Characterisation and field deployment of a novel quantitative Time-of-Flight Aerosol Mass Spectrometer (ToF-AMS)

Das Time-of-Flight Aerosol Mass Spectrometer (ToF-AMS) der Firma Aerodyne ist eine Weiterentwicklung des Aerodyne Aerosolmassenspektrometers (Q-AMS). Dieses ist gut charakterisiert und kommt weltweit zum Einsatz. Beide Instrumente nutzen eine aerodynamische Linse, aerodynamische Partikelgrößenbestimmung, thermische Verdampfung und Elektronenstoß-Ionisation. Im Gegensatz zum Q-AMS, wo ein Quadrupolmassenspektrometer zur Analyse der Ionen verwendet wird, kommt beim ToF-AMS ein Flugzeit-Massenspektrometer zum Einsatz. In der vorliegenden Arbeit wird anhand von Laborexperimenten und Feldmesskampagnen gezeigt, dass das ToF-AMS zur quantitativen Messung der chemischen Zusammensetzung von Aerosolpartikeln mit hoher Zeit- und Größenauflösung geeignet ist. Zusätzlich wird ein vollständiges Schema zur ToF-AMS Datenanalyse vorgestellt, dass entwickelt wurde, um quantitative und sinnvolle Ergebnisse aus den aufgenommenen Rohdaten, sowohl von Messkampagnen als auch von Laborexperimenten, zu erhalten. Dieses Schema basiert auf den Charakterisierungsexperimenten, die im Rahmen dieser Arbeit durchgeführt wurden. Es beinhaltet Korrekturen, die angebracht werden müssen, und Kalibrationen, die durchgeführt werden müssen, um zuverlässige Ergebnisse aus den Rohdaten zu extrahieren. Beträchtliche Arbeit wurde außerdem in die Entwicklung eines zuverlässigen und benutzerfreundlichen Datenanalyseprogramms investiert. Dieses Programm kann zur automatischen und systematischen ToF-AMS Datenanalyse und –korrektur genutzt werden.

Reactive halogen compounds in the marine boundary layer: method developments and field measurements

Reactive halogen compounds are known to play an important role in a wide variety of atmospheric processes such as atmospheric oxidation capacity and coastal new particle formation. In this work, novel analytical approaches combining diffusion denuder/impinger sampling techniques with gas chromatographic–mass spectrometric (GC–MS) determination are developed to measure activated chlorine compounds (HOCl and Cl2), activated bromine compounds (HOBr, Br2, BrCl, and BrI), activated iodine compounds (HOI and ICl), and molecular iodine (I2). The denuder/GC–MS methods have been used to field measurements in the marine boundary layer (MBL). High mixing ratios (of the order of 100 ppt) of activated halogen compounds and I2 are observed in the coastal MBL in Ireland, which explains the ozone destruction observed. The emission of I2 is found to correlate inversely with tidal height and correlate positively with the levels of O3 in the surrounding air. In addition the release is found to be dominated by algae species compositions and biomass density, which proves the “hot-spot” hypothesis of atmospheric iodine chemistry. The observations of elevated I2 concentrations substantially support the existence of higher concentrations of littoral iodine oxides and thus the connection to the strong ultra-fine particle formation events in the coastal MBL.

Exchange of nitrogen dioxide (NO 2) between plants and the atmosphere under laboratory and field conditions

Nitrogen is an essential nutrient. It is for human, animal and plants a constituent element of proteins and nucleic acids. Although the majority of the Earth’s atmosphere consists of elemental nitrogen (N2, 78 %) only a few microorganisms can use it directly. To be useful for higher plants and animals elemental nitrogen must be converted to a reactive oxidized form. This conversion happens within the nitrogen cycle by free-living microorganisms, symbiotic living Rhizobium bacteria or by lightning. Humans are able to synthesize reactive nitrogen through the Haber-Bosch process since the beginning of the 20th century. As a result food security of the world population could be improved noticeably. On the other side the increased nitrogen input results in acidification and eutrophication of ecosystems and in loss of biodiversity. Negative health effects arose for humans such as fine particulate matter and summer smog. Furthermore, reactive nitrogen plays a decisive role at atmospheric chemistry and global cycles of pollutants and nutritive substances.rnNitrogen monoxide (NO) and nitrogen dioxide (NO2) belong to the reactive trace gases and are grouped under the generic term NOx. They are important components of atmospheric oxidative processes and influence the lifetime of various less reactive greenhouse gases. NO and NO2 are generated amongst others at combustion process by oxidation of atmospheric nitrogen as well as by biological processes within soil. In atmosphere NO is converted very quickly into NO2. NO2 is than oxidized to nitrate (NO3-) and to nitric acid (HNO3), which bounds to aerosol particles. The bounded nitrate is finally washed out from atmosphere by dry and wet deposition. Catalytic reactions of NOx are an important part of atmospheric chemistry forming or decomposing tropospheric ozone (O3). In atmosphere NO, NO2 and O3 are in photosta¬tionary equilibrium, therefore it is referred as NO-NO2-O3 triad. At regions with elevated NO concentrations reactions with air pollutions can form NO2, altering equilibrium of ozone formation.rnThe essential nutrient nitrogen is taken up by plants mainly by dissolved NO3- entering the roots. Atmospheric nitrogen is oxidized to NO3- within soil via bacteria by nitrogen fixation or ammonium formation and nitrification. Additionally atmospheric NO2 uptake occurs directly by stomata. Inside the apoplast NO2 is disproportionated to nitrate and nitrite (NO2-), which can enter the plant metabolic processes. The enzymes nitrate and nitrite reductase convert nitrate and nitrite to ammonium (NH4+). NO2 gas exchange is controlled by pressure gradients inside the leaves, the stomatal aperture and leaf resistances. Plant stomatal regulation is affected by climate factors like light intensity, temperature and water vapor pressure deficit. rnThis thesis wants to contribute to the comprehension of the effects of vegetation in the atmospheric NO2 cycle and to discuss the NO2 compensation point concentration (mcomp,NO2). Therefore, NO2 exchange between the atmosphere and spruce (Picea abies) on leaf level was detected by a dynamic plant chamber system under labo¬ratory and field conditions. Measurements took place during the EGER project (June-July 2008). Additionally NO2 data collected during the ECHO project (July 2003) on oak (Quercus robur) were analyzed. The used measuring system allowed simultaneously determina¬tion of NO, NO2, O3, CO2 and H2O exchange rates. Calculations of NO, NO2 and O3 fluxes based on generally small differences (∆mi) measured between inlet and outlet of the chamber. Consequently a high accuracy and specificity of the analyzer is necessary. To achieve these requirements a highly specific NO/NO2 analyzer was used and the whole measurement system was optimized to an enduring measurement precision.rnData analysis resulted in a significant mcomp,NO2 only if statistical significance of ∆mi was detected. Consequently, significance of ∆mi was used as a data quality criterion. Photo-chemical reactions of the NO-NO2-O3 triad in the dynamic plant chamber’s volume must be considered for the determination of NO, NO2, O3 exchange rates, other¬wise deposition velocity (vdep,NO2) and mcomp,NO2 will be overestimated. No significant mcomp,NO2 for spruce could be determined under laboratory conditions, but under field conditions mcomp,NO2 could be identified between 0.17 and 0.65 ppb and vdep,NO2 between 0.07 and 0.42 mm s-1. Analyzing field data of oak, no NO2 compensation point concentration could be determined, vdep,NO2 ranged between 0.6 and 2.71 mm s-1. There is increasing indication that forests are mainly a sink for NO2 and potential NO2 emissions are low. Only when assuming high NO soil emissions, more NO2 can be formed by reaction with O3 than plants are able to take up. Under these circumstance forests can be a source for NO2.

Laboratory study on the optical properties of absorbing atmospheric aerosols and field applications

The interaction between aerosols and sun light plays an important role in the radiative balance of Earth’s atmosphere. This interaction is obtained by measuring the removal (extinction), redistribution (scattering), and transformation into heat (absorption) of light by the aerosols; i.e. their optical properties. Knowledge of these properties is crucial for our understanding of the atmospheric system. rn Light absorption by aerosols is a major contributor to the direct and indirect effects on our climate system, and an accurate and sensitive measurement method is crucial to further our understanding. A homebuilt photoacoustic sensor (PAS), measuring at a 532nm wavelength, was fully characterized and its functionality validated for measurements of absorbing aerosols. The optical absorption cross-sections of absorbing polystyrene latex spheres, to be used as a standard for aerosol absorption measurements, were measured and compared to literature values. Additionally, a calibration method using absorbing aerosol of known complex refractive index was presented.rn A new approach to retrieve the effective broadband refractive indices (mbroad,eff) of aerosol particles by a white light aerosol spectrometer (WELAS) optical particle counter (OPC) was achieved. Using a tandem differential mobility analyzer (DMA)-OPC system, the nbroad,eff are obtained for both laboratory and field applications. This method was tested in the laboratory using substances with a wide range of optical properties and it was used in ambient measurements to retrieve the nbroad,eff of biomass burning aerosols in a nationwide burning event in Israel. The retrieved effective broadband refractive indices for laboratory generated scattering aerosols were: ammonium sulfate (AS), glutaric acid (GA), and sodium chloride, all within 4% of literature values. For absorbing substances, nigrosine and various mixtures of nigrosine with AS and GA were measured, as well as a lightly absorbing substance, Suwannee river fulvic acid (SRFA). For the ambient measurements, the calibration curves generated from this method were to follow the optical evolution of biomass burning (BB) aerosols. A decrease in the overall aerosol absorption and scattering for aged aerosols during the day after the fires compared to the smoldering phase of the fires was found. rn The connection between light extinction of aerosols, their chemical composition and hygroscopicity for particles with different degrees of absorption was studied. The extinction cross-section (σext) at 532nm for different mobility diameters was measured at 80% and 90% relative humidity (RH), and at an RH<10%. The ratio of the humidified aerosols to the dry ones, fRHext(%RH,Dry), is presented. For purely scattering aerosols, fRHext(%RH,Dry) is inversely proportional with size; this dependence was suppressed for lightly absorbing ones. In addition, the validity of the mixing rules for water soluble absorbing aerosols is explored. The difference between the derived and calculated real parts of the complex RIs were less than 5.3% for all substances, wavelengths, and RHs. The obtained imaginary parts for the retrieved and calculated RIs were in good agreement with each other, and well within the measurement errors of retrieval from pulsed CRD spectroscopy measurements. Finally, a core-shell structure model is also used to explore the differences between the models, for substances with low growth factors, under these hydration conditions. It was found that at 80% RH and for size parameters less than 2.5, there is less than a 5 % difference between the extinction efficiencies calculated with both models. This difference is within measurement errors; hence, there is no significant difference between the models in this case. However, for greater size parameters the difference can be up to 10%. For 90% RH the differences below a size parameter of 2.5 were up to 7%.rn Finally, the fully characterized PAS together with a cavity ring down spectrometer (CRD), were used to study the optical properties of soot and secondary organic aerosol (SOA) during the SOOT-11 project in the AIDA chamber in Karlsruhe, Germany. The fresh fractal-like soot particles were allowed to coagulate for 28 hours before stepwise coating them with SOA. The single scattering albedo for fresh fractal-like soot was measured to be 0.2 (±0.03), and after allowing the soot to coagulate for 28 hours and coating it with SOA, it increased to 0.71(±0.01). An absorption enhancement of the coated soot of up to 1.71 (±0.03) times from the non-coated coagulated soot was directly measured with the PAS. Monodisperse measurements of SOA and soot coated with SOA were performed to derive the complex refractive index (m) of both aerosols. A complex refractive index of m = 1.471(±0.008) + i0.0(±0.002) for the SOA-αO3 was retrieved. For the compact coagulated soot a preliminary complex refractive index of m = 2.04(+0.21/-0.14) + i0.34(+0.18/-0.06) with 10nm(+4/-6) coating thickness was retrieved.rn These detail properties can be use by modelers to decrease uncertainties in assessing climatic impacts of the different species and to improve weather forecasting.rn

Laboratory and field measurements of enantiomeric and non-enantiomeric biogenic VOCs and anthropogenic BTEX compounds

This doctoral thesis was focused on the investigation of enantiomeric and non-enantiomeric biogenic organic compound (BVOC) emissions from both leaf and canopy scales in different environments. In addition, the anthropogenic compounds benzene, toluene, ethylbenzene, and xylenes (BTEX) were studied. BVOCs are emitted into the lower troposphere in large quantities (ca. 1150 Tg C ·yr-1), approximately an order of magnitude greater than the anthropogenic VOCs. BVOCs are particularly important in tropospheric chemistry because of their impact on ozone production and secondary organic aerosol formation or growth. The BVOCs examined in this study were: isoprene, (-)/ (+)-α-pinene, (-)/ (+)-ß-pinene, Δ-3-carene, (-)/ (+)-limonene, myrcene, eucalyptol and camphor, as these were the most abundant BVOCs observed both in the leaf cuvette study and the ambient measurements. In the laboratory cuvette studies, the sensitivity of enantiomeric enrichment change from the leaf emission has been examined as a function of light (0-1600 PAR) and temperature (20-45°C). Three typical Mediterranean plant species (Quercus ilex L., Rosmarinus officinalis L., Pinus halepensis Mill.) with more than three individuals of each have been investigated using a dynamic enclosure cuvette. The terpenoid compound emission rates were found to be directly linked to either light and temperature (e.g. Quercus ilex L.) or mainly to temperature (e.g. Rosmarinus officinalis L., Pinus halepensis Mill.). However, the enantiomeric signature showed no clear trend in response to either the light or temperature; moreover a large variation of enantiomeric enrichment was found during the experiment. This enantiomeric signature was also used to distinguish chemotypes beyond the normal achiral chemical composition method. The results of nineteen Quercus ilex L. individuals, screened under standard conditions (30°C and 1000 PAR) showed four different chemotypes, whereas the traditional classification showed only two. An enclosure branch cuvette set-up was applied in the natural boreal forest environment from four chemotypes of Scots pine (Pinus sylvestris) and one chemotype of Norway spruce (Picea abies) and the direct emissions compared with ambient air measurements above the canopy during the HUMPPA-COPEC 2010 summer campaign. The chirality of a-pinene was dominated by (+)-enantiomers from Scots pine while for Norway spruce the chirality was found to be opposite (i.e. Abstract II (-)-enantiomer enriched) becoming increasingly enriched in the (-)-enantiomer with light. Field measurements over a Spanish stone pine forest were performed to examine the extent of seasonal changes in enantiomeric enrichment (DOMINO 2008). These showed clear differences in chirality of monoterpene emissions. In wintertime the monoterpene (-)-a-pinene was found to be in slight enantiomeric excess over (+)-a-pinene at night but by day the measured ratio was closer to one i.e. racemic. Samples taken the following summer in the same location showed much higher monoterpene mixing ratios and revealed a strong enantiomeric excess of (-)-a-pinene. This indicated a strong seasonal variance in the enantiomeric emission ratio which was not manifested in the day/night temperature cycles in wintertime. A clear diurnal cycle of enantiomeric enrichment in a-pinene was also found over a French oak forest and the boreal forest. However, while in the boreal forest (-)-a-pinene enrichment increased around the time of maximum light and temperature, the French forest showed the opposite tendency with (+)-a-pinene being favored. For the two field campaigns (DOMINO 2008 and HUMPPA-COPEC 2010), the BTEX were also investigated. For the DOMINO campaign, mixing ratios of the xylene isomers (meta- and para-) and ethylbenzene, which are all well resolved on the ß-cyclodextrin column, were exploited to estimate average OH radical exposures to VOCs from the Huelva industrial area. These were compared to empirical estimates of OH based on JNO2 measured at the site. The deficiencies of each estimation method are discussed. For HUMPPA-COPEC campaign, benzene and toluene mixing ratios can clearly define the air mass influenced by the biomass burning pollution plume from Russia.

Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity

Among the different approaches for a construction of a fundamental quantum theory of gravity the Asymptotic Safety scenario conjectures that quantum gravity can be defined within the framework of conventional quantum field theory, but only non-perturbatively. In this case its high energy behavior is controlled by a non-Gaussian fixed point of the renormalization group flow, such that its infinite cutoff limit can be taken in a well defined way. A theory of this kind is referred to as non-perturbatively renormalizable. In the last decade a considerable amount of evidence has been collected that in four dimensional metric gravity such a fixed point, suitable for the Asymptotic Safety construction, indeed exists. This thesis extends the Asymptotic Safety program of quantum gravity by three independent studies that differ in the fundamental field variables the investigated quantum theory is based on, but all exhibit a gauge group of equivalent semi-direct product structure. It allows for the first time for a direct comparison of three asymptotically safe theories of gravity constructed from different field variables. The first study investigates metric gravity coupled to SU(N) Yang-Mills theory. In particular the gravitational effects to the running of the gauge coupling are analyzed and its implications for QED and the Standard Model are discussed. The second analysis amounts to the first investigation on an asymptotically safe theory of gravity in a pure tetrad formulation. Its renormalization group flow is compared to the corresponding approximation of the metric theory and the influence of its enlarged gauge group on the UV behavior of the theory is analyzed. The third study explores Asymptotic Safety of gravity in the Einstein-Cartan setting. Here, besides the tetrad, the spin connection is considered a second fundamental field. The larger number of independent field components and the enlarged gauge group render any RG analysis of this system much more difficult than the analog metric analysis. In order to reduce the complexity of this task a novel functional renormalization group equation is proposed, that allows for an evaluation of the flow in a purely algebraic manner. As a first example of its suitability it is applied to a three dimensional truncation of the form of the Holst action, with the Newton constant, the cosmological constant and the Immirzi parameter as its running couplings. A detailed comparison of the resulting renormalization group flow to a previous study of the same system demonstrates the reliability of the new equation and suggests its use for future studies of extended truncations in this framework.

Electronic transport in the heavy fermion superconductors UPd 2 Al 3 and UNi 2 Al 3

This work addresses the electronical properties of the superconductors UPd2Al3 and UNi2Al3 on the basis of thin film experiments. These isotructural compounds are ideal candiates to study the interplay of magnetism and superconductivity due to the differences of their magnetically ordered states, as well as the experimental evidence for a magnetic pairing mechanism in UPd2Al3. Epitaxial thin film samples of UPd2Al3 and UNi2Al3 were prepared using UHV Molecular Beam Epitaxy (MBE). For UPd2Al3, the change of the growth direction from the intrinsic (001) to epitaxial (100) was predicted and sucessfully demonstrated using LaAlO3 substrates cut in (110) direction. With optimized deposition process parameters for UPd2Al3 (100) on LaAlO3 (110) superconducting samples with critical temperatures up to Tc = 1.75K were obtained. UPd2Al3-AlOx-Ag mesa junctions with superconducting base electrode were prepared and shown to be in the tunneling regime. However, no signatures of a superconducting density of states were observed in the tunneling spectra. The resistive superconducting transition was probed for a possible dependence on the current direction. In contrast to UNi2Al3, the existence of such feature was excluded in UPd2Al3 (100) thin films. The second focus of this work is the dependence of the resisitive transition in UNi2Al3 (100) thin films on the current direction. The experimental fact that the resisitive transition occurs at slightly higher temperatures for I║a than for I║c can be explained within a model of two weakly coupled superconducting bands. Evidence is presented for the key assumption of the two-band model, namely that transport in and out of the ab-plane is generated on different, weakly coupled parts of the Fermi surface. Main indications are the angle dependence of the superconducting transition and the dependence of the upper critical field Bc2 on current and field orientation. Additionally, several possible alternative explanations for the directional splitting of the transition are excluded in this work. An origin due to scattering on crystal defects or impurities is ruled out, likewise a relation to ohmic heating or vortex dynamics. The shift of the transition temperature as function of the current density was found to behave as predicted by the Ginzburg-Landau theory for critical current depairing, which plays a significant role in the two-band model. In conclusion, the directional splitting of the resisitive transition has to be regarded an intrinsic and unique property of UNi2Al3 up to now. Therefore, UNi2Al3 is proposed as a role model for weakly coupled multiband superconductivity. Magnetoresistance in the normalconducting state was measured for UPd2Al3 and UNi2Al3. For UNi2Al3, a negative contribution was observed close to the antiferromagnetic ordering temperature TN only for I║a, which can be associated to reduced spin-disorder scattering. In agreement with previous results it is concluded that the magnetic moments have to be attributed to the same part of the Fermi surface which generates transport in the ab-plane.

Pore structure and column efficiency of silica monoliths in high performance liquid chromatography (HPLC)

Five different methods were critically examined to characterize the pore structure of the silica monoliths. The mesopore characterization was performed using: a) the classical BJH method of nitrogen sorption data, which showed overestimated values in the mesopore distribution and was improved by using the NLDFT method, b) the ISEC method implementing the PPM and PNM models, which were especially developed for monolithic silicas, that contrary to the particulate supports, demonstrate the two inflection points in the ISEC curve, enabling the calculation of pore connectivity, a measure for the mass transfer kinetics in the mesopore network, c) the mercury porosimetry using a new recommended mercury contact angle values. rnThe results of the characterization of mesopores of monolithic silica columns by the three methods indicated that all methods were useful with respect to the pore size distribution by volume, but only the ISEC method with implemented PPM and PNM models gave the average pore size and distribution based on the number average and the pore connectivity values.rnThe characterization of the flow-through pore was performed by two different methods: a) the mercury porosimetry, which was used not only for average flow-through pore value estimation, but also the assessment of entrapment. It was found that the mass transfer from the flow-through pores to mesopores was not hindered in case of small sized flow-through pores with a narrow distribution, b) the liquid penetration where the average flow-through pore values were obtained via existing equations and improved by the additional methods developed according to Hagen-Poiseuille rules. The result was that not the flow-through pore size influences the column bock pressure, but the surface area to volume ratio of silica skeleton is most decisive. Thus the monolith with lowest ratio values will be the most permeable. rnThe flow-through pore characterization results obtained by mercury porosimetry and liquid permeability were compared with the ones from imaging and image analysis. All named methods enable a reliable characterization of the flow-through pore diameters for the monolithic silica columns, but special care should be taken about the chosen theoretical model.rnThe measured pore characterization parameters were then linked with the mass transfer properties of monolithic silica columns. As indicated by the ISEC results, no restrictions in mass transfer resistance were noticed in mesopores due to their high connectivity. The mercury porosimetry results also gave evidence that no restrictions occur for mass transfer from flow-through pores to mesopores in the small scaled silica monoliths with narrow distribution. rnThe prediction of the optimum regimes of the pore structural parameters for the given target parameters in HPLC separations was performed. It was found that a low mass transfer resistance in the mesopore volume is achieved when the nominal diameter of the number average size distribution of the mesopores is appr. an order of magnitude larger that the molecular radius of the analyte. The effective diffusion coefficient of an analyte molecule in the mesopore volume is strongly dependent on the value of the nominal pore diameter of the number averaged pore size distribution. The mesopore size has to be adapted to the molecular size of the analyte, in particular for peptides and proteins. rnThe study on flow-through pores of silica monoliths demonstrated that the surface to volume of the skeletons ratio and external porosity are decisive for the column efficiency. The latter is independent from the flow-through pore diameter. The flow-through pore characteristics by direct and indirect approaches were assessed and theoretical column efficiency curves were derived. The study showed that next to the surface to volume ratio, the total porosity and its distribution of the flow-through pores and mesopores have a substantial effect on the column plate number, especially as the extent of adsorption increases. The column efficiency is increasing with decreasing flow through pore diameter, decreasing with external porosity, and increasing with total porosity. Though this tendency has a limit due to heterogeneity of the studied monolithic samples. We found that the maximum efficiency of the studied monolithic research columns could be reached at a skeleton diameter of ~ 0.5 µm. Furthermore when the intention is to maximize the column efficiency, more homogeneous monoliths should be prepared.rn

Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.

Liquid crystalline hexabenzocoronenes as organic molecular materials - synthesis, characterization and application

Die vorliegende Arbeit 'Liquid Crystalline Hexabenzocoronenes as Organic Molecular Materials - Synthesis, Characterization and Application' war durch drei Schwerpunkte definiert:1. Verbesserung der Synthese von Hexabenzocoronen Derivaten mit sechsfacher Alkyl-Substitution,2. Entwicklung von molekularen Materialien mit verbesserten Eigenschaften wie zum Beispiel Löslichkeit und Verarbeitbarkeit,3. Einsatz der entwickelten Moleküle in optoelektronischen Bauteilen wie zum Beispiel organischen Solarzellen und Feld-Effekt-Transistoren.Mit Hilfe einer neuen Syntheseroute ist es gelungen Aryl-Aryl und Aryl-Alkyl Kupplungen sehr spät in der Reaktionssequenz von Hexabenzocoronenen einzusetzen. Dies führte zu einer Vielzahl substituierter HBC Derivate. Die Einführung eines Phenyl Spacers zwischen den HBC Kern und die äußeren Alkylketten, wie zum Beispiel in HBC-PhC12, hatte eine Vielzahl positiver Effekte wie dramatisch verbesserte Löslichkeit und Flüssigkristallinität bei Raumtemperatur zur Folge. Die Kombination dieser Phänomene ermöglichte die Bildung hochgeordneter Filme, welche sehr wichtig für den Einsatz in organischen Bauelementen sind. Mit Hilfe von STM Techniken an der Fest-Flüssig Phasengrenze wurden hochgeordnete 2-D Strukturen der HBC Moleküle gefunden. Die Kombination von extrem hoher kolumnarer Ordnung, bestimmt mit Hilfe der Festkörper NMR Spektroskopie, mit einer konstant hohen Ladungsträgerbeweglichkeit, führte zu dem sehr erfolgreichen Einsatz von HBC-PhC12 in organischen Solarzellen.