Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

Calix[4]arenes in the 1,3-alternate conformation

Calix[4]arenes fixed in the 1,3-alternate conformation offer an interesting platform for the attachment of further functionalities which has been less frequently used than the cone conformer. Several synthetic strategies were developed to attach four amino functions to the narrow rim, to the wide rim and to both rims of the calix[4]arene fixed in the 1,3-alternate conformation. Using different precursor groups (nitrile/phthalimide or nitro/phthalimide) which can be independently converted into amino functions opens the possibility to attach further groups selectively to the amino functions. Here the groups which is newly attached will determine the reaction sequence.

Structure formation as studied by EPR spectroscopy: From simple solutions to nanoparticles

In this thesis, three nitroxide based ionic systems were used to investigate structure and dynamics of their respective solutions in mixed solvents by means of electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) spectroscopy at X- and W-band (9.5 and 94.5 GHz, respectively). rnFirst, the solvation of the inorganic radical Fremy’s salt (K2ON(SO3)2) in isotope substituted binary solvent mixtures (methanol/water) was investigated by means of high-field (W-band) pulse ENDOR spectroscopy and molecular dynamics (MD) simulations. From the analysis of orientation-selective 1H and 2H ENDOR spectra the principal components of the hyperfine coupling (hfc) tensor for chemically different protons (alcoholic methyl vs. exchangeable protons) were obtained. The methyl protons of the organic solvent approach with a mean distance of 3.5 Å perpendicular to the approximate plane spanned by ON(S)2 of the probe molecule. Exchangeable protons were found to be distributed isotropically, approaching closest to Fremy’s salt from the hydrogen-bonded network around the sulfonate groups. The distribution of exchangeable and methyl protons as found in MD simulations is in full agreement with the ENDOR results. The solvation was found to be similar for the studied solvent ratios between 1:2.3 and 2.3:1 and dominated by an interplay of H-bond (electrostatic) interactions and steric considerations with the NO group merely involved into H-bonds.rnFurther, the conformation of spin labeled poly(diallyldimethylammonium chloride) (PDADMAC) solutions in aqueous alcohol (methanol, ethanol, n-propanol, ethylene glycol, glycerol) mixtures in dependence of divalent sodium sulfate was investigated with double electron-electron resonance (DEER) spectroscopy. The DEER data was analyzed using the worm-like chain model which suggests that in organic-water solvent mixtures the polymer backbones are preferentially solvated by the organic solvent. We found a less serve impact on conformational changes due to salt than usually predicted in polyelectrolyte theory which stresses the importance of a delicate balance of hydrophobic and electrostatic interactions, in particular in the presence of organic solvents.rnFinally, the structure and dynamics of miniemulsions and polymerdispersions prepared with anionic surfactants, that were partially replaced by a spin labeled fatty acid in presence and absence of a lanthanide beta-diketonate complex was characterized by CW EPR spectroscopy. Such miniemulsions form multilayers with the surfactant head group bound to the lanthanide ion. Beta-diketonates were formerly used as NMR shift reagents and nowadays find application as luminescent materials in OLEDs and LCDs and as contrast agent in MRT. The embedding of the complex into a polymer matrix results in an easy processable material. It was found that the structure formation takes place in miniemulsion and is preserved during polymerization. For surfactants with carboxyl-head group a higher order of the alkyl chains and less lateral diffusion is found than for sulfat-head groups, suggesting a more uniform and stronger coordination to the metal ion. The stability of these bilayers depends on the temperature and the used surfactant which should be considered for the used polymerization temperature if a maximum output of the structured regions is wished.

Enzyme tRNA interaction and (t)RNA conformation probed via environmentally sensitive cyanine dyes

Nukleosidmodifikationen beeinflussen Dynamik und Konformation von RNArnund sind epigenetisch wirksam. Wenig verstanden sind konformationelle Dynamik und enzymatische Erkennung von tRNA, sowie der Einfluss des mutmaßlichen kovalenten Inhibitors 5-Fluorouridine (5FU) auf Y Synthasen, die Pseudouridin (Y) erzeugen. Frühere Arbeiten nutzten mit den Fluorophoren Cy3 und Cy5rnmarkierte tRNA, um diese Fragen zu adressieren.rnDie vorliegende Arbeit weitet Cy3-Cy5-Markierung auf Hefe tRNArnPhernaus undrnnutzt Thermophorese und fortschrittliche Fluoreszenzspektroskopie. In der Thermophorese zeigte sich eine hohe Toleranz gegenüber Fluoreszenzmarkierung beirngleichzeitiger Erhöhung der Cy5 Fluoreszenz durch Enzymbindung. Zudem konnte die Konformation verschiedener Mutanten human mitochondrialer tRNArnLysrnund die Bindung von SAM durch SAM-I Riboswitch RNA untersucht werden.rnUm etwaige Unterschiede in der Interaktion von Y55 Synthase TruB mit Cy5-gelabelter U55- bzw. 5FU55-tRNA aufzudecken, wurde eine Kombination ausrnThermophorese, zeit- und polarisationsaufgelöster Fluoreszenzspektroskopie undrn’gel shift’ Experimenten genutzt. Alle Ergebnisse zeigten übereinstimmend einernreversible Bindung ähnlicher Affinität für beide tRNAs und widersprechen somit einer kovalenten Inhibition durch 5FU. Folgerichtig wurde der SDS-stabilernKomplex von TruB mit 5FU-tRNA neu evaluiert, da er bisher als kovalent interpretiert wurde. Es erfolgte eine schnelle Komplexbildung in hoher Ausbeute auchrnfür schlechte Substrate, außerdem ließ sich die Komplexausbeute nicht durch andere Reaktionsbedingungen beeinflussen. Somit kann der SDS stabile Komplexrnnur den ersten, nicht-kovalenten Kontakt von Enzym und 5FU55-tRNA darstellen und repräsentiert kein kovalentes Addukt späterer Katalyse.