislang konnten große magnetfeldinduzierte Dehnungen nur für Einkristalle und Polykristalle mit hoher Porosität („foams") nachgewiesen werden. Um den Effekt für Anwendungen nutzbar zu machen, werden allerdings Konzepte zur Miniaturisierung benötigt. Eine Möglichkeit bieten epitaktische dünne Filme, die im Rahmen dieser Arbeit hergestellt und untersucht werden sollen. Im Fokus stehen dabei die Optimierung der Herstellungsparameter, sowie die Präparation von freitragenden Schichten. Zudem werden verschiedene Konzepte zur Herstellung freistehender Mikrostrukturen erprobt. Mittels Röntgendiffraktometrie konnte die komplizierte Kristallstruktur für verschiedene Wachstumsrichtungen verstanden und die genaue Verteilung der Zwillingsvarianten aufgedeckt werden. In Verbindung mit Mikroskopie-Methoden konnte so die Zwillingsstruktur auf verschiedenen Längenskalen geklärt werden. Die Ergebnisse erklären das Ausbleiben des MFG Effekts in den Proben mit (100) Orientierung. Andererseits wurde für Schichten mit (110) Wachstum eine vielversprechende Mikrostruktur entdeckt, die einen guten Ausgangspunkt für weitere Untersuchungen bietet.rnDurch die spezielle Geometrie der Proben war es möglich, Spektroskopie-Experimente in Transmission durchzuführen. Die Ergebnisse stellen den ersten experimentellen Nachweis der Änderungen in der elektronischen Struktur einer metallischen Verbindung während des martensitischen Phasenübergangs dar. Durch Messen des magnetischen Zirkulardichroismus in der Röntgenabsorption konnten quantitative Aussagen über die magnetischen Momente von Ni und Mn getroffen werden. Die Methode erlaubt überdies die Beiträge von Spin- und Bahn-Moment separat zu bestimmen. Durch winkelabhängige Messungen gelang es, die mikroskopische Ursache der magnetischen Anisotropie aufzuklären. Diese Ergebnisse tragen wesentlich zum Verständnis der komplexen magnetischen und strukturellen Eigenschaften von Ni2MnGa bei.rn

Smart magnetic dispersions - from switchable release to well-defined hybrid nanofibers

The synthesis, characterization and application of aqueous dispersions of superparamagnetic/polymer hybrid nanoparticles and capsules is described. Implementation of the superparamagnetic moiety into the polymer matrix enables a response of the nanomaterials towards an external magnetic field. Application of the external field is used for two main purposes: i) As heat generator, when an alternating magnetic field is applied. ii) As structuring agent to self-assemble superparamagnetic nanoparticles in the external field.rnIn the first part, superparamagnetic nanoparticles were used as heat generators in order to achieve a magnetic field induced release of an active compound from nanocontainers. To achieve such a release in remote-controlled fashion, the encapsulation of superparamagnetic nanoparticles into polymer nanocapsules was combined with the integration of a thermolabile compound into the shell of the nanocontainers. The magnetic nanoparticles acted as generators for heat, which decomposed the thermolabile compound. Pores were created in the degrading shell and an active substance was released.rn Additionally, the self-assembly of polymer nanoparticles, which were labeled with a superparamagnetic moiety as structuring agent, could be demonstrated. A combination of a magnetic field induced self-assembly and a sintering of neighboring particles upon an increase in temperature above the glass transition temperature of the polymer was used to form stable architectures. Various structures with tunable periodicity could be obtained ranging from smooth linear nanofibers to zigzag fibers. Besides solely creating linear architectures, the frugal process additionally allowed the creation of arrangements in analogy to more complex polymer architectures: By the introduction of defined junction points, the generation of branched structures and networks was demonstrated. Additionally, by tailoring the interaction of differently sized particles, the preparation of nanoparticle arrangements in statistical or block copolymer fashion was shown. Moreover, a reversible linear assembly and linkage of the nanoparticles was demonstrated following a lock/unlock mechanism. Therefore, the particles were locked in their linear assembly by a stable iron(III) hydroxamato-complex and unlocked by addition of a reducing agent and formation of a less stable iron(II)-complex.Further, in various projects with collaboration partners, nanoparticles and nanocapsules were labeled with a superparamagnetic moiety for their use as contrast agents in magnetic resonance imaging or as magnetically separable dispersions.

Multifunctional polyether architectures : versatile materials for surface attachment and functionalization

Chapter 1 of this thesis comprises a review of polyether polyamines, i.e., combinations of polyether scaffolds with polymers bearing multiple amino moieties. Focus is laid on controlled or living polymerization methods. Furthermore, fields in which the combination of cationic, complexing, and pH-sensitive properties of the polyamines and biocompatibility and water-solubility of polyethers promise enormous potential are presented. Applications include stimuli-responsive polymers with a lower critical solution temperature (LCST) and/or the ability to gel, preparation of shell cross-linked (SCL) micelles, gene transfection, and surface functionalization.rnIn Chapter 2, multiaminofunctional polyethers relying on the class of glycidyl amine comonomers for anionic ring-opening polymerization (AROP) are presented. In Chapter 2.1, N,N-diethyl glycidyl amine (DEGA) is introduced for copolymerization with ethylene oxide (EO). Copolymer microstructure is assessed using online 1H NMR kinetics, 13C NMR triad sequence analysis, and differential scanning calorimetry (DSC). The concurrent copolymerization of EO and DEGA is found to result in macromolecules with a gradient structure. The LCSTs of the resulting copolymers can be tailored by adjusting DEGA fraction or pH value of the environment. Quaternization of the amino moieties by methylation results in polyelectrolytes. Block copolymers are used for PEGylated gold nanoparticle formation. Chapter 2.2 deals with a glycidyl amine monomer with a removable protecting group at the amino moiety, for liberation of primary amines at the polyether backbone, which is N,N-diallyl glycidyl amine (DAGA). Its allyl groups are able to withstand the harsh basic conditions of AROP, but can be cleaved homogeneously after polymerization. Gradient as well as block copolymers poly(ethylene glycol)-PDAGA (PEG-PDAGA) are obtained. They are analyzed regarding their microstructure, LCST behavior, and cleavage of the protecting groups. rnChapter 3 describes applications of multi(amino)functional polyethers for functionalization of inorganic surfaces. In Chapter 3.1, they are combined with an acetal-protected catechol initiator, leading to well-defined PEG and heteromultifunctional PEG analogues. After deprotection, multifunctional PEG ligands capable of attaching to a variety of metal oxide surfaces are obtained. In a cooperative project with the Department of Inorganic and Analytical Chemistry, JGU Mainz, their potential is demonstrated on MnO nanoparticles, which are promising candidates as T1 contrast agents in magnetic resonance imaging. The MnO nanoparticles are solubilized in aqueous solution upon ligand exchange. In Chapter 3.2, a concept for passivation and functionalization of glass surfaces towards gold nanorods is developed. Quaternized mPEG-b-PqDEGA diblock copolymers are attached to negatively charged glass surfaces via the cationic PqDEGA blocks. The PEG blocks are able to suppress gold nanorod adsorption on the glass in the flow cell, analyzed by dark field microscopy.rnChapter 4 highlights a straightforward approach to poly(ethylene glycol) macrocycles. Starting from commercially available bishydroxy-PEG, cyclic polymers are available by perallylation and ring-closing metathesis in presence of Grubbs’ catalyst. Purification of cyclic PEG is carried out using α-cyclodextrin. This cyclic sugar derivative forms inclusion complexes with remaining unreacted linear PEG in aqueous solution. Simple filtration leads to pure macrocycles, as evidenced by SEC and MALDI-ToF mass spectrometry. Cyclic polymers from biocompatible precursors are interesting materials regarding their increased blood circulation time compared to their linear counterparts.rnIn the Appendix, A.1, a study of the temperature-dependent water-solubility of polyether copolymers is presented. Macroscopic cloud points, determined by turbidimetry, are compared with microscopic aggregation phenomena, monitored by continuous wave electron paramagnetic resonance (CW EPR) spectroscopy in presence of the amphiphilic spin probe and model drug (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO). These thermoresponsive polymers are promising candidates for molecular transport applications. The same techniques are applied in Chapter A.2 to explore the pH-dependence of the cloud points of PEG-PDEGA copolymers in further detail. It is shown that the introduction of amino moieties at the PEG backbone allows for precise manipulation of complex phase transition modes. In Chapter A.3, multi-hydroxyfunctional polysilanes are presented. They are obtained via copolymerization of the acetal-protected dichloro(isopropylidene glyceryl propyl ether)methylsilane monomer. The hydroxyl groups are liberated through acidic work-up, yielding versatile access to new multifunctional polysilanes.

Integration von Heizern in thermotrope flüssigkristalline Elastomer-Aktoren und deren Anwendung beim technischen Nachbau eines menschlichen Auges

Flüssigkristalline Elastomere (LCE) zeigen eine reversible Kontraktion und werden in der Literatur auch als „künstliche Muskeln“ bezeichnet. In dieser Arbeit werden sie mit einem integrierten Heizer versehen, um eine schnelle und präzise Ansteuerung zu ermöglichen. Anschließend werden diese als Aktoren zur Realisierung eines technischen Nachbaus des menschlichen Auges verwendet. rnDas einzigartige Verhalten der flüssigkristallinen Elastomere beruht auf der Kombination der Entropie Elastizität des Elastomers mit der Selbstorganisation der flüssigkristallinen Einheiten (Mesogene). Diese beiden Eigenschaften ermöglichen eine reversible, makroskopische Verformung beim Phasenübergang des Flüssigkristalls in die isotrope Phase. Hierbei ist es wichtig eine homogene Orientierung der Mesogene zu erzeugen, was in dieser Arbeit durch ein Magnetfeld erreicht wird. Da es sich um ein thermotropes flüssigkristallines Elastomer handelt, werden in dieser Arbeit zwei Ansätze vorgestellt, um den LCE intern zu heizen. Zum einen werden Kohlenstoffnanoröhren integriert, um diese über Strahlung oder Strom zu heizen und zum anderen wird ein flexibler Heizdraht integriert, welcher ebenfalls über Strom geheizt wird. rnUm den technischen Nachbau des menschlichen Auges zu realisieren, ist die Herstellung einer flüssigkristallinen Iris gezeigt. Hierzu wird ein radiales Magnetfeld aufgebaut, welches eine radiale Orientierung des Mesogene ermöglicht, wodurch wiederum eine radiale Kontraktion ermöglicht wird. Außerdem sind zwei Konzepte vorgestellt, um eine Elastomer Linse zu verformen. Zum einen wird diese mit einem ringförmigen LCE auseinandergezogen und somit abgeflacht. Zum anderen sind acht Aktoren über Anker an einer Linse angebracht, welche ebenfalls eine Vergrößerung der Linse bewirken. In beiden Fällen werden LCE mit dem zuvor präsentierten integrierten Heizdraht verwendet. Abschließend ist das Zusammensetzen des technische Nachbaus des menschlichen Auges dargestellt, sowie Aufnahmen, welche mit diesem erzeugt wurden.