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The presented study was motivated by the dynamic phenomena observed in basic catalytic surface reactions, especially by bi- and tristability, and the interactions between these stable states. In this regard, three reaction-diffusion models were developed and examined using bifurcation theory and numerical simulations.
A first model was designed to extend the bistable CO oxidation on Ir(111) to include hydrogen and its oxidation. The differential equation system was analyzed within the framework of bifurcation theory, revealing three branches of stable solutions.
One state is characterized by high formation rates (upper rate state, UR), while the other two branches display low formation rates (lower rate (LR) \& very low rate (VLR) states).
The overlapping branches form the shape of a `swallowtail', the curve of saddle-node bifurcations forming two cusps. Increasing the temperature leads to a subsequent unfolding and hence decreases the system complexity.
A series of numerical simulations representing possible experiments was conducted to illustrate the experimental accessibility (or the lack) of said states. Relaxation experiments show partially long decay times. Quasistatic scanning illustrates the existence of all three states within the tristable regime and their respective conversion once crossing a fold.
A first attempt regarding the state dominance in reaction-diffusion fronts was done. While UR seems to dominate in 1D, a 2D time-evolution shows that LR invades the interphase between UR and VLR.
Subsequently, a generic monospecies mock model was used for the comprehensive study of reaction-diffusion fronts. A quintic polynomial as reaction term was chosen, derived by the sixth-order potential associated with the `butterfly bifurcation'. This ensures up to three stable solutions($u_{0}$,$u_{1}$,$u_{2}$), depending on the four-dimensional parameter space.
The model was explored extensively, identifying regions with similar behaviors.
A term for the front velocity connecting two stable states was derived, depending only on the relative difference of the states' potential wells.
Equipotential curves were found, where the front velocity vanishes of a given front. Numerical simulations on a two-dimensional, finite disk using a triangulated mesh supported these findings.
Additionally, the front-splitting instability was observed for certain parameters. The front solution $u_{02}$ becomes unstable and divides into $u_{01}$ and $u_{12}$, exhibiting different front velocities. A good estimate for the limit of the front splitting region was given and tested using time evolutions.
Finally, the established mock model was modified from continuous to discrete space, utilizing a simple domain in 1D and three different lattices in 2D (square, hexagonal, triangular).
For low diffusivities or large distances between coupling nodes, fronts can become pinned, if the parameters are within range of the equipotential lines. This phenomenon is known as propagation failure and its extent in parameter space was explored in 1D. In 2D, an estimate was given for remarkable front orientations respective to the lattice using a pseudo-2D approximation. Near the pinning region, front velocities differ significantly from the continuous expectation as the shape of the curve potential becomes significant. Factors that decide the size and shape of the pinning regions are the coupling strength, the lattice, the front orientation relative to the lattice, and the front itself. The bifurcation diagram shows a snaking curve in the pinning region, each alternating branch representing a stable or unstable frozen front solution. Numerical simulations supported the observations concerning propagation failure and lattice dependence.
Furthermore, the influence of front orientation on the front velocity was explored in greater detail, showing that fronts with certain lattice-dependent orientations are more or less prone to propagation failure. This leads to the possibility of pattern formation, reflecting the lattice geometry. An attempt to quantify the front movement depending on angular front orientation has shown reasonable results and good agreement with the pseudo-2D approach.
Different techniques (weight loss, electrochemical, and spray
corrosion measurements) have been used to evaluate four sarcosine derivatives to inhibit corrosion and one commercial compound as synergist. The basic metal was low carbon steel CR4 tested at different conditions. As working media mainly neutral water and 0.1 M NaCl was applied. The protective film was formed on the steel surface via direct absorption of the tested substances during the immersion process. A highly improved corrosion protection with direct correlation to the molecular weight and carbon chain length of the tested compounds was detected. The protection of steel CR4 against corrosion in 0.1 M NaCl enhanced with increasing concentration of selected sarcosine compounds. The best inhibitor throughout all tested concentrations and all evaluation systems was Oleoylsarcosine (O) with efficiencies up to 97 % in potentiodynamic polarization (PP), 83 % electrochemical impedance spectroscopy (EIS), and 85 % weight loss (WL) at 100 mmol/L as highest concentration tested here. The second best inhibitor was Myristoylsarcosine (M) with efficiencies up to 82 % in PP, 69 % in EIS, and 75 % in WL at highest concentration. The inhibitor with the shortest hydrocarbon chain in this series is Lauroylsarcosine (L). It showed lowest effects to inhibit corrosion compared to O and M. The efficiencies of L were a bit more than 50 % at 75 and 100 mmol/L and less than 50 % at 25 and 50 mmol/L in all used evaluation systems. Furthermore, the overall efficiency is promoted with longer dip coating times during the steel CR4 immersion as shown for 50 mmol/L for all present derivatives. This survey indicated 10 min as best time in respect of cost and protection efficiency. The commercial inhibitor Oley-Imidazole (OI) improved significantly the effectiveness of compound Cocoylsarcosine (C), which contains the naturally mixture of carbon chain lengths from coconut oil (C8 - C18), and enhanced protection when used in combination (C+OI, 1:1 molar ration). In this system the efficiency increased from 47 % to 91 % in PP, from 40 % to 84 % in EIS, and from 45 % to 82 % in WL at highest concentration. Spray corrosion tests were used to evaluate all present sarcosine substances on steel CR4 in a more realistic system. The best inhibitor after a 24 h test was O followed by the combination C+OI and M with efficiencies up to 99 %, 80 %, and 79 %, respectively. The obtained results indicate a good stability of the protective film formed by the present inhibitors even after 24 h. All evaluation systems used in the current investigation were in good agreement and resulted in the same inhibitor sequence. Furthermore, the adsorption process of the tested compounds is assumed to follow the Langmuir type isotherm. Response surface methodology (RSM) is an optimization method depending on Box- Behnken Design (BBD). It was used in the current system to find the optimum efficiency for inhibitor O to protect steel CR4 against corrosion in salt water. Four independent variables were used here: inhibitor concentration (A), dip coating time (B), temperature (C), and NaCl concentration (D); each with three respective levels: lower (-1), mid (0), and upper (+1). According to the present result, temperature has the greatest effect on the protection process as individual parameter followed by the inhibitor concentration itself. In this investigation an optimum efficiency of 99 % is calculated by the following parameter and level combination: upper level (+1) for inhibitor concentration, dip coating time, and NaCl concentration while lower level (-1) for temperature.
The three biodegradable polymers polylactic acid (PLA), polyhydroxybutyrate (PHB) and polybutylene adipate terephthalate (PBAT) were coated with hydrogenated amorphous carbon layers (a-C:H) in the context of this thesis. A direct alignment of the sample surface to the source was chosen, resulting in the deposition of a robust, r-type a-C:H. At the same time, a partly covered silicon wafer was placed together with the polymers in the coating chamber and was coated. Silicon is a hard material and serves as a reference for the applied layers. Due to the hardness of the material, no mixed phase occurs between the substrate and the applied layer (no interlayer formation). In addition, the thickness of the applied layer can be estimated with the help of the silicon sample.
The deposition of the layer was realized by radio frequency plasma enhanced chemical vapor deposition (RF-PECVD). For the coating the samples were pre-treated with an oxygen plasma. Acetylene was used as precursor gas for the plasma coating. Coatings with increasing thickness in 50 nm steps from 0-500 nm were realised.
The surface analysis was performed using several techniques: The morphology and layer stability were analyzed with scanning electron microscopy (SEM) measurements. The wettability was determined by contact angle technique. In addition, the contact angles provide macroscopic information about the bond types of the carbon atoms present on the surface. For microscopic analysis of the chemical composition of the sample and layer surfaces, diffuse reflectance Fourier transform infrared spectroscopy (DRIFT) as well as synchrotron based X-ray photon spectroscopy (XPS) and near edge X-ray absorption fine structure spectroscopy (NEXAFS) were used.
All coated polymers showed several cases of layer failure due to internal stress in the layers. However, these were at different layer thicknesses, so there was a substrate effect. In addition, it is visible in the SEM images that the coatings of PLA and PHB can cause the applied layer to wave, the so-called cord buckling. This does not occur with polymer PBAT, which indicates a possible better bonding of the layer to the polymer. The chemical analyses of the layer surfaces show for each material a layer thickness dependent ratio of sp² to sp³ bonds of carbon, which alternately dominate the layer. In all polymers, the sp³ bond initially dominates, but the sp² to sp³ ratio changes at different intervals. Although the polymers were coated in the same plasma, i.e. the respective layer thicknesses (50 nm, 100 nm, ...) were applied in the same plasma process, the respective systems differed considerably from each other. A substrate effect is therefore demonstrably present. In addition, it was found that a change in the dominant bond from sp³ to sp² is an indication ofan upcoming layer failure of the a-C:H layer deposited on the polymer. In the case of PLA, this occurs immediately with change to sp² as the dominant bond; in the case of PHB and PBAT, this occurs with different delay to increased layer thicknesses (at PHB 100 nm, at PBAT approx. 200 nm.
Overall, this thesis shows that there is a substrate effect in the coating of the biodegradable polymers PLA, PHB and PBAT, since despite the same coating there is a different chemical composition of the surface at the respective layer thicknesses. In addition, a layer failure can be predicted by analyzing the existing bond.
To render the surface of a material capable of withstanding mechanical and electrochemical loads, and to perform well in service, the deposition of a thin film or coating is a solution. In this project, such a thin film deposition is carried out. The coating material chosen is titanium nitride (TiN) which is a ceramic material known to possess a high hardness (>10 GPa) as well as good corrosion resistance. The method of deposition selected is high power impulse magnetron sputtering (HiPIMS) that results in coatings with high quality and enhanced properties. Sputtering is a physical process that represents the removal or dislodgment of surface atoms by energetic particle bombardment. The term magnetron indicates that a magnetic field is utilized to increase the efficiency of the sputtering process. In HiPIMS, a high power is applied in pulses of low duty cycles to a cathode that is sputtered and that consists of the coating material. As result of the high power, the ionization of the sputtered material takes place giving the possibility to control these species with electric and magnetic field allowing thereby the improvement and tuning of coating properties. However, the drawback of HiPIMS is a low deposition rate.
In this project, it is demonstrated first that it is possible to deposit TiN coating using HiPIMS with an optimized deposition rate, by varying the magnetic field strength. It was found that low magnetic field strength (here 22mT) results in a deposition rate similar to that of conventional magnetron sputtering in which the average power is applied continuously, called also direct current magnetron sputtering (dcMS). The high deposition rate at low magnetic field strength was attributed to a reduction in the back attraction probability of the sputtered species. The magnetic field strength did not show noticeable influence on the mechanical properties. The proposed explanation was that the considered peak current density interval 1.22-1.72 A∙cm-2 does not exhibit dramatic changes in the plasma dynamics.
In a second part, using the optimized deposition rate, the optimized chemical composition of TiN was determined. It was shown that the chemical composition of TiN does not significantly influence the corrosion performance but impacts considerably the mechanical properties. It was also shown that the corrosion resistance of the coatings deposited using HiPIMS was higher than that of the coatings deposited using dcMS.
The third study was the effect of annealing post deposition on the properties of TiN coating deposited using HiPIMS. The hardness of the coatings showed a maximum at 400°C reaching 24.8 GPa. Above 400°C however, a lowering of the hardness was measured and was due to the oxidation of TiN which led to the formation of TiN-TiO2 composites with lower mechanical properties.
The coating microscopic properties such as crystal orientation, residual stresses, average grain size were determined from X-ray diffraction data and the roughness was measured using atomic force microscopy. These properties were found to vary with the magnetic field strength, the chemical composition as well as the annealing temperature.
Fachdidaktische und pädagogische Kompetenzen angehender Mathematiklehrkräfte für die Realschule
(2019)
Studien zur Wirksamkeit der Ausbildung von Lehrerinnen und Lehrern sind in der Regel fragebogenbasiert. In der vorliegenden Untersuchung wird ein anderer Ansatz gewählt, um die Kompetenzen angehender Mathematiklehrkräfte zu erheben und zu evaluieren. Die Studie untersucht anhand der unterrichtlichen Performanz, welche Kompetenzen Anwärterinnen und Anwärter in ihrer praktischen Ausbildung erworben haben. Der Analyse liegen 137 anonymisierte Niederschriften zu benote-ten Lehrproben von Anwärterinnen und Anwärtern im Fach Mathematik zugrunde. Diese bilden die Ausbildungsjahrgänge von 2004 bis 2011 ab. Die Anwärterinnen und Anwärter werden unterrichtspraktisch anhand der Niederschriften in Anlehnung an eine qualitative Inhaltsanalyse auf ihre Kompetenzausprägungen hin getestet. Dies erfolgt schwerpunktmäßig in den Bereichen Fachdidaktik, Fachmethodik, Classroom-Management und Gesprächsführung. Im Verlauf der Untersuchung wird deutlich, dass die Teilneh-mergruppe vor allem Stärken im methodischen Bereich hat. Hier können durchgehend gute Kompetenzausprägungen festgestellt werden. Über den gesamten Erhebungszeitraum zeigen sich hingegen in den Bereichen Classroom-Management und Gesprächsführung deutliche Defizite. Die fachdidaktischen Kompetenzen der angehenden Lehrkräfte entwickeln sich negativ: Ist zu Beginn der Erhebung noch etwa die Hälfte der Anwärterinnen und Anwärter im Bereich der Fachdidaktik zufriedenstellend einzustufen, gilt das im letzten Erhebungsjahrgang nur noch für knapp ein Fünftel der Probandinnen und Probanden. Es kann gezeigt werden, dass eine gute Notenfestsetzung eng mit den er-forderlichen Kompetenzen in der Fachdidaktik zusammenhängt.
Die vorliegende Studie bestätigt im Bereich der Fachdidaktik die Ergebnisse jener Studien, die auf Fragebögen basieren.
Es konnte zudem ein statistischer Zusammenhang zwischen den fachdidaktischen Fähigkeiten und den Steuerungskompetenzen hergestellt werden.
The biodegradable polymers polylactic acid (PLA) and polyhydroxybutyrate (PHB) produced from renewable raw materials were coated with hydrogenated amorphous carbon layers (a-C:H) at different deposition angles with various thicknesses as part of this thesis. Similar to conventional polymers, biopolymers often have unsuitable surface properties for industrial purposes, e.g. low hardness. For some applications, it is therefore necessary and advantageous to modify the surface properties of biopolymers while retaining the main properties of the substrate material. A suitable surface modification is the deposition of thin a-C:H layers. Their properties depend essentially on the sp² and sp³ hybridization ratio of the carbon atoms and the content of hydrogen atoms. The sp²/sp³ ratio was to be controlled in the present work by varying the coating geometry. Since coatings at 0°, directly in front of the plasma source, contain a higher percentage of sp³ and indirectly coated (180°) a higher amount of sp², it is shown in this work that it is possible to control the sp²/sp³ ratio. For this purpose, the samples are placed in front of the plasma source at angles of 0, 30, 60, 90, 120, 150 and 180° and coated for 2.5, 5.0, 7.5 and 10.0 minutes. For the angles 0°, the layer thicknesses were 25, 50, 75 and 100 nm. The a-C:H layers were all deposited using radio-frequency plasma-enhanced chemical vapor deposition and acetylene as C and H sources after being pretreated with an oxygen plasma for 10 minutes. Following the O₂ treatment and the a-C:H deposition, the surfaces are examined using macroscopic and microscopic measurement methods and the data is then analyzed. The surface morphology is recorded using scanning electron microscopy and atomic force microscopy. In addition, data on the stability of the layer and the surface roughness can be collected. Contact angle (CA) measurements are used to determine not only the wettability, but also the contact angle hysteresis by pumping the drop volume up and down. By measuring the CA with different liquids and comparing them, the surface free energy (SFE) and its polar and disperse components are determined. The changes in barrier properties are verified by water vapor transmission rate tests (WVTR). The chemical analysis of the surface is carried out on the one hand by Fourier transform infrared spectroscopy with specular reflection and on the other hand by synchrotron-supported techniques such as near-edge X-ray absorption fine structure and X-ray photoelectron spectroscopy. When analyzing the surfaces after the O₂ treatment, which was initially assumed to serve only to clean and activate the surface for the a-C:H coating, it was found that the changes were more drastic than originally assumed. For example, if PLA is treated at 0° for 10 minutes, the roughness increases fivefold. As the angle increases, it decreases again until it returns to the initial value at 180°. This can be recognized to a lesser extent with PHB at 30°. For both polymers, it can be shown that the polar fraction of the SFE increases. In the WVTR, a decrease in permeability can be observed for PLA and an increase in the initial value for PHB. The chemical surface analysis shows that the O₂ treatment has little effect on the surface bonds. Overall, it can be shown in this work that the O₂ treatment has an effect on the properties of the surface and cannot be regarded exclusively as a cleaning and activation process. With direct a-C:H coating (at 0°), a layer failure due to internal stress can be observed for both PLA and PHB. This also occurs with PHB at 30°, but to a lesser extent. Permeability of the polymers is reduced by 47% with a five-minute coating and the layer at 10.0 minutes continues to have this effect despite cracks appearing. The application of a-C:H layers shows a dominance of sp³ bonds for both polymer types with direct coating. This decreases with increasing angle and sp² bonds become dominant for indirect coatings. This result is similar for all coating thicknesses, only the angle at which the change of the dominant bond takes place is different. It is shown that it is possible to control the surface properties by an angle-dependent coating and thus to control the ratio sp²/sp³.
During the development phase of plastic components, simulations are being used to an increasing extent. Against the background of product requirements and the inevitable necessity of conserving resources, the expanded use of simulation tools is an essential part of the solution. Among available methods, but so far underutilized with respect to real-life processes, is the molecular dynamics simulation. By the use of this method it is possible to visualize the physical processes occurring on the microscopic level, as e.g. those that arise during plastics processing. This thesis examines how boundary conditions, which mimic the extrusion blow molding process, affect the behavior of polyethylene on the microscopic level. A mesoscopic model (coarse-graining) is applied to describe the polymer. Initially, this model is verified by determining material properties. The uniaxial tensile test is modeled on the micro-scale to identify parameters such as the elastic modulus, yield stress, and Poisson’s ratio. Additionally, thermal properties, particularly those characterizing the crystallization behavior, are identified. The objective of these investigations is the microscopic observation and quantification of effects that occur during dynamic stretching and crystallization processes. The calculated properties show good agreement with the experimental data, especially regarding the thermal parameters. Qualitatively, the stress-strain behavior is reproduced in alignment with experimentally observed results. However, the short time scale of the simulation models leads to micromechanical behavior that is more extreme than what is monitored on a macroscopic level. By extending the simulation models, biaxial stretching processes are simulated. These stretching processes resemble the situation during the inflation of the parison in the extrusion blow molding process. The examination of various cooling conditions, particularly by the use of mold constraints, is another focus of the investigations. The analysis of the biaxially stretched simulations reveals that disentanglement processes during stretching dominate the further development of polymer systems. It is possible to quantify the dynamics of crystallization processes depending on the degree of stretching and cooling conditions through various parameters (distribution of entanglement points, local orientations). The results indicate that coarse-grained molecular dynamics simulations are able to significantly enhance the micromechanical understanding of local events occurring during plastic processing.