A molecular dynamics study of the influence of chain branching on the properties of polymer systems

Die vorliegende Arbeit beschäftigt sich mit dem Einfluß von Kettenverzweigungen unterschiedlicher Topologien auf die statischen Eigenschaften von Polymeren. Diese Untersuchungen werden mit Hilfe von Monte-Carlo- und Molekular-Dynamik-Simulationen durchgeführt.Zunächst werden einige theoretische Konzepte und Modelle eingeführt, welche die Beschreibung von Polymerketten auf mesoskopischen Längenskalen gestatten. Es werden wichtige Bestimmungsgrößen eingeführt und erläutert, welche zur quantitativen Charakterisierung von Verzweigungsstrukturen bei Polymeren geeignet sind. Es wird ebenso auf die verwendeten Optimierungstechniken eingegangen, die bei der Implementierung des Computerprogrammes Verwendung fanden. Untersucht werden neben linearen Polymerketten unterschiedliche Topolgien -Sternpolymere mit variabler Armzahl, Übergang von Sternpolymeren zu linearen Polymeren, Ketten mit variabler Zahl von Seitenketten, reguläre Dendrimere und hyperverzweigte Strukturen - in Abhängigkeit von der Lösungsmittelqualität. Es wird zunächst eine gründliche Analyse des verwendeten Simulationsmodells an sehr langen linearen Einzelketten vorgenommen. Die Skalierungseigenschaften der linearen Ketten werden untersucht in dem gesamten Lösungsmittelbereich vom guten Lösungsmittel bis hin zu weitgehend kollabierten Ketten im schlechten Lösungsmittel. Ein wichtiges Ergebnis dieser Arbeit ist die Bestätigung der Korrekturen zum Skalenverhalten des hydrodynamischen Radius Rh. Dieses Ergebnis war möglich aufgrund der großen gewählten Kettenlängen und der hohen Qualität der erhaltenen Daten in dieser Arbeit, insbesondere bei den linearen ketten, und es steht im Widerspruch zu vielen bisherigen Simulations-Studien und experimentellen Arbeiten. Diese Korrekturen zum Skalenverhalten wurden nicht nur für die linearen Ketten, sondern auch für Sternpolymere mit unterchiedlicher Armzahl gezeigt. Für lineare Ketten wird der Einfluß von Polydispersität untersucht.Es wird gezeigt, daß eine eindeutige Abbildung von Längenskalen zwischen Simulationsmodell und Experiment nicht möglich ist, da die zu diesem Zweck verwendete dimensionslose Größe eine zu schwache Abhängigkeit von der Polymerisation der Ketten besitzt. Ein Vergleich von Simulationsdaten mit industriellem Low-Density-Polyäthylen(LDPE) zeigt, daß LDPE in Form von stark verzweigten Ketten vorliegt.Für reguläre Dendrimere konnte ein hochgradiges Zurückfalten der Arme in die innere Kernregion nachgewiesen werden.

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.

Extended arm polyphenylene dendrimers

In order to eliminate the de Gennes packing problem, which usually limits the attainable size of dendrimers, a new branching unit containing para-tetraphenylene ethynyl arms has been synthesized and utilized in the preparation of dendrimers of the Müllen type. The divergent principle of synthesis, based on the Dilthey reaction, could be carried up to sixth generation which contains 2776 benzene rings and possesses a diameter in the 27 nm range ("exploded dendrimer"). Monodispersity and dimensions of this and the lower generation species have been studied by MALDI-TOF MS (including the very recent superconducting tunnel junction detector), by size-exclusion chromatography, dynamic light scattering, transmission electron microscopy, and atomic force microscopy. Interesting features, apart from the huge dimension, are the low density and high porosity of these giant molecules which cause extensive aggregation in the gas phase, flattening on solid support (AFM) and the ready incorporation of guest molecules in the condensed phase. Since the synthesis of the para-tetraphenylene arms is quite elaborate, similar dendrimers containing para-terphenylene arms have been prepared; they are accessible more economically ("semi-exploded dendrimers"). It has been shown that they in several aspects mimic the features of the "exploded dendrimers". In order to take advantage of the presence of large internal cavities in this dendrimer type, dendrons containing -C≡C- triple bonds have also been incorporated. Surprisingly, they are readily hydrogenated under the condition of heterogeneous catalysis (Pd/C) which demonstrates the large size of the cavities. As revealed by a quartz microbalance study the post-hydrogenation dendrimers are less prone to incorporate guest molecules than before hydrogenation. Obviously, the more flexible nature of the former reduces porosity, it also leads to significant shrinkage. An interesting perspective is the use of homogeneous hydrogenation catalysts of variable size with the aim of determining the dimension of internal free space.

Mutually catalytic branching at infinite rate

The purpose of this doctoral thesis is to prove existence for a mutually catalytic random walk with infinite branching rate on countably many sites. The process is defined as a weak limit of an approximating family of processes. An approximating process is constructed by adding jumps to a deterministic migration on an equidistant time grid. As law of jumps we need to choose the invariant probability measure of the mutually catalytic random walk with a finite branching rate in the recurrent regime. This model was introduced by Dawson and Perkins (1998) and this thesis relies heavily on their work. Due to the properties of this invariant distribution, which is in fact the exit distribution of planar Brownian motion from the first quadrant, it is possible to establish a martingale problem for the weak limit of any convergent sequence of approximating processes. We can prove a duality relation for the solution to the mentioned martingale problem, which goes back to Mytnik (1996) in the case of finite rate branching, and this duality gives rise to weak uniqueness for the solution to the martingale problem. Using standard arguments we can show that this solution is in fact a Feller process and it has the strong Markov property. For the case of only one site we prove that the model we have constructed is the limit of finite rate mutually catalytic branching processes as the branching rate approaches infinity. Therefore, it seems naturalto refer to the above model as an infinite rate branching process. However, a result for convergence on infinitely many sites remains open.

From amphiphilic block copolymers to ferrocenyl-functionalized polymers for biosensoric applications

The present thesis can be divided in three main parts. In all parts new polymer architecturesrnwere synthesized and characterized concerning their special features.rnThe first part will emphasize the advantage of a polystyrene-block-(hyperbranchedrnpolyglycerol) copolymer in comparison to an analogue polystyrene-block-(linear polyglycerol)rncopolymer. Therefore a synthethic route to prepare linear block copolymersrnhas been developed. Two strategies were examined. One strategy was based on thernclassic, sequential anionic polymerization; the second strategy was based on arn“Click-Chemistry” coupling reaction. In a following step glycidol was hypergraftedrnfrom these block copolymers by applying a hypergrafting reaction with glycidol. Thernbehavior of the amphiphilic block copolymers synthesized was studied in differentrnsolvents. Furthermore the polarity of the solvent was changed to form the correspondingrninverse micelles. DLS, SLS, SEC-MALLS-VISCO, AFM and Cyro TEMrnmeasurements were performed to obtain a visual image from the appearance of thernaggregates. It was found that a linear-hyperbranched architecture is necessary, ifrnwell defined, monodisperse aggregates are required, e.g. for the preparation of orderedrnnanoarrays. Linear-linear block copolymers formed only polydisperse aggregates.rnAdditionally it was found that size distribution could be improved dramaticallyrnby passing the aggregates through a SEC column with large pores. The SEC columnsrnacted like a template in which the aggregates adopt a more stable conformation.rnIn the second part anionic polymerization was employed to synthesize silaneendfunctionalizedrnmacromonomers with different molecular weights based on polybutadienernand polyisoprene. These were polymerized by a hydrosilylation reaction inrnbulk to obtain branched polymers, using Karstedt’s catalyst. Surprisingly the additionrnof monofunctional silanes during the polymerization had only a minimal effect concerningrnthe degree of polymerization. It was possible to introduce silanes without increasingrnthe overall number of reaction steps by a very convenient “pseudo-copolymerization”rnmethod. All branched polymers were analyzed by SEC, SEC-MALLS,rnSEC-viscometry, 1H-NMR-spectroscopy and DSC concerning their branching ratio.rnThe branching parameters for the branched polymers exhibited similar characteristicsrnas hyperbranched polymers based on AB2 monomers. Detailed kinetic study showedrnthat the polymerization occurred very rapidly in comparison to the hydrosilylation polymerizationrnof classical AB2 type carbosilanes monomers.rnThe last part will deal with ferrocenyl-functionalized polymers. On the one hand,rnferrocenyl-functionalized polyglycerols (PG) were studied. Esterification of PGs withrndifferent molecular weight using ferrocenemonocarboxylic acid gave the ferrocenylrnfuntionalized polymers in high yields. On the other hand three different block copolymersrnwere prepared with different ratios of styrene to butadiene units (10:1, 4:1, 2:1).rnThe double bonds of the 1,2-PB block were hydrosilylated using silanes bearing onern(HSiMe2Fc) or two (HSiMeFc2) ferrocene units. High degrees of functionalizationrnwere obtained (up to 83 %). In this manner, six different ferrocenyl-rich block copolymersrnwith different fractions of ferrocene were prepared and analyzed, employingrnNMR-spectroscopy, SEC, SEC/MALLS/viscometry, DLS and cyclic voltammetry. Thernredox properties of the studied polymers varied primarily with the nature of the silanernunit attached. Additionally, the redox properties in solution of the studied polymersrnwere influenced by the block length ratio of the block copolymers. Unexpectedly, withrnincreasing block length of the ferrocenyl block the fraction of active ferrocenes decreased.rnNevertheless, in case of thin monolayer films this behaviour was not observed.rnAll polymers (PG and PS-b-PB based) exhibited good electrochemical propertiesrnin a wide range of solvents, which rendered them very interesting for biosensoricrnapplications.

Automatic induction of lexical features

This thesis concerns artificially intelligent natural language processing systems that are capable of learning the properties of lexical items (properties like verbal valency or inflectional class membership) autonomously while they are fulfilling their tasks for which they have been deployed in the first place. Many of these tasks require a deep analysis of language input, which can be characterized as a mapping of utterances in a given input C to a set S of linguistically motivated structures with the help of linguistic information encoded in a grammar G and a lexicon L: G + L + C → S (1) The idea that underlies intelligent lexical acquisition systems is to modify this schematic formula in such a way that the system is able to exploit the information encoded in S to create a new, improved version of the lexicon: G + L + S → L' (2) Moreover, the thesis claims that a system can only be considered intelligent if it does not just make maximum usage of the learning opportunities in C, but if it is also able to revise falsely acquired lexical knowledge. So, one of the central elements in this work is the formulation of a couple of criteria for intelligent lexical acquisition systems subsumed under one paradigm: the Learn-Alpha design rule. The thesis describes the design and quality of a prototype for such a system, whose acquisition components have been developed from scratch and built on top of one of the state-of-the-art Head-driven Phrase Structure Grammar (HPSG) processing systems. The quality of this prototype is investigated in a series of experiments, in which the system is fed with extracts of a large English corpus. While the idea of using machine-readable language input to automatically acquire lexical knowledge is not new, we are not aware of a system that fulfills Learn-Alpha and is able to deal with large corpora. To instance four major challenges of constructing such a system, it should be mentioned that a) the high number of possible structural descriptions caused by highly underspeci ed lexical entries demands for a parser with a very effective ambiguity management system, b) the automatic construction of concise lexical entries out of a bulk of observed lexical facts requires a special technique of data alignment, c) the reliability of these entries depends on the system's decision on whether it has seen 'enough' input and d) general properties of language might render some lexical features indeterminable if the system tries to acquire them with a too high precision. The cornerstone of this dissertation is the motivation and development of a general theory of automatic lexical acquisition that is applicable to every language and independent of any particular theory of grammar or lexicon. This work is divided into five chapters. The introductory chapter first contrasts three different and mutually incompatible approaches to (artificial) lexical acquisition: cue-based queries, head-lexicalized probabilistic context free grammars and learning by unification. Then the postulation of the Learn-Alpha design rule is presented. The second chapter outlines the theory that underlies Learn-Alpha and exposes all the related notions and concepts required for a proper understanding of artificial lexical acquisition. Chapter 3 develops the prototyped acquisition method, called ANALYZE-LEARN-REDUCE, a framework which implements Learn-Alpha. The fourth chapter presents the design and results of a bootstrapping experiment conducted on this prototype: lexeme detection, learning of verbal valency, categorization into nominal count/mass classes, selection of prepositions and sentential complements, among others. The thesis concludes with a review of the conclusions and motivation for further improvements as well as proposals for future research on the automatic induction of lexical features.

Molekularbiologische Charakterisierung der beiden Untereinheiten des Mega-Hämocyanins der Schnecke Melanoides tuberculata

Bei dem 2010 von unserer Arbeitsgruppe entdeckten Mega-Hämocyanin handelt es sich um einen stark abgewandelten Typ des respiratorischen Proteins Hämocyanin, bestehend aus zwei flankierenden regulären Dekameren und einem zentralen Mega-Dekamer. Diese sind aus zwei immunologisch verschiedenen Untereinheiten mit ~400 bzw. ~550 kDa aufgebaut, die in unserer Arbeitsgruppe bereits proteinbiochemisch charakterisiert wurden. Im Zuge dieser Untersuchungen konnte zudem eine 3D-Rekonstruktion des Oligomers (13,5 MDa) mit einer Auflösung von 13Å erstellt werden. Das Ziel der vorliegenden Arbeit war die Aufklärung der Primärstruktur beider Polypeptide bei der Schnecke Melanoides tuberculata (MtH). Es gelang, die cDNAs der beiden Untereinheiten vollständig zu sequenzieren. Die zu typischen Dekameren assemblierende MtH400-Untereinheit umfasst 3445 Aminosäuren und besitzt eine theoretische Molekularmasse von 390 kDa. Nach dem Signalpeptid von 23 Aminosäuren Länge folgen die für Gastropoden-Hämocyanine typischen funktionellen Einheiten FU-a bis FU-h. Insgesamt verfügt die MtH400-Untereinheit über sechs potentielle N-Glykosylierungsstellen. Die MtH550-Untereinheit, welche mit 10 Kopien das Mega-Dekamer bildet, umfasst 4999 Aminosäuren und besitzt eine theoretische Molekularmasse von 567 kDa. Damit handelt es sich bei dieser Untereinheit um die zweitgrößte jemals bei einem Protein detektierte Polypeptidkette. Die MtH550-Untereinheit besteht aus einem Signalpeptid von 20 Aminosäuren Länge und den typischen Wand-FUs (FU-a bis FU-f). Daran anschließend folgen sechs weitere Varianten der FU-f (FU-f1 bis FU-f6). Die MtH550-Untereinheit verfügt über insgesamt zwölf potentielle N-Glykosylierungsstellen. Anhand der ermittelten Primärstrukturdaten wird klar, dass der auffällig vergrößerte Kragenbereich des Mega-Dekamers aus je 10 Kopien der FU-f1 bis FU-f6 besteht. Die ermittelten Sequenzdaten der beiden MtH-Untereinheiten weisen im Vergleich zu anderen Hämocyanin Sequenzen einige sehr charakteristische Indels sowie unübliche N-Glykosylierungsstellen auf. Es war zudem möglich, anhand einer molekularen Uhr den Entstehungszeitpunkt des Mega-Hämocyanins zu datieren (145 ± 35 MYA). Sowohl die Topologie als auch die berechneten Trennungszeitpunkte des an allen Verzweigungen gut unterstützten Stammbaums stimmen mit den bisher publizierten und auf Hämocyanindaten basierenden molekularen Uhren überein.

Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.