Quantification of deformation processes in the Torlesse accretionary wedge, New Zealand

Zusammenfassung:In dieser Studie werden Deformationsprozesse im mesozoischen Torlesse Akkretionskeil (Neuseeland) quantifiziert, um Aufschluß über die Dynamik in Akkretionskeilen zu erhalten. Absolute und relative Verformungsmessungen zeigen sowohl im lokalen als auch regionalen Maßstab eine stark heterogene Deformation des Torlesse Keils. Die regionale Deformation wurde mit Hilfe einer Tensordurchschnittsberechnung, unter Benutzung einzelner lokaler Verformungsdaten, als uniaxiale Verkürzung entlang einer subvertikalen, maximalen Verkürzungsachse charakterisiert. Absolute Verformungsmessungen an niedriggradigen Metasandsteinen belegen darüber hinaus durchschnittliche Volumenverluste von ca. 20% SiO2. Volumenveränderungen in tieferkrustalen Aufschlüssen wurden mittels einer geochemischen Massenbilanzanalyse abgeschätzt. Chemische Zusammensetzungen höhergradiger Zonen weichen je nach Grad der Volumenverformung von der Protolitzusammensetzung ab und zeigen somit Verluste von 15% SiO2 an. Da Speicherorte für das gelöste Material nicht bekannt sind, muss angenommen werden, dass das Material aus dem Keil abtransportiert wurde. Die Verformungsergebnisse geben weiterhin Aufschluß über den Grad der Kopplung zwischen Akkretionskeil und subduzierter Platte. Die ermittelten Scherwerte in den Gesteinen liegen deutlich unter den zu erwartenden Scherwerten, die mittels eines einfachen Modells berechnet wurden, das sowohl verschiedene Konvergenzgeschwindigkeiten als auch Exhumierungsraten berücksichtigt. Dies belegt, dass der Torlesse Keil stark von der subduzierten pazifischen Platte entkoppelt war und die Deformation hauptsächlich durch den Fluß der Sedimente in und aus dem Keil bestimmt wurde.

Structuring of polymer surface by evaporation of sessile microdrops

In this thesis, we investigated the evaporation of sessile microdroplets on different solid substrates. Three major aspects were studied: the influence of surface hydrophilicity and heterogeneity on the evaporation dynamics for an insoluble solid substrate, the influence of external process parameters and intrinsic material properties on microstructuring of soluble polymer substrates and the influence of an increased area to volume ratio in a microfluidic capillary, when evaporation is hindered. In the first part, the evaporation dynamics of pure sessile water drops on smooth self-assembled monolayers (SAMs) of thiols or disulfides on gold on mica was studied. With increasing surface hydrophilicity the drop stayed pinned longer. Thus, the total evaporation time of a given initial drop volume was shorter, since the drop surface, through which the evaporation occurs, stays longer large. Usually, for a single drop the volume decreased linearly with t1.5, t being the evaporation time, for a diffusion-controlled evaporation process. However, when we measured the total evaporation time, ttot, for multiple droplets with different initial volumes, V0, we found a scaling of the form V0 = attotb. The more hydrophilic the substrate was, the more showed the scaling exponent a tendency to an increased value up to 1.6. This can be attributed to an increasing evaporation rate through a thin water layer in the vicinity of the drop. Under the assumption of a constant temperature at the substrate surface a cooling of the droplet and thus a decreased evaporation rate could be excluded as a reason for the different scaling exponent by simulations performed by F. Schönfeld at the IMM, Mainz. In contrast, for a hairy surface, made of dialkyldisulfide SAMs with different chain lengths and a 1:1 mixture of hydrophilic and hydrophobic end groups (hydroxy versus methyl group), the scaling exponent was found to be ~ 1.4. It increased to ~ 1.5 with increasing hydrophilicity. A reason for this observation can only be speculated: in the case of longer hydrophobic alkyl chains the formation of an air layer between substrate and surface might be favorable. Thus, the heat transport to the substrate might be reduced, leading to a stronger cooling and thus decreased evaporation rate. In the second part, the microstructuring of polystyrene surfaces by drops of toluene, a good solvent, was investigated. For this a novel deposition technique was developed, with which the drop can be deposited with a syringe. The polymer substrate is lying on a motorized table, which picks up the pendant drop by an upward motion until a liquid bridge is formed. A consecutive downward motion of the table after a variable delay, i.e. the contact time between drop and polymer, leads to the deposition of the droplet, which can evaporate. The resulting microstructure is investigated in dependence of the processes parameters, i.e. the approach and the retraction speed of the substrate and the delay between them, and in dependence of the intrinsic material properties, i.e. the molar mass and the type of the polymer/solvent system. The principal equivalence with the microstructuring by the ink-jet technique was demonstrated. For a high approach and retraction speed of 9 mm/s and no delay between them, a concave microtopology was observed. In agreement with the literature, this can be explained by a flow of solvent and the dissolved polymer to the rim of the pinned droplet, where polymer is accumulated. This effect is analogue to the well-known formation of ring-like stains after the evaporation of coffee drops (coffee-stain effect). With decreasing retraction speed down to 10 µm/s the resulting surface topology changes from concave to convex. This can be explained with the increasing dissolution of polymer into the solvent drop prior to the evaporation. If the polymer concentration is high enough, gelation occurs instead of a flow to the rim and the shape of the convex droplet is received. With increasing delay time from below 0 ms to 1s the depth of the concave microwells decreases from 4.6 µm to 3.2 µm. However, a convex surface topology could not be obtained, since for longer delay times the polymer sticks to the tip of the syringe. Thus, by changing the delay time a fine-tuning of the concave structure is accomplished, while by changing the retraction speed a principal change of the microtopolgy can be achieved. We attribute this to an additional flow inside the liquid bridge, which enhanced polymer dissolution. Even if the pendant drop is evaporating about 30 µm above the polymer surface without any contact (non-contact mode), concave structures were observed. Rim heights as high as 33 µm could be generated for exposure times of 20 min. The concave structure exclusively lay above the flat polymer surface outside the structure even after drying. This shows that toluene is taken up permanently. The increasing rim height, rh, with increasing exposure time to the solvent vapor obeys a diffusion law of rh = rh0  tn, with n in the range of 0.46 ~ 0.65. This hints at a non-Fickian swelling process. A detailed analysis showed that the rim height of the concave structure is modulated, unlike for the drop deposition. This is due to the local stress relaxation, which was initiated by the increasing toluene concentration in the extruded polymer surface. By altering the intrinsic material parameters i.e. the polymer molar mass and the polymer/solvent combination, several types of microstructures could be formed. With increasing molar mass from 20.9 kDa to 1.44 MDa the resulting microstructure changed from convex, to a structure with a dimple in the center, to concave, to finally an irregular structure. This observation can be explained if one assumes that the microstructuring is dominated by two opposing effects, a decreasing solubility with increasing polymer molar mass, but an increasing surface tension gradient leading to instabilities of Marangoni-type. Thus, a polymer with a low molar mass close or below the entanglement limit is subject to a high dissolution rate, which leads to fast gelation compared to the evaporation rate. This way a coffee-rim like effect is eliminated early and a convex structure results. For high molar masses the low dissolution rate and the low polymer diffusion might lead to increased surface tension gradients and a typical local pile-up of polymer is found. For intermediate polymer masses around 200 kDa, the dissolution and evaporation rate are comparable and the typical concave microtopology is found. This interpretation was supported by a quantitative estimation of the diffusion coefficient and the evaporation rate. For a different polymer/solvent system, polyethylmethacrylate (PEMA)/ethylacetate (EA), exclusively concave structures were found. Following the statements above this can be interpreted with a lower dissolution rate. At low molar masses the concentration of PEMA in EA most likely never reaches the gelation point. Thus, a concave instead of a convex structure occurs. At the end of this section, the optically properties of such microstructures for a potential application as microlenses are studied with laser scanning confocal microscopy. In the third part, the droplet was confined into a glass microcapillary to avoid evaporation. Since here, due to an increased area to volume ratio, the surface properties of the liquid and the solid walls became important, the influence of the surface hydrophilicity of the wall on the interfacial tension between two immiscible liquid slugs was investigated. For this a novel method for measuring the interfacial tension between the two liquids within the capillary was developed. This technique was demonstrated by measuring the interfacial tensions between slugs of pure water and standard solvents. For toluene, n-hexane and chloroform 36.2, 50.9 and 34.2 mN/m were measured at 20°C, which is in a good agreement with data from the literature. For a slug of hexane in contact with a slug of pure water containing ethanol in a concentration range between 0 and 70 (v/v %), a difference of up to 6 mN/m was found, when compared to commercial ring tensiometry. This discrepancy is still under debate.

Drainage of thin aqueous films between solid surfaces measured with the colloidal probe technique

Understanding liquid flow at the vicinity of solid surfaces is crucial to the developmentrnof technologies to reduce drag. One possibility to infer flow properties at the liquid-solid interface is to compare the experimental results to solutions of the Navier-Stokes equations assuming the no-slip boundary condition (BC) or the slip BC. There is no consensus in the literature about which BC should be used to model the flow of aqueous solutions over hydrophilic surfaces. Here, the colloidal probe technique is used to systematically address this issue, measuring forces acting during drainage of water over a surface. Results show that experimental variables, especially the cantilever spring constant, lead to the discrepancy observed in the literature. Two different parameters, calculated from experimental variables, could be used to separate the data obtained in this work and those reported in the literature in two groups: one explained with the no-slip BC, and another with the slip BC. The observed residual slippage is a function of instrumental variables, showing a trend incompatible with the available physical justifications. As a result, the no-slip is the more appropriate BC. The parameters can be used to avoid situations where the no-slip BC is not satisfied.

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