Fourier-transform rheology on anionically synthesised polymer melts and solutions of various topology

Aim of this thesis was to further extend the applicability of the Fourier-transform (FT) rheology technique especially for non-linear mechanical characterisation of polymeric materials on the one hand and to investigated the influence of the degree of branching on the linear and non-linear relaxation behaviour of polymeric materials on the other hand. The latter was achieved by employing in particular FT-rheology and other rheological techniques to variously branched polymer melts and solutions. For these purposes, narrowly distributed linear and star-shaped polystyrene and polybutadiene homo-polymers with varying molecular weights were anionically synthesised using both high-vacuum and inert atmosphere techniques. Furthermore, differently entangled solutions of linear and star-shaped polystyrenes in di-sec-octyl phthalate (DOP) were prepared. The several linear polystyrene solutions were measured under large amplitude oscillatory shear (LAOS) conditions and the non-linear torque response was analysed in the Fourier space. Experimental results were compared with numerical predictions performed by Dr. B. Debbaut using a multi-mode differential viscoelastic fluid model obeying the Giesekus constitutive equation. Apart from the analysis of the relative intensities of the harmonics, a detailed examination of the phase information content was developed. Further on, FT-rheology allowed to distinguish polystyrene melts and solutions due to their different topologies where other rheological measurements failed. Significant differences occurred under LAOS conditions as particularly reflected in the phase difference of the third harmonic, Ħ3, which could be related to shear thinning and shear thickening behaviour.

Rheology and Fourier-transform rheology on water-based systems

The influence of shear fields on water-based systems was investigated within this thesis. The non-linear rheological behaviour of spherical and rod-like particles was examined with Fourier-Transform rheology under LAOS conditions. As a model system for spherical particles two different kinds of polystyrene dispersions, with a solid content higher than 0.3 each, were synthesised within this work. Due to the differences in polydispersity and Debye-length, differences were also found in the rheology. In the FT-rheology both kinds of dispersions showed a similar rise in the intensities of the magnitudes of the odd higher harmonics, which were predicted by a model. The in some cases additionally appearing second harmonics were not predicted. A novel method to analyse the time domain signal was developed, that splits the time domain signal up in four characteristic functions. Those characteristic functions correspond to rheological phenomena. In some cases the intensities of the Fourier components can interfere negatively. FD-virus particles were used as a rod-like model system, which already shows a highly non-linear behaviour at concentrations below 1. % wt. Predictions for the dependence of the higher harmonics from the strain amplitude described the non-linear behaviour well at large, but no so good at small strain amplitudes. Additionally the trends of the rheological behaviour could be described by a theory for rod-like particles. An existing rheo-optical set-up was enhanced by reducing the background birefringence by a factor of 20 and by increasing the time resolution by a factor of 24. Additionally a combination of FT-rheology and rheo-optics was achieved. The influence of a constant shear field on the crystallisation process of zinc oxide in the presence of a polymer was examined. The crystallites showed a reduction in length by a factor of 2. The directed addition of polymers in combination with a defined shear field can be an easy way for a defined change of the form of crystallites.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn