Periodic Higgs-de Rham flows and representations of algebraic fundamental groups

Let k := bar{F}_p for p > 2, W_n(k) := W(k)/p^n and X_n be a projective smooth W_n(k)-scheme which is W_{n+1}(k)-liftable. For all n > 1, we construct explicitly a functor, which we call the inverse Cartier functor, from a subcategory of Higgs bundles over X_n to a subcategory of flat Bundles over X_n. Then we introduce the notion of periodic Higgs-de Rham flows and show that a periodic Higgs-de Rham flow is equivalent to a Fontaine-Faltings module. Together with a p-adic analogue of Riemann-Hilbert correspondence established by Faltings, we obtain a coarse p-adic Simpson correspondence.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Generalized soluble groups of finite co-central rank

Eine Gruppe G hat endlichen Prüferrang (bzw. Ko-zentralrang) kleiner gleich r, wenn für jede endlich erzeugte Gruppe H gilt: H (bzw. H modulo seinem Zentrum) ist r-erzeugbar. In der vorliegenden Arbeit werden, soweit möglich, die bekannten Sätze über Gruppen von endlichem Prüferrang (kurz X-Gruppen), auf die wesentlich größere Klasse der Gruppen mit endlichem Ko-zentralrang (kurz R-Gruppen) verallgemeinert.Für lokal nilpotente R-Gruppen, welche torsionsfrei oder p-Gruppen sind, wird gezeigt, dass die Zentrumsfaktorgruppe eine X-Gruppe sein muss. Es folgt, dass Hyperzentralität und lokale Nilpotenz für R-Gruppen identische Bediungungen sind. Analog hierzu sind R-Gruppen genau dann lokal auflösbar, wenn sie hyperabelsch sind. Zentral für die Strukturtheorie hyperabelscher R-Gruppen ist die Tatsache, dass solche Gruppen eine aufsteigende Normalreihe abelscher X-Gruppen besitzen. Es wird eine Sylowtheorie für periodische hyperabelsche R-Gruppen entwickelt. Für torsionsfreie hyperabelsche R-Gruppen wird deren Auflösbarkeit bewiesen. Des weiteren sind lokal endliche R-Gruppen fast hyperabelsch. Für R-Gruppen fallen sehr große Gruppenklassen mit den fast hyperabelschen Gruppen zusammen. Hierzu wird der Begriff der Sektionsüberdeckung eingeführt und gezeigt, dass R-Gruppen mit fast hyperabelscher Sektionsüberdeckung fast hyperabelsch sind.

Complexes of polyelectrolytes with defined charge distance and different dendrimer counterions

Complexes of polyelectrolytes with defined charge distance and different dendrimer counterions Magdalena Chelmecka Max Planck Institute for Polymer Research; Ackermannweg 10; D-55128 Mainz ; Tel.: (+49) 06131- 379 – 226 A study of complexes in solution is of interest to investigate whether the formation of well-defined assemblies like in classical surfactant systems is possible. Aim of this thesis is to investigate the electrostatic self-assembly of linear polycations of varying charge distance with “large” counterions of varying architecture. We especially investigate the morphology of objects formed, but also their stability under salt free condition and after low molecular mass salt addition. As polycations, Poly(dialkylimino)-alkylene salts (Ionenes) I65MeBr and I25MeBr were chosen. Ionenes are synthesized via Menschutkin reaction and characterized by standard methods. Counterions are Polyamidoamine (PAMAM) dendrimers of generations G2.5, G5.5, G7.5 with -COONa surface groups and shape-persistent, Polyphenylene dendrimers of generation G1 with surface -COOH groups. A complex interplay of interactions is expected to direct the self assembly via electrostatic interaction, geometric factors, hydrophobic interaction or hydrogen bonds. Methods used for the investigation of complexes are: UV-spectroscopy, pH-metric techniques, dynamic and static light scattering, small angle neutron scattering,  potential measurements and potentiometric titration. Under certain conditions, (i.e. charge ratio of compounds, charge density of ionene and dendrimer also concentration of sample) polyelectrolyte systems composed of ionenes and dendrimers build complexes in solution. System compounds are typical polyelectrolytes, but structures which they build behave not usual for typical polyelectrolytes. In a one diffusion mode regime aggregates of about 100 nm hydrodynamic radius have been found. Such aggregates are core-shell or anisotropic core shell structures in the case of ionenes/PAMAM dendrimers complexes. These complexes are stable even at high ionic strength. In case of ionenes with poly(phenylene) dendrimers, hard sphere-like objects or spherical objects with hairy-like surface have been found in a one diffusion mode regime. Their stability at high ionic strength is lower. For the ionenes/poly(phenylene) dendrimers systems one transition point has been found from one to two diffusion processes, towards increasing ionene concentration, i.e. for the samples with fixed dendrimer concentration towards increasing ionic strength. For the diffusion profile of ionene/PAMAM dendrimers in most cases two transition regimes are observed. One at very low ionene concentration, the second one at high ionene concentrations, which again means for the samples with fixed dendrimer concentration, also at higher ionic strength. Both two mode regimes are separated by the one mode regime. As was confirmed experimentally, the one diffusion mode regime is caused by the motion of well defined assemblies. The two diffusion mode regimes are caused by the movement of different sized species in solution, large aggregates and middle-size aggregates (oligoaggregates). The location and also the number of transition points in the diffusion profiles is dependent on the ionene to dendrimer charge ratio, charge density of the compounds and concentration. No influence of the molecular mass of the ionene has been found. The aggregates are found to be charged on the surface, however this surface charge does not significantly influence the diffusion properties of the system.

Synthesis and characterization of temperature- and light-responsive polymers and block copolymers

In summary, thermoresponsive polyacrylamides with various amounts of different photoswitchable side groups, i. e. azobenzene, salicylideneaniline and fulgimide were successfully prepared. As such, in a first step three different chromophores with an amine functionality were synthesized. The synthesis of the stimuli-responsive materials was based on the RAFT polymerization of activated ester acrylates followed by a polymer analogous reaction with different amines. The procedure has been designed to allow the synthesis of well-defined materials with functional groups. All copolymers prepared in this way showed a LCST in aqueous solution. The LCST was in general decreased by increasing the amount of hydrophobic dye incorporated into the thermoresponsive polymer. However, in the case of the fulgimide, the LCST was hardly affected by the chromophore. For azobenzene containing PNIPAM polymers and analogues, higher LCST values were measured after irradiation of the polymer sample solutions with UV-light (Delta LCSTmax = 7.3°C). A reversible light-induced solubility change within a certain temperature range was possible. In contrast to this, irradiated samples of salicylideneaniline containing thermoresponsive copolymers showed an irreversible increase in the LCST (Delta LCSTmax = 13.0°C). Fulgimide chromophores did not influence the LCST of PNIPAM based copolymers after UV-light exposure.rnSimilar to the thermoresponsive polyacrylamides with azobenzene side groups, poly(oligo(ethylene glycol) methyl ether methacrylate) [P(OEGMA)] polymers with azobenzene end groups showed a LCST shift upon UV-irradiation. These polymers were synthesized by RAFT polymerization using a functional chain transfer agent (CTA). For this, PFP-CTA was used as a RAFT-agent for end group functionalization of (thermoresponsive) polymers. In contrast to the statistically arranged copolymers with azobenzene side groups, P(OEGMA) polymers with terminal azobenzene showed a linear increase of the LCST shifts with increasing amount of chromophore (Delta LCSTmax = 4.3°C). Noteworthy, the chemical nature of the end group exhibited a strong influence on the LCST in the case of short thermoresponsive P(OEGMA) polymers.rnThe investigation on temperature- and lightresponsive polymers was transferred onto block copolymers capable to self-assemble into polymeric micelles. Therefore, PEO-b-PNIPAM block copolymers with azobenzene moieties were synthesized successfully. These polymers showed a “smart” behavior in aqueous solution, as the reversible formation and disruption of the micelles could either be controlled by temperature or using light as a stimulus. The usefulness of these materials was demonstrated by encapsulation of a hydrophobic dye in the core of the micelle. Such materials might have a great potential as a model system for several technical or biological applications.rnFinally, double thermoresponsive block copolymers forming micellar structures in a certain temperature range with functional end groups could successfully be synthesized. These “smart materials” based on POEGMA-b-PNIPMAM have been demonstrated to be very promising for a temperature selective immobilization on a protein surface. This might be a suitable concept for further biological applications.rnConcluding, different thermoresponsive copolymers and block copolymers with lightresponsive moieties arranged along the backbone or located at the chain ends were successfully prepared and investigated. By controlling the nature of functional groups and their respective incorporation ratios, the LCST could be dialed in precisely. Further, the LCST of the polymers could be triggered by light. A light-controlled disruption of micellar structures could be shown for functional block copolymers. The importance of end groups of thermoresponsive polymers was demonstrated by a temperature-controlled protein-polymer binding of a terminal biotin-functionalized double thermoresponsive polymer. The synthetic approaches and the material properties presented here should be promising for further research and applications beyond this dissertation.rn

Feasibility studies of the pp pi 0 e + e - electromagnetic channel at PANDA

Among all possible realizations of quark and antiquark assembly, the nucleon (the proton and the neutron) is the most stable of all hadrons and consequently has been the subject of intensive studies. Mass, shape, radius and more complex representations of its internal structure are measured since several decades using different probes. The proton (spin 1/2) is described by the electric GE and magnetic GM form factors which characterise its internal structure. The simplest way to measure the proton form factors consists in measuring the angular distribution of the electron-proton elastic scattering accessing the so-called Space-Like region where q2 < 0. Using the crossed channel antiproton proton <--> e+e-, one accesses another kinematical region, the so-called Time-Like region where q2 > 0. However, due to the antiproton proton <--> e+e- threshold q2th, only the kinematical domain q2 > q2th > 0 is available. To access the unphysical region, one may use the antiproton proton --> pi0 e+ e- reaction where the pi0 takes away a part of the system energy allowing q2 to be varied between q2th and almost 0. This thesis aims to show the feasibility of such measurements with the PANDA detector which will be installed on the new high intensity antiproton ring at the FAIR facility at Darmstadt. To describe the antiproton proton --> pi0 e+ e- reaction, a Lagrangian based approach is developed. The 5-fold differential cross section is determined and related to linear combinations of hadronic tensors. Under the assumption of one nucleon exchange, the hadronic tensors are expressed in terms of the 2 complex proton electromagnetic form factors. An extraction method which provides an access to the proton electromagnetic form factor ratio R = |GE|/|GM| and for the first time in an unpolarized experiment to the cosine of the phase difference is developed. Such measurements have never been performed in the unphysical region up to now. Extended simulations were performed to show how the ratio R and the cosine can be extracted from the positron angular distribution. Furthermore, a model is developed for the antiproton proton --> pi0 pi+ pi- background reaction considered as the most dangerous one. The background to signal cross section ratio was estimated under different cut combinations of the particle identification information from the different detectors and of the kinematic fits. The background contribution can be reduced to the percent level or even less. The corresponding signal efficiency ranges from a few % to 30%. The precision on the determination of the ratio R and of the cosine is determined using the expected counting rates via Monte Carlo method. A part of this thesis is also dedicated to more technical work with the study of the prototype of the electromagnetic calorimeter and the determination of its resolution.

Global modeling of pollutant transport and deposition from anthropogenic emission hot spots on global scale

Urban centers significantly contribute to anthropogenic air pollution, although they cover only a minor fraction of the Earth's land surface. Since the worldwide degree of urbanization is steadily increasing, the anthropogenic contribution to air pollution from urban centers is expected to become more substantial in future air quality assessments. The main objective of this thesis was to obtain a more profound insight in the dispersion and the deposition of aerosol particles from 46 individual major population centers (MPCs) as well as the regional and global influence on the atmospheric distribution of several aerosol types. For the first time, this was assessed in one model framework, for which the global model EMAC was applied with different representations of aerosol particles. First, in an approach with passive tracers and a setup in which the results depend only on the source location and the size and the solubility of the tracers, several metrics and a regional climate classification were used to quantify the major outflow pathways, both vertically and horizontally, and to compare the balance between pollution export away from and pollution build-up around the source points. Then in a more comprehensive approach, the anthropogenic emissions of key trace species were changed at the MPC locations to determine the cumulative impact of the MPC emissions on the atmospheric aerosol burdens of black carbon, particulate organic matter, sulfate, and nitrate. Ten different mono-modal passive aerosol tracers were continuously released at the same constant rate at each emission point. The results clearly showed that on average about five times more mass is advected quasi-horizontally at low levels than exported into the upper troposphere. The strength of the low-level export is mainly determined by the location of the source, while the vertical transport is mainly governed by the lifting potential and the solubility of the tracers. Similar to insoluble gas phase tracers, the low-level export of aerosol tracers is strongest at middle and high latitudes, while the regions of strongest vertical export differ between aerosol (temperate winter dry) and gas phase (tropics) tracers. The emitted mass fraction that is kept around MPCs is largest in regions where aerosol tracers have short lifetimes; this mass is also critical for assessing the impact on humans. However, the number of people who live in a strongly polluted region around urban centers depends more on the population density than on the size of the area which is affected by strong air pollution. Another major result was that fine aerosol particles (diameters smaller than 2.5 micrometer) from MPCs undergo substantial long-range transport, with about half of the emitted mass being deposited beyond 1000 km away from the source. In contrast to this diluted remote deposition, there are areas around the MPCs which experience high deposition rates, especially in regions which are frequently affected by heavy precipitation or are situated in poorly ventilated locations. Moreover, most MPC aerosol emissions are removed over land surfaces. In particular, forests experience more deposition from MPC pollutants than other land ecosystems. In addition, it was found that the generic treatment of aerosols has no substantial influence on the major conclusions drawn in this thesis. Moreover, in the more comprehensive approach, it was found that emissions of black carbon, particulate organic matter, sulfur dioxide, and nitrogen oxides from MPCs influence the atmospheric burden of various aerosol types very differently, with impacts generally being larger for secondary species, sulfate and nitrate, than for primary species, black carbon and particulate organic matter. While the changes in the burdens of sulfate, black carbon, and particulate organic matter show an almost linear response for changes in the emission strength, the formation of nitrate was found to be contingent upon many more factors, e.g., the abundance of sulfuric acid, than only upon the strength of the nitrogen oxide emissions. The generic tracer experiments were further extended to conduct the first risk assessment to obtain the cumulative risk of contamination from multiple nuclear reactor accidents on the global scale. For this, many factors had to be taken into account: the probability of major accidents, the cumulative deposition field of the radionuclide cesium-137, and a threshold value that defines contamination. By collecting the necessary data and after accounting for uncertainties, it was found that the risk is highest in western Europe, the eastern US, and in Japan, where on average contamination by major accidents is expected about every 50 years.

Synthese cyclischer Peptide und von Kohlenhydraten abgeleitete Katalysatoren zur enantioselektiven Darstellung von Cyanhydrinen

Der Suche nach neuen Wirkstoffen für den chemischen Pflanzenschutz kommt insbesondere vor dem Hintergrund der steigenden Weltbevölkerung und weniger zur Verfügung stehenden kulturfähigen Ackerflächen eine stetig wachsende Bedeutung zu. Ziel dieser Arbeit war die Synthese von cyclischen Peptiden und Depsipeptiden, die aufgrund ihrer biologischen Aktivität als potentielle Insektizide für den chemischen Pflanzenschutz in Frage kommen. Darüber hinaus sollten von Kohlenhydraten abgeleitete Katalysatoren zur enantioselektiven Cyanhydrinsynthese entwickelt werden, um einen leichten Zugang zu den Bausteinen der Depsipeptide zu ermöglichen. Als vielversprechender Naturstoff mit insektiziden Eigenschaften gilt das cyclische Pentapeptid Cycloaspeptid E, dessen Totalsynthese in 10 Stufen mit einer Gesamtausbeute von 25% erreicht wurde, sodass die Verbindung für biologische Tests bereitgestellt werden konnte. Zusätzlich gelang die Kristallisation der Verbindung, was eine Röntgenstrukturanalyse ermöglichte. Ein Derivat von Cycloaspeptid E sollte 2-Aminonicotinsäure anstelle von Anthranilsäure enthalten. Die Synthese dieser Verbindung wurde auf drei Wegen versucht. Dabei zeigte sich, dass es bei einer zur Totalsynthese des Naturstoffs analogen Strategie zur quantitativen Bildung eines Diketopiperazins kommt. Auf den anderen Routen ließ sich entweder ein Kupplungsschritt nicht realisieren, oder die Verbindung erwies sich unter den gewählten Bedingungen als instabil. Die Darstellung eines 2-Aminonicotinsäure-Derivats von Cycloaspeptid E bleibt daher weiterhin ein ungelöstes Problem, das weiterer Forschung bedarf. Verticilid A1 ist ein cyclisches Depsipeptid, das aufgrund seiner Bindungsfähigkeit an den Ryanodinrezeptor von Insekten, als Leitstruktur für die Suche nach neuen Insektiziden von Interesse ist. Um zu untersuchen, wie wichtig die Esterbindungen im Molekül für die biologische Aktivität sind, sollte das entsprechende Amid-Derivat und das Cyclodepsipeptid mit nur zwei statt vier Esterbindungen hergestellt werden. Hierbei zeigte sich, dass eine zur Darstellung von Verticilid A1 analoge Syntheseroute zu einer ausgeprägten Epimerisierung führt. Eine lineare Synthese der Derivate endet in der Bildung des Diketopiperazins. Weiterhin wurden zwei neue, zueinander pseudoenantiomere Vanadium(IV)-Katalysatoren auf Basis von D-Glucose einerseits und L-Xylose andererseits dargestellt. Diese lassen sich in fünf bzw. 14 Stufen synthetisieren und liefern in der enantioselektiven Katalyse von Mandelsäurenitril Enantiomerenüberschüsse von 89% bzw. 91% bei hohen Ausbeuten. Zusammenfassend lässt sich feststellen, dass im Rahmen dieser Arbeit die Totalsynthese von Cycloaspeptid E erfolgreich durchgeführt wurde, und die Syntheseversuche von weiteren cyclischen Peptiden wichtige Erkenntnisse für weitere Synthesen lieferten. Mit den beiden hergestellten Vanadium(IV)-Komplexen wurden zwei potente, auf Kohlenhydraten basierende Katalysatoren für die enantioselektive Synthese von Cyanhydrinen entwickelt.

Expanding the scope of poly(ethylene glycol)s for bioconjugation to squaric acid-mediated PEGylation and pH-sensitivity

Poly(ethylene glycol) (PEG) is used in a broad range of applications due to its unique combination of properties and is approved use in formulations for body-care products, edibles and medicine. This thesis aims at the synthesis and characterization of novel heterofunctional PEG structures and the establishment of diethyl squarate as a suitable linker for the covalent attachment to proteins. Chapter 1 is an introduction on the properties and applications of PEG as well as the fascinating chemistry of squaric acid derivatives. In Chapter 1.1, the synthesis and properties of PEG are described, and the versatile applications of PEG derivatives in everyday products are emphasized with a focus on PEG-based pharmaceuticals and nonionic surfactants. This chapter is written in German, as it was published in the German Journal Chemie in unserer Zeit. Chapter 1.2 deals with PEGs major drawbacks, its non-biodegradability, which impedes parenteral administration of PEG conjugates with polyethers exceeding the renal excretion limit, although these would improve blood circulation times and passive tumor targeting. This section gives a comprehensive overview of the cleavable groups that have been implemented in the polyether backbone to tackle this issue as well as the synthetic strategies employed to accomplish this task. Chapter 1.3 briefly summarizes the chemical properties of alkyl squarates and the advantages in protein conjugation chemistry that can be taken from its use as a coupling agent. In Chapter 2, the application of diethyl squarate as a coupling agent in the PEGylation of proteins is illustrated. Chapter 2.1 describes the straightforward synthesis and characterization of squaric acid ethyl ester amido PEGs with terminal hydroxyl functions or methoxy groups. The reactivity and selectivity of theses activated PEGs are explored in kinetic studies on the reactions with different lysine and other amino acid derivatives, followed by 1H NMR spectroscopy. Further, the efficient attachment of the novel PEGs to a model protein, i.e., bovine serum albumin (BSA), demonstrates the usefulness of the new linker for the PEGylation with heterofunctional PEGs. In Chapter 2.3 initial studies on the biocompatibility of polyether/BSA conjugates synthesized by the squaric acid mediated PEGylation are presented. No cytotoxic effects on human umbilical vein endothelial cells exposed to various concentrations of the conjugates were observed in a WST-1 assay. A cell adhesion molecule - enzyme immunosorbent assay did not reveal the expression of E-selectin or ICAM-1, cell adhesion molecules involved in inflammation processes. The focus of Chapter 3 lies on the syntheses of novel heterofunctional PEG structures which are suitable candidates for the squaric acid mediated PEGylation and exhibit superior features compared to established PEGs applied in bioconjugation. Chapter 3.1 describes the synthetic route to well-defined, linear heterobifunctional PEGs carrying a single acid-sensitive moiety either at the initiation site or at a tunable position in the polyether backbone. A universal concept for the implementation of acetal moieties into initiators for the anionic ring-opening polymerization (AROP) of epoxides is presented and proven to grant access to the degradable PEG structures aimed at. The hydrolysis of the heterofunctional PEG with the acetal moiety at the initiating site is followed by 1H NMR spectroscopy in deuterium oxide at different pH. In an exploratory study, the same polymer is attached to BSA via the squarate acid coupling and subsequently cleaved from the conjugate under acidic conditions. Furthermore, the concept for the generation of acetal-modified AROP initiators is demonstrated to be suitable for cholesterol, and the respective amphiphilic cholesteryl-PEG is cleaved at lowered pH. In Chapter 3.2, the straightforward synthesis of α-amino ω2-dihydroxyl star-shaped three-arm PEGs is described. To assure a symmetric length of the hydroxyl-terminated PEG arms, a novel AROP initiator is presented, who’s primary and secondary hydroxyl groups are separated by an acetal moiety. Upon polymerization of ethylene oxide for these functionalities and subsequent cleavage of the acid-labile unit no difference in the degree of polymerization is seen for both polyether fragments.