Untersuchung der Ordnung und Diffusion von Polymerdispersionen bei ihrer Verfilmung

Im Rahmen dieser Arbeit wurde die, für industrielle Applikationen sehr wichtige, Trocknung und Verfilmung von Latexdispersionen untersucht. Unter der Verfilmung wird in diesem Zusammenhang allgemein der Übergang einer Polymerdispersion in einen transparenten, mechanisch stabilen Polymerfilm während ihrer Trocknung verstanden. Für die Untersuchungen wurden schwerpunktmäßig Streumethoden verwendet. Die Untersuchungen haben gezeigt, daß die Streuung eine besonders geeignete Methode zur Untersuchung der Verfilmung ist, die in Abhängigkeit des beobachteten Streuvektorbereichs, der verwendeten Strahlung, der Probenpräparation und des resultierenden Kontrasts eine Vielzahl unterschiedlicher Informationen über die Verfilmung in ihren verschiedenen Phasen liefert. Von besonderem Interesse war es, den prinzipiellen Verlauf der Verfilmung bei den heterogen trocknenden Reinacrylatlatices zu untersuchen. Dazu wurde mit Hilfe der Röntgenultrakleinwinkelstreuung gezielt der Zustand der Partikel in den einzelnen Phasen der heterogen trocknenden Proben beobachtet. Mit Hilfe der Neutronenkleinwinkelstreuung konnte das Verhalten des Emulgators während der Verfilmung und dessen Verteilung im resultierenden Film genauer untersucht werden. Die Röntgenkleinwinkelstreuung erlaubte eine eingehende Untersuchung der Kristallisation des Emulgators im trockenen Film. Geeignete Kontrastierung durch gezielte Deuterierung ermöglichte die Untersuchung des Comonomereinflusses auf die Interdiffusion von Latexpartikeln mit Neutronenkleinwinkelstreuung. Aus den Meßergebnissen wurde ein Modell zur heterogenen Trocknung von Latexdispersionen entwickelt, das den Ablauf der Verfilmung in einem konsistenten Bild zusammenfaßt.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Diffusion of laser polarized gases in MRI

The use of Magnetic Resonance Imaging (MRI) as a diagnostic tool is increasingly employing functional contrast agents to study or contrast entire mechanisms. Contrast agents in MRI can be classified in two categories. One type of contrast agents alters the NMR signal of the protons in its surrounding, e.g. lowers the T1 relaxation time. The other type enhances the Nuclear Magnetic Resonance (NMR) signal of specific nuclei. For hyperpolarized gases the NMR signal is improved up to several orders of magnitude. However, gases have a high diffusivity which strongly influences the NMR signal strength, hence the resolution and appearance of the images. The most interesting question in spatially resolved experiments is of course the achievable resolution and contrast by controlling the diffusivity of the gas. The influence of such diffusive processes scales with the diffusion coefficient, the strength of the magnetic field gradients and the timings used in the experiment. Diffusion may not only limit the MRI resolution, but also distort the line shape of MR images for samples, which contain boundaries or diffusion barriers within the sampled space. In addition, due to the large polarization in gaseous 3He and 129Xe, spin diffusion (different from particle diffusion) could play a role in MRI experiments. It is demonstrated that for low temperatures some corrections to the NMR measured diffusion coefficient have to be done, which depend on quantum exchange effects for indistinguishable particles. Physically, if these effects can not change the spin current, they can do it indirectly by modifying the velocity distribution of the different spin states separately, so that the subsequent collisions between atoms and therefore the diffusion coefficient can eventually be affected. A detailed study of the hyperpolarized gas diffusion coefficient is presented, demonstrating the absence of spin diffusion (different from particle diffusion) influence in MRI at clinical conditions. A novel procedure is proposed to control the diffusion coefficient of gases in MRI by admixture of inert buffer gases. The experimental measured diffusion agrees with theoretical simulations. Therefore, the molecular mass and concentration enter as additional parameters into the equations that describe structural contrast. This allows for setting a structural threshold up to which structures contribute to the image. For MRI of the lung this allows for images of very small structural elements (alveoli) only, or in the other extreme, all airways can be displayed with minimal signal loss due to diffusion.

Diffusion in polymer systems studied by fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a powerful technique to determine the diffusion of fluorescence molecules in various environments. The technique is based on detecting and analyzing the fluctuation of fluorescence light emitted by fluorescence species diffusing through a small and fixed observation volume, formed by a laser focused into the sample. Because of its great potential and high versatility in addressing the diffusion and transport properties in complex systems, FCS has been successfully applied to a great variety of systems. In my thesis, I focused on the application of FCS to study the diffusion of fluorescence molecules in organic environments, especially in polymer melts. In order to examine our FCS setup and a developed measurement protocol, I first utilized FCS to measure tracer diffusion in polystyrene (PS) solutions, for which abundance data exist in the literature. I studied molecular and polymeric tracer diffusion in polystyrene solutions over a broad range of concentrations and different tracer and matrix molecular weights (Mw). Then FCS was further established to study tracer dynamics in polymer melts. In this part I investigated the diffusion of molecular tracers in linear flexible polymer melts [polydimethylsiloxane (PDMS), polyisoprene (PI)], a miscible polymer blend [PI and poly vinyl ethylene (PVE)], and star-shaped polymer [3-arm star polyisoprene (SPI)]. The effects of tracer sizes, polymer Mw, polymer types, and temperature on the diffusion coefficients of small tracers were discussed. The distinct topology of the host polymer, i.e. star polymer melt, revealed the notably different motion of the small tracer, as compared to its linear counterpart. Finally, I emphasized the advantage of the small observation volume which allowed FCS to investigate the tracer diffusions in heterogeneous systems; a swollen cross-linked PS bead and silica inverse opals, where high spatial resolution technique was required.

Diffusion maps in the Subriemannian motion group and perceptual grouping

Il presente lavoro è motivato dal problema della constituzione di unità percettive a livello della corteccia visiva primaria V1. Si studia dettagliatamente il modello geometrico di Citti-Sarti con particolare attenzione alla modellazione di fenomeni di associazione visiva. Viene studiato nel dettaglio un modello di connettività. Il contributo originale risiede nell'adattamento del metodo delle diffusion maps, recentemente introdotto da Coifman e Lafon, alla geometria subriemanniana della corteccia visiva. Vengono utilizzati strumenti di teoria del potenziale, teoria spettrale, analisi armonica in gruppi di Lie per l'approssimazione delle autofunzioni dell'operatore del calore sul gruppo dei moti rigidi del piano. Le autofunzioni sono utilizzate per l'estrazione di unità percettive nello stimolo visivo. Sono presentate prove sperimentali e originali delle capacità performanti del metodo.

Tracer diffusion at water-oil interfaces studied by fluorescence correlation spectroscopy

The adsorption of particles and surfactants at water-oil interfaces has attracted continuous attention because of its emulsion stabilizing effect and the possibility to form two-dimensional materials. Herein, I studied the interfacial diffusion of single molecules and nanoparticles at water-oil interfaces using fluorescence correlation spectroscopy. rnrnFluorescence correlation spectroscopy (FCS) is a promising technique to study diffusion of fluorescent tracers in diverse conditions. This technique monitors and analyzes the fluorescence fluctuation caused by single fluorescent tracers coming in and out of a diffraction-limited observation volume “one at a time”. Thus, this technique allows a combination of high precision, high spatial resolution and low tracer concentration. rnrnIn chapter 1, I discussed some controversial questions regarding the properties of water-hydrophobic interfaces and also introduced the current progress on the stability and dynamic of single nanoparticles at water-oil interfaces. The materials and setups I used in this thesis were summarized in chapter 2. rnrnIn chapter 3, I presented a new strategy to study the properties of water-oil interfaces. The two-dimensional diffusion of isolated molecular tracers at water/n-alkane interfaces was measured using fluorescence correlation spectroscopy. The diffusion coefficients of larger tracers with a hydrodynamic radius of 4.0 nm agreed well with the values calculated from the macroscopic viscosities of the two bulk phases. However, for small molecule tracers with hydrodynamic radii of only 1.0 and 0.6 nm, notable deviations were observed, indicating the existence of an interfacial region with a reduced effective viscosity. rnrnIn chapter 4, the interfacial diffusion of nanoparticles at water-oil interfaces was investigated using FCS. In stark contrast to the interfacial diffusion of molecular tracers, that of nanoparticles at any conditions is slower than the values calculated in accordance to the surrounding viscosity. The diffusion of nanoparticles at water-oil interfaces depended on the interfacial tension of liquid-liquid interfaces, the surface properties of nanoparticles, the particle sizes and the viscosities of surrounding liquid phases. In addition, the interfacial diffusion of nanoparticles with Janus motif is even slower than that of their symmetric counterparts. Based on the experimental results I obtained, I drew some possibilities to describe the origin of nanoparticle slowdown at water-oil interfaces.

Preconditioning strategies for the numerical solution of convection-diffusion partial differential equations

Il trattamento numerico dell'equazione di convezione-diffusione con le relative condizioni al bordo, comporta la risoluzione di sistemi lineari algebrici di grandi dimensioni in cui la matrice dei coefficienti è non simmetrica. Risolutori iterativi basati sul sottospazio di Krylov sono ampiamente utilizzati per questi sistemi lineari la cui risoluzione risulta particolarmente impegnativa nel caso di convezione dominante. In questa tesi vengono analizzate alcune strategie di precondizionamento, atte ad accelerare la convergenza di questi metodi iterativi. Vengono confrontati sperimentalmente precondizionatori molto noti come ILU e iterazioni di tipo inner-outer flessibile. Nel caso in cui i coefficienti del termine di convezione siano a variabili separabili, proponiamo una nuova strategia di precondizionamento basata sull'approssimazione, mediante equazione matriciale, dell'operatore differenziale di convezione-diffusione. L'azione di questo nuovo precondizionatore sfrutta in modo opportuno recenti risolutori efficienti per equazioni matriciali lineari. Vengono riportati numerosi esperimenti numerici per studiare la dipendenza della performance dei diversi risolutori dalla scelta del termine di convezione, e dai parametri di discretizzazione.

Speziation von Plutonium bei der Sorption und Diffusion in Opalinuston

Die vorliegende Arbeit wurde im Rahmen des BMWi-Verbundprojektes Wechselwirkung und Transport von Aktiniden im natürlichen Tongestein unter Berücksichtigung von Huminstoffen und Tonorganika – Wechselwirkung von Neptunium und Plutonium mit natürlichem Tongestein“ durchgeführt. Um die langfristige Sicherheit der nuklearen Endlager beurteilen zu können, muss eine mögliche Migration der radiotoxischen Abfälle in die Umwelt betrachtet werden. Wegen seiner langen Halbwertszeit (24000 a) leistet Pu-239 einen wesentlichen Beitrag zur Radiotoxizität abgebrannter Kernbrennstoffe in einem Endlager. Das redox-sensitive Pu tritt in Lösung unter umweltrelevanten Bedingungen in den Oxidationsstufen +III bis +VI auf und kann nebeneinander in bis zu vier Oxidationsstufen vorliegen. Tonsteinformationen werden als mögliches Wirtsgestein für Endlager hoch-radioaktiver Abfälle betrachtet. Deshalb sind ausführliche Informationen zur Mobilisierung und Immobilisierung des Pu durch/in das Grundwasser aus einem Endlager von besonderer Bedeutung. In dieser Arbeit wurden neue Erkenntnisse über die Wechselwirkung zwischen Pu und dem natürlichen Tongestein Opalinuston (OPA, Mont Terri, Schweiz) mit Hinblick auf die Endlagerung wärmeentwickelnder radioaktiver Abfälle in einem geologischen Tiefenlager gewonnen.rnDer Fokus der Arbeit lag dabei auf der Bestimmung der Speziation von Pu an der Mineraloberfläche nach Sorptions- und Diffusionsprozessen mittels verschiedener synchrotronbasierter Methoden (µ-XRF, µ-XANES/EXAFS, µ-XRD, XANES/EXAFS). rnDie Wechselwirkung zwischen Pu und OPA wurde zunächst in Batch- und Diffusionsexperimenten in Abhängigkeit verschiedener experimenteller Parameter (u.a. pH, Pu-Oxidationsstufe) untersucht. In Sorptionsexperimenten konnte gezeigt werden, dass einige Parameter (z.B. Temperatur, Huminsäure) einen deutlichen Einfluss auf die Sorption von Pu haben.rnDie Speziationsuntersuchungen wurden zum einen an Pulverproben aus Batchexperimenten und zum anderen an OPA-Dünnschliffen bzw. Diffusionsproben in Abhängigkeit verschiedener experimenteller Parameter durchgeführt. Die EXAFS-Messungen an der Pu LIII-Kante der Pulverproben ergaben, dass eine innersphäriche Sorption von Pu(IV) an Tongestein unabhängig von dem Ausgangsoxidationszustand des Plutoniums in Lösung stattgefunden hat. Durch die Kombination der ortsaufgelösten Methoden wurde erstmalig mittels μ-XRF die Verteilung von Pu und anderen in OPA enthaltenen Elementen bestimmt. µ-XANES-Spektren an Pu-Anreicherungen auf OPA-Dünnschliffen und in Diffusionsproben bestätigen, dass das weniger mobile Pu(IV) die dominierende Spezies nach den Sorptions- und Diffusionsprozessen ist. Darüber hinaus wurde zum ersten Mal ein Diffusionsprofil von Pu in OPA mittels µ-XRF gemessen. Die Speziationsuntersuchungen mittels μ-XANES zeigten, dass das eingesetzte Pu(V) entlang seines Diffusionspfades zunehmend zu Pu(IV) reduziert wird. Mit µ-XRD wurde Illit als dominierende Umgebung, in der Pu angereichert wurde, identifiziert und Siderit als eine redoxaktive Phase auftreten kann. Die Ergebnisse dieser Arbeit zeigen, dass die Sicherheit von OPA als Wirtsgestein eines Endlagers hoch-radioaktiver Abfälle positiv zu bewerten ist. rn

Diffusion in heterogeneous systems studied by laser scanning confocal microscopy and fluorescence correlation spectroscopy

Understanding and controlling the mechanism of the diffusion of small molecules, macromolecules and nanoparticles in heterogeneous environments is of paramount fundamental and technological importance. The aim of the thesis is to show, how by studying the tracer diffusion in complex systems, one can obtain information about the tracer itself, and the system where the tracer is diffusing. rnIn the first part of my thesis I will introduce the Fluorescence Correlation Spectroscopy (FCS) which is a powerful tool to investigate the diffusion of fluorescent species in various environments. By using the main advantage of FCS namely the very small probing volume (<1µm3) I was able to track the kinetics of phase separation in polymer blends at late stages by looking on the molecular tracer diffusion in individual domains of the heterogeneous structure of the blend. The phase separation process at intermediate stages was monitored with laser scanning confocal microscopy (LSCM) in real time providing images of droplet coalescence and growth. rnIn a further project described in my thesis I will show that even when the length scale of the heterogeneities becomes smaller than the FCS probing volume one can still obtain important microscopic information by studying small tracer diffusion. To do so, I will introduce a system of star shaped polymer solutions and will demonstrate that the mobility of small molecular tracers on microscopic level is nearly not affected by the transition of the polymer system to a “glassy” macroscopic state. rnIn the last part of the thesis I will introduce and describe a new stimuli responsive system which I have developed, that combines two levels of nanoporosity. The system is based on poly-N-isopropylacrylamide (PNIPAM) and silica inverse opals (iOpals), and allows controlling the diffusion of tracer molecules. rn

Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Plasmonic nanoparticles as sensors : a novel approach to quantify adsorption and diffusion kinetics

Biosensors find wide application in clinical diagnostics, bioprocess control and environmental monitoring. They should not only show high specificity and reproducibility but also a high sensitivity and stability of the signal. Therefore, I introduce a novel sensor technology based on plasmonic nanoparticles which overcomes both of these limitations. Plasmonic nanoparticles exhibit strong absorption and scattering in the visible and near-infrared spectral range. The plasmon resonance, the collective coherent oscillation mode of the conduction band electrons against the positively charged ionic lattice, is sensitive to the local environment of the particle. I monitor these changes in the resonance wavelength by a new dark-field spectroscopy technique. Due to a strong light source and a highly sensitive detector a temporal resolution in the microsecond regime is possible in combination with a high spectral stability. This opens a window to investigate dynamics on the molecular level and to gain knowledge about fundamental biological processes.rnFirst, I investigate adsorption at the non-equilibrium as well as at the equilibrium state. I show the temporal evolution of single adsorption events of fibrinogen on the surface of the sensor on a millisecond timescale. Fibrinogen is a blood plasma protein with a unique shape that plays a central role in blood coagulation and is always involved in cell-biomaterial interactions. Further, I monitor equilibrium coverage fluctuations of sodium dodecyl sulfate and demonstrate a new approach to quantify the characteristic rate constants which is independent of mass transfer interference and long term drifts of the measured signal. This method has been investigated theoretically by Monte-Carlo simulations but so far there has been no sensor technology with a sufficient signal-to-noise ratio.rnSecond, I apply plasmonic nanoparticles as sensors for the determination of diffusion coefficients. Thereby, the sensing volume of a single, immobilized nanorod is used as detection volume. When a diffusing particle enters the detection volume a shift in the resonance wavelength is introduced. As no labeling of the analyte is necessary the hydrodynamic radius and thus the diffusion properties are not altered and can be studied in their natural form. In comparison to the conventional Fluorescence Correlation Spectroscopy technique a volume reduction by a factor of 5000-10000 is reached.