We consider a system of infinitely many hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional Stochastic Differential Equation with a local time term. We prove that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.

New ABC triblock copolymers were synthesized by controlled free-radical polymerization via Reversible Addition-Fragmentation chain Transfer (RAFT). Compared to amphiphilic diblock copolymers, the prepared materials formed more complex self-assembled structures in water due to three different functional units. Two strategies were followed: The first approach relied on double-thermoresponsive triblock copolymers exhibiting Lower Critical Solution Temperature (LCST) behavior in water. While the first phase transition triggers the self-assembly of triblock copolymers upon heating, the second one allows to modify the self-assembled state. The stepwise self-assembly was followed by turbidimetry, dynamic light scattering (DLS) and 1H NMR spectroscopy as these methods reflect the behavior on the macroscopic, mesoscopic and molecular scale. Although the first phase transition could be easily monitored due to the onset of self-assembly, it was difficult to identify the second phase transition unambiguously as the changes are either marginal or coincide with the slow response of the self-assembled system to relatively fast changes of temperature. The second approach towards advanced polymeric micelles exploited the thermodynamic incompatibility of “triphilic” block copolymers – namely polymers bearing a hydrophilic, a lipophilic and a fluorophilic block – as the driving force for self-assembly in water. The self-assembly of these polymers in water produced polymeric micelles comprising a hydrophilic corona and a microphase-separated micellar core with lipophilic and fluorophilic domains – so called multi-compartment micelles. The association of triblock copolymers in water was studied by 1H NMR spectroscopy, DLS and cryogenic transmission electron microscopy (cryo-TEM). Direct imaging of the polymeric micelles in solution by cryo-TEM revealed different morphologies depending on the block sequence and the preparation conditions. While polymers with the sequence hydrophilic-lipophilic-fluorophilic built core-shell-corona micelles with the core being the fluorinated compartment, block copolymers with the hydrophilic block in the middle formed spherical micelles where single or multiple fluorinated domains “float” as disks on the surface of the lipophilic core. Increasing the temperature during micelle preparation or annealing of the aqueous solutions after preparation at higher temperatures induced occasionally a change of the micelle morphology or the particle size distribution. By RAFT polymerization not only the desired polymeric architectures could be realized, but the technique provided in addition a precious tool for molar mass characterization. The thiocarbonylthio moieties, which are present at the chain ends of polymers prepared by RAFT, absorb light in the UV and visible range and were employed for end-group analysis by UV-vis spectroscopy. A variety of dithiobenzoate and trithiocarbonate RAFT agents with differently substituted initiating R groups were synthesized. The investigation of their absorption characteristics showed that the intensity of the absorptions depends sensitively on the substitution pattern next to the thiocarbonylthio moiety and on the solvent polarity. According to these results, the conditions for a reliable and convenient end-group analysis by UV-vis spectroscopy were optimized. As end-group analysis by UV-vis spectroscopy is insensitive to the potential association of polymers in solution, it was advantageously exploited for the molar mass characterization of the prepared amphiphilic block copolymers. / Die Arbeit widmet sich der Synthese von neuen amphiphilen ternären "ABC" Block-Copolymeren und der Untersuchung ihrer Selbstorganisation zu mizellaren Überstrukturen in wässriger Lösung. Die Block-Copolymere wurden durch kontrollierte radikalische Polymerisation mittels des sogenannten „RAFT“ Prozesses (radical addition fragmentation chain transfer) hergestellt. Neben der Realisierung der gewünschten Polymerarchitekturen erlaubte es die Methode, die Molmassen der Polymere durch Endgruppenanalyse zu bestimmen. Die Kettenenden der Polymere tragen infolge des Polymerisationsmechanismus’ definierte Funktionalitäten, welche UV- und sichtbares Licht absorbieren und somit durch UV-vis-Spektroskopie quantifizierbar sind. Das Absorptionsverhalten der Endgruppen wurde untersucht und die UV-vis-Endgruppenanalyse optimiert. Es zeigte sich, dass die Vorteile der Methode ihre generelle Anwendbarkeit und ihre Unempfindlichkeit gegenüber der Assoziation von Polymeren in Lösung sind. Aufgrund ihrer drei unterschiedlichen Blöcke bilden die synthetisierten ABC Triblockcopolymere komplexere selbstorganisierte Strukturen als die bisher üblichen Diblockcopolymere. Die Triebkraft für ihre Selbstorganisation in wässriger Lösung ist im wesentlichen der hydrophobe Effekt. Es wurden zwei unterschiedliche Ansätze verfolgt: Zum einen wurden doppelt-schaltbare Triblockcopolymere hergestellt, von denen ein Block permanent wasserlöslich ist, während die anderen Blöcke jeweils eine untere Entmischungstemperatur in wässriger Lösung aufweisen. Diese Blöcke „schalten“ beim Erwärmen von hydrophil auf hydrophob. Oberhalb des ersten Phasenübergangs - bei der niedrigeren Entmischungstemperatur - assoziieren die Makromoleküle und bilden Polymermizellen im Nanometerbereich. Beim weiteren Erwärmen „schaltet“ auch der zweite Block und modifiziert den selbstorganisierten Zustand, während der permanent wasserlösliche Block für die Stabilisierung der Aggregate sorgt. Die Assoziation der Block-Copolymere ist nach Abkühlen der wässrigen Lösung vollständig reversibel. Die stufenweise Selbstorganisation wurde mit Hilfe von Turbidimetrie, Dynamischer Lichtstreuung (DLS) und 1H-NMR-Spektroskopie untersucht, da diese Methoden das Verhalten auf der makroskopischen, mesoskopischen und molekularen Skala widerspiegeln. Obwohl der einsetzende Selbstorganisationsprozess problemlos zu detektieren war, konnten die Veränderungen infolge des zweiten Phasenübergang nicht immer eindeutig identifiziert werden, da sie zum Teil mit der langsamen Reaktion des Systems auf relativ schnelle Temperaturänderungen zusammenfielen. Außerdem hängt die Aggregatbildung nicht nur sensibel von der detaillierten Polymerarchitektur ab, sondern unterliegt auch teilweise einer kinetischen Kontrolle. Der zweite Ansatz zu komplexeren Polymermizellen basierte auf der Inkompatibilität „triphiler“ Blockcopolymere als Triebkraft für die Selbstorganisation. Das heißt, die Block-Copolymere bestehen aus einem hydrophilen, einen lipophilen und einen fluorophilen (Fluorkohlenwasserstoff-liebenden) Teil, die jeweils miteinander unverträglich sind. Die Polymere assoziierten in Wasser zu Polymermizellen mit einer hydrophilen Korona und einem unterstrukturierten Mizellkern mit separaten Kohlenwasserstoff- und Fluorkohlenwasserstoff-Domänen – sogenannten Multi-Kompartiment-Mizellen. Die Assoziation der Triblock-Copolymere wurde mit 1H-NMR-Spektroskopie, DLS und cryogener Transmissionselektronenmikroskopie (cryo-TEM) untersucht. Die unmittelbare Abbildung der Polymermizellen in Lösung mittels cryo-TEM enthüllte unterschiedliche Morphologien in Abhängigkeit von der Blocksequenz und den Präparationsbedingungen. Während Polymere mit der Blocksequenz hydrophil-lipophil-fluorophil Kern-Schale-Korona-Mizellen mit der Fluor-Domäne als Kern bildeten, wurde eine neue, unerwartete Mizellmorphologie für die Polymere mit dem hydrophilen Block in der Mitte gefunden: Einzelne oder mehrere Fluordomänen “schwimmen” als Scheiben auf dem lipophilen Kern. Die beobachteten Morphologien sind weitgehend stabil, unterliegen aber ebenfalls - zumindest teilweise - einer kinetischen Kontrolle. So führten erhöhte Temperaturen während der Mizellpräparation gelegentlich zu einer Veränderung der Mizellmorphologie oder Partikelgröße.

És difícil dibuixar una frontera, dins la Teoria de Sistemas Dinàmics, entre lleis de conservació i simetries doncs, sovint, les seves característiques es confonen. Un clar exemple d'aquest fenómen el constitueixen els sistemes Hamiltonians i els sistemes reversibles.Breument, un sistema dinàmic es diu temps-reversible (o, per nosaltres, simplement reversible) si és invariant sota l'acció d'un difeomorfisme involutiu a l'espai i una inversió en el sentit del temps. és en aquest marc on cal situar aquesta memòria. Concretament, ens centrem en dos punts molt particulars: la Teoria de Formes Normals i el fenómen del trencament de separatrius, tots dos introduïts per Poincaré a la seva tesi (1890).Respecte al primer d'aquests punts, en aquesta tesi s'introdueix el concepte de Pseudo Forma Normal (breument PNF), inspirat en idees d'en Moser, i que permet transformar, sota certes hipotesis, un sistema analític en un d'equivalent d'aspecte el més simple possible. Aquesta PNF és una generalització de la coneguda Forma Normal de Birkhoff amb la qual coincideix si el sistema considerat és Hamiltonià o reversible. Com a conseqüència, s'obté, en determinats casos, l'equivalència local entre aquests dos tipus de sistemes. Aquesta PNF pot esdevenir una eina útil per estudiar la dinàmica d'un sistema analític a l'entorn d'un equilibri (un punt, una òrbita periòdica o un tor).El segon punt, l'escissió de separatrius, fa referència a l'intersecció transversal de varietats invariants procedent del trencament d'una certa connexió homoclínica a l'afegir al sistema una petita pertorbació. Un dels motius d'interés sobre aquest fenòmen és que és un dels principals causants de comportament estocàstic en sistemes Hamiltonians.Un problema relacionat amb aquest trencament de separatrius és el de mesurar-lo, sigui a partir del càlcul de l'angle amb el que es troben aquestes varietats per primer cop, per l'àrea que tanquen entre elles, etc. El mètode habitualment utilitzat per a estimar-lo és l'anomenat mètode de Poincaré-Melnikov. Malhauradament, si la pertorbació és ràpidament oscil-latòria els termes que proporciona aquest mètode són exponencialment petits en el paràmetre pertorbador, fet que dificulta el seu càlcul. En aquesta tesi s'ha demostrat, tal i com passa en el cas Hamiltonià, que en el cas d'un sistema reversible, respecte a una involució lineal, 2-dimensional i pertorbat de manera ràpidament periòdica i reversible, el mètode de Poincaré-Melnikov és correcte i dóna en primer ordre l'anomenada funció de Melnikov. / It is difficult, in the Theory of Dynamical Systems, to draw a boundary line between conservation laws and symmetries because often their effects on the dynamics are very similar. This is the case of the Hamiltonian and the Reversible systems.Briefly, a dynamical system is called time-reversible (or, simply, reversible) if it is invariant under the action of an involutive spatial diffeomorphism and a reversion in time's arrow. This is the frame where this work must be placed. Precisely, we focus our attention in two particular points: the Theory of Normal Forms and the phenomenon of the splitting of separatrices, both introduced by Poincare in his thesis (1890).Regarding the first one of this topics, we introduce the concept of Pseudo-normal Form (PNF in short). It comes from ideas of Moser and allows to transform, under suitable conditions, an analytic system around an equilibrium in another equivalent one having a quite simple form. This PNF is a generalization of the celebrated Birkhoff Normal Form and both coincide if the system is Hamiltonian or reversible. Consequently, the local equivalence between both types of systems is derived in some cases. This PNF can become a useful tool to study the dynamics of an analytic system in a neighborhood of an equilibrium (a fixed point, a periodic orbit or a torus).The second topic, the splitting of separatrices, is related to the transversal intersection of invariant manifolds derived from the splitting of a given homoclinic connection when some small perturbation is considered. One of the reasons that makes this phenomenon interesting is that it seems to be one of the main causes of the stochastic behavior in Hamiltonian systems.One problem related to this splitting of separatrices becomes to measure it, studying, for instance, some angle the form when they meet for the first time, the area of the first lobe, etc. The standard method to estimate this size is the celebrated Poincaré-Melnikov method. Unfortunately, if the perturbation oscillates rapidly the terms provided by this method are exponentially small in the perturbation parameter, and this fact makes this computation more involved. In this work we prove, like it happens in the Hamiltonian case, that in the case of a 2-dimensional analytic reversible system (reversible with respect to a linear spatial involution) perturbed by a rapidly periodic reversible perturbation, the Poincaré-Melnikov method works and it provides, at first order, the well known Melnikov Function.

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The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientific fields such as economics, finance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.

We develop, characterize, and apply novel solvent systems for enhanced separations. The field of separations has long been explored by chemical engineers. One way to optimize separations is through solvent manipulation. Through molecular design, smart solvents can be created which accomplish this task. Smart solvents undergo step or gradual changes in properties when activated by a stimulus. These property changes enable unique chemistry and separations. This thesis explores the application of two different types of smart solvents: switchable and tunable solvents. First we show that a neutral liquid can react with carbon dioxide and be switched into an ionic liquid which can then be thermally reversed back to its molecular form. Each form that the solvent takes has unique properties that can be structurally tuned to span a large range. We also look at a tunable solvent system based on polyethylene glycol/dioxane that is initially homogeneous, but induced to a heterogeneous system through carbon dioxide pressurization. Finally, we look at the advantage of using carbon dioxide as a co-solvent that is easily removed post-reaction for the grafting of silanes onto polyolefin backbones.

Novel solvents utilizing a reversible CO₂ induced property switch are presented. The synthetic procedure for designing the solvents is discussed, along with detailed characterizations on both solvent forms to serve as a tool for optimal solvent identification as well as future solvent design. A reflectance infrared spectroscopic technique is introduced to allow for the examination of CO₂ and solvent composition under high pressures and temperatures. The magnitude of solvent property changes afforded by this "switch" creates opportunities for sustainable processing; discussed are the application to coupling reactions and separations, and CO₂ capture. The switchable solvents are shown to serve as effective media for running reactions, with the switch providing facile recovery of products and catalysts for solvent recycling. Lastly, the switch itself is exploited to provide for the separation of CO₂ from low partial pressure feed streams, and structure-property relationships were successfully used to develop next generation materials with enhanced absorption capacities. The viscosity of the solvents, as a function of temperature and composition, is also presented.

The thermal degradation of polyvinyl chloride (PVC) is a significant processing challenge which can lead to deleterious mechanical and optical properties in a wide range of products. Synergetic studies on PVC model compounds and blends of bulk PVC provide unique insights into the thermal degradation and stabilization pathways in the presence of common additives. Model PVC compounds were selected to replicate specific defects (e.g., allylic, vicinal and tertiary) and tacticity (i.e., utilizing stereochemistry to investigate tacticity) commonly found in PVC. Model studies were conducted neat (solvent-free) with metal carboxylates. Experimental results highlight that the allylic and tertiary defects are more reactive than pristine PVC and isotactic sites are more reactive than their syndiotactic counterparts. Zinc stearate was found to act not in the role of substituent, but as a Lewis acid by facilitating dehydrochlorination of labile chlorides. This prevents the accumulation of hydrogen chloride and autocatalytic chain unzipping. In contrast, calcium stearate delayed the formation of zinc chloride, a much stronger Lewis acid than zinc stearate, through an ion exchange process to form calcium chloride. Thermal weight loss studies using blends of bulk PVC proved critical in transferring mechanistic insights into the context of a polymeric matrix. Post-combustion carbon capture has traditionally involved the use of aqueous alkanol amine solutions. The regeneration of such systems, however, can be costly and energy intensive. We have developed an alternative system utilizing silylated alkylamines to reversibly capture CO2 under near ambient conditions. The silyl amines developed capture CO2 through chemical reaction to form reversible ionic liquids (RevIL). RevILs utilize no added water and are tunable by molecular design allowing us to influence industrially relevant carbon capture properties such as viscosity, temperature of reversal, and enthalpy of regeneration, while maximizing overall CO2 capture capacity. We demonstrate a strong structure-property relationship among the silyl amines where minor structural modifications lead to significant changes in the bulk properties of the RevIL. Amine containing substrates are important building blocks for a variety of biological and pharmaceutical compounds. However, application of the otherwise versatile Suzuki reaction to these substrates has proved challenging due to either ligation of the amine to the palladium or to electronic effects slowing the oxidative addition step. Conventional methods to overcome these challenges involve protection-deprotection strategies or the use of designer ligands to facilitate reaction. We have shown that application of CO2 pressure and adjusting the water content of the reaction system facilitate the Suzuki coupling of 4-amino-2-halopyridines in high yield with the simple Pd(TPP)2Cl2 catalyst. The protocol was expanded to 2-halopyridines. The results of these investigations will be discussed.

This work reports an investigation of colloidal suspensions during sedimentation in what is known as the intermediate concentration range; one notoriously difficult to study. Two materials were examined: titanium dioxide P25 nanoparticles and magnesium hydroxide. The characterisation of these materials highlighted their high tendency to form aggregates under certain conditions. By the use of laser diffraction, measurements of the cluster size were conducted at under various conditions of shear. The use of sonication energy suggested the identification and classification of two classes of clusters related to their strength: high strength , and low strength clusters. A mathematical model which considered cluster formation and the occurrence of breakage predicted the aggregation and disaggregation kinetics. The approach was based on cluster-cluster interactions rather than particle-particle interactions. The results obtained by particle size analysis were compared with the size obtained using permeability analysis and settling velocity. In both cases the calculated sizes were comparable with the data obtained from size analysis; however, for magnesium hydroxide the predicted cluster size was a little higher and this may be due to the formation of channels giving faster settling. For the titanium dioxide it was noticeable that different mixing strategies exhibited different cluster size, network formation and settling behaviour. Finally, a novel modelling approach based on the presence of clusters rather than particles is presented. It is a combined model which considers the settling curve divided into two zones: a zone below the gel point modelled by a Kynch type approach and a zone above the gel point modelled by consolidation theory. This combined approach was only applicable to the settling data of titanium dioxide, where the settling data encompassed the gel point and the gel point could be identified by consideration of the Richardson and Zaki plots. For magnesium hydroxide, only the consolidation model was needed as all the initial settling concentrations were above the gel point.

Recently, researchers have been interested in reversible computing because of its ability to dissipate nearly zero heat and because of its applications in quantum computing and low power VLSI design. Synthesis and testing are two important areas of reversible logic. The thesis first presents an approach for the synthesis of reversible circuits from the exclusive- OR sum-of-products (ESOP) representation of functions, which makes better use of shared functionality among multiple outputs, resulting in up to 75% minimization of quantum cost compared to the previous approach. This thesis also investigates the previous work on constructing the online testable circuits and points out some design issues. A simple approach for online fault detection is proposed for a particular type of ESOP-based reversible circuit, which is also extended for any type of Toffoli circuits. The proposed online testable designs not only address the problems of the previous designs but also achieve significant improvements of up to 78% and 99% in terms of quantum cost and garbage outputs, respectively. / xii, 82 leaves : ill. ; 29 cm