Monte-Carlo simulation of hard spherocylinders under confinement

When a liquid crystal is confined to a cavity its director field becomes subject to competing forces: on the one hand, the surface of the cavity orients the director field (``surface anchoring''), on the other hand deformations of the director field cost elastic energy. Hence the equilibrium director field is determined by a compromise between surface anchoring and elasticity. One example of a confined liquid crystal that has attracted particular interest from physicists is the nematic droplet. In this thesis a system of hard rods is considered as the simplest model for nematic liquid crystals consisting of elongated molecules. First, systems of hard spherocylinders in a spherical geometry are investigated by means of canonical Monte Carlo simulations. In contrast to previous simulation work on this problem, a continuum model is used. In particular, the effects of ordering near hard curved walls are studied for the low-density regime. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We study how the surface order, the adsorption and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall in a cavity is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations. As a next step, an extension of the Asakura-Oosawa-Vrij model for colloid-polymer mixtures to anisotropic colloids is considered. By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or ``tactoids'' that so form are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we estimate the surface anchoring strength.

Electrical spectroscopy of rubrene bulk and thin film crystals

One of the most diffused electronic device is the field effect transistor (FET), contained in number of billions in each electronic device. Organic optoelectronics is an emerging field that exploits the unique properties of conjugated organic materials to develop new applications that require a combination of performance, low cost and processability. Organic single crystals are the material with best performances and purity among the variety of different form of organic semiconductors. This thesis is focused on electrical and optical characterization of Rubrene single crystal bulk and thin films. Rubrene bulk is well known but for the first time we studied thin films. The first Current-voltage characterization has been performed for the first time on three Rubrene thin films with three different thickness to extract the charge carriers mobility and to assess its crystalline structure. As results we see that mobility increase with thickness. Field effect transistor based on Rubrene thin films on $SiO_2$ have been characterize by current-voltage (I-V) analyses (at several temperatures) and reveals a hopping conduction. Hopping behavior probably is due to the lattice mismatch with the substrate or intrinsic defectivity of the thin films. To understand effects of contact resistance we tested thin films with the Transmission Line Method (TLM) method. The TLM method revealeds that contact resistance is negligible but evidenced a Schottky behavior in a limited but well determined range of T. To avoid this effect we carried out annealing treatment after the electrode evaporation iswe performed a compete I-V characterization as a function of in temperature to extract the electronic density of states (DOS) distribution through the Space Charge Limited Current (SCLC) method. The results show a DOS with an exponential trenddistribution, as expected. The measured mobility of thin films is about 0.1cm^2/Vs and it increases with the film thickness. Further studies are necessary to investigate the reason and improve performances. From photocurrent spectrum we calculated an Eg of about 2.2eV and both thin films and bulk have a good crystal order. Further measurement are necessary to solve some open problems

Design and Characterization of Curved and Spherical Flexure Hinges for Planar and Spatial Compliant Mechanisms

A flexure hinge is a flexible connector that can provide a limited rotational motion between two rigid parts by means of material deformation. These connectors can be used to substitute traditional kinematic pairs (like bearing couplings) in rigid-body mechanisms. When compared to their rigid-body counterpart, flexure hinges are characterized by reduced weight, absence of backlash and friction, part-count reduction, but restricted range of motion. There are several types of flexure hinges in the literature that have been studied and characterized for different applications. In our study, we have introduced new types of flexures with curved structures i.e. circularly curved-beam flexures and spherical flexures. These flexures have been utilized for both planar applications (e.g. articulated robotic fingers) and spatial applications (e.g. spherical compliant mechanisms). We have derived closed-form compliance equations for both circularly curved-beam flexures and spherical flexures. Each element of the spatial compliance matrix is analytically computed as a function of hinge dimensions and employed material. The theoretical model is then validated by comparing analytical data with the results obtained through Finite Element Analysis. A case study is also presented for each class of flexures, concerning the potential applications in the optimal design of planar and spatial compliant mechanisms. Each case study is followed by comparing the performance of these novel flexures with the performance of commonly used geometries in terms of principle compliance factors, parasitic motions and maximum stress demands. Furthermore, we have extended our study to the design and analysis of serial and parallel compliant mechanisms, where the proposed flexures have been employed to achieve spatial motions e.g. compliant spherical joints.

Mechanical behavior of flat and curved laminates interleaved by electrospun nanofibers

A major weakness of composite materials is that low-velocity impact, introduced accidentally during manufacture, operation or maintenance of the aircraft, may result in delaminations between the plies. Therefore, the first part of this study is focused on mechanics of curved laminates under impact. For this aim, the effect of preloading on impact response of curved composite laminates is considered. By applying the preload, the stress through the thickness and curvature of the laminates increased. The results showed that all impact parameters are varied significantly. For understanding the contribution rate of preloading and pre-stress on the obtained results another test is designed. The interesting phenomenon is that the preloading can decrease the damaged area when the curvature of the both specimens is the same. Finally the effect of curvature type, concave and convex, is investigated under impact loading. In the second part, a new composition of nanofibrous mats are developed to improve the efficiency of curved laminates under impact loading. Therefore, at first some fracture tests are conducted to consider the effect of Nylon 6,6, PCL, and their mixture on mode I and mode II fracture toughness. For this goal, nanofibers are electrospun and interleaved between mid-plane of laminate composite to conduct mode I and mode II tests. The results shows that efficiency of Nylon 6,6 is better than PCL in mode II, while the effect of PCL on fracture toughness of mode I is more. By mixing these nanofibers the shortage of the individual nanofibers is compensated and so the Nylon 6,6/PCL nanofibers could increased mode I and II fracture toughness. Then all these nanofibers are used between all layers of composite layers to investigate their effect on damaged area. The results showed that PCL could decrease the damaged area about 25% and Nylon 6,6 and mixed nanofibers about 50%.

Transport Properties and Novel Sensing Applications of Organic Semiconducting Crystals

The present thesis is focused on the study of Organic Semiconducting Single Crystals (OSSCs) and crystalline thin films. In particular solution-grown OSSC, e.g. 4-hdroxycyanobenzene (4HCB) have been characterized in view of their applications as novel sensors of X-rays, gamma-rays, alpha particles radiations and chemical sensors. In the field of ionizing radiation detection, organic semiconductors have been proposed so far mainly as indirect detectors, i.e. as scintillators or as photodiodes. I first study the performance of 4HCB single crystals as direct X-ray detector i.e. the direct photon conversion into an electrical signal, assessing that they can operate at room temperature and in atmosphere, showing a stable and linear response with increasing dose rate. A dedicated study of the collecting electrodes geometry, crystal thickness and interaction volume allowed us to maximize the charge collection efficiency and sensitivity, thus assessing how OSSCs perform at low operating voltages and offer a great potential in the development of novel ionizing radiation sensors. To better understand the processes generating the observed X-ray signal, a comparative study is presented on OSSCs based on several small-molecules: 1,5-dinitronaphthalene (DNN), 1,8-naphthaleneimide (NTI), Rubrene and TIPS-pentacene. In addition, the proof of principle of gamma-rays and alpha particles has been assessed for 4HCB single crystals. I have also carried out an investigation of the electrical response of OSSCs exposed to vapour of volatile molecules, polar and non-polar. The last chapter deals with rubrene, the highest performing molecular crystals for electronic applications. We present an investigation on high quality, millimeter-sized, crystalline thin films (10 – 100 nm thick) realized by exploiting organic molecular beam epitaxy on water-soluble substrates. Space-Charge-Limited Current (SCLC) and photocurrent spectroscopy measurements have been carried out. A thin film transistor was fabricated onto a Cytop® dielectric layer. The FET mobility exceeding 2 cm2/Vs, definitely assess the quality of RUB films.

Structure, Dynamics and Reactivity in the Organic Solid State: Anthracene Derivatives and Charge Transfer Crystals

The work presented in this thesis tackles some important points concerning the collective properties of two typical categories of molecular crystals, i.e., anthracene derivatives and charge transfer crystals. Anthracene derivatives have constituted the class of materials from which systematical investigations of crystal-to-crystal photodimerization reactions started, developed and have been the subject of a new awakening in the recent years. In this work some of these compounds, namely, 9-cyanoanthacene, 9-anthacenecarboxylic acid and 9-methylanthracene, have been selected as model systems for a phenomenological approach to some key properties of the solid state, investigated by spectroscopic methods. The present results show that, on the basis of the solid state organization and the chemical nature of each compound, photo-reaction dynamics and kinetics display distinctive behaviors, which allows for a classification of the various processes in topochemical, non topochemical, reversible or topophysical. The second part of the thesis was focused on charge transfer crystals, binary systems formed by stoichiometric combinations of the charge donating perylene (D) and the charge accepting tetracyano-quinodimethane (A), this latter also in its fluorinated derivatives. The work was focused on the growth of single crystals, some of which not yet reported in the literature, by PVT technique. Structural and spectroscopic characterizations have been performed, with the aim of determining the degree of charge transfer between donor and acceptor in the co-crystals. An interesting outcome of the systematic search performed in this work is the definition of the experimental conditions which drive the crystal growth of the binary systems either towards the low (1:1) or the high ratio (3:1 or 3:2) stoichiometries.

Computer simulations of two-dimensional colloidal crystals under confinement and shear

In this thesis we are presenting a broadly based computer simulation study of two-dimensional colloidal crystals under different external conditions. In order to fully understand the phenomena which occur when the system is being compressed or when the walls are being sheared, it proved necessary to study also the basic motion of the particles and the diffusion processes which occur in the case without these external forces. In the first part of this thesis we investigate the structural transition in the number of rows which occurs when the crystal is being compressed by placing the structured walls closer together. Previous attempts to locate this transition were impeded by huge hysteresis effects. We were able to determine the transition point with higher precision by applying both the Schmid-Schilling thermodynamic integration method and the phase switch Monte Carlo method in order to determine the free energies. These simulations showed not only that the phase switch method can successfully be applied to systems with a few thousand particles and a soft crystalline structure with a superimposed pattern of defects, but also that this method is way more efficient than a thermodynamic integration when free energy differences are to be calculated. Additionally, the phase switch method enabled us to distinguish between several energetically very similar structures and to determine which one of them was actually stable. Another aspect considered in the first result chapter of this thesis is the ensemble inequivalence which can be observed when the structural transition is studied in the NpT and in the NVT ensemble. The second part of this work deals with the basic motion occurring in colloidal crystals confined by structured walls. Several cases are compared where the walls are placed in different positions, thereby introducing an incommensurability into the crystalline structure. Also the movement of the solitons, which are created in the course of the structural transition, is investigated. Furthermore, we will present results showing that not only the well-known mechanism of vacancies and interstitial particles leads to diffusion in our model system, but that also cooperative ring rotation phenomena occur. In this part and the following we applied Langevin dynamics simulations. In the last chapter of this work we will present results on the effect of shear on the colloidal crystal. The shear was implemented by moving the walls with constant velocity. We have observed shear banding and, depending on the shear velocity, that the inner part of the crystal breaks into several domains with different orientations. At very high shear velocities holes are created in the structure, which originate close to the walls, but also diffuse into the inner part of the crystal.

Atomistic simulations of liquid crystals in the bulk and at their interfaces

In this thesis, we have dealt with several problems concerning liquid crystals (LC) phases, either in the bulk or at their interfaces, by the use of atomistic molecular dynamics (MD) simulations. We first focused our attention on simulating and characterizing the bulk smectic phase of 4-n-octyl-4'-cyanobiphenyl (8CB), allowing us to investigate the antiparallel molecular arrangement typical of SmAd smectic phases. A second topic of study was the characterization of the 8CB interface with vacuum by simulating freely suspended thin films, which allowed us to determine the influence of the interface on the orientational and positional order. Then we investigated the LC-water and LC-electrolyte water solution interface. This interface has recently found application in the development of sensors for several compounds, including biological molecules, and here we tried to understand the re-orientation mechanism of LC molecules at the interface which is behind the functioning of these sensors. The characterization of this peculiar interface has incidentally led us to develop a polarizable force field for the pentyl-cyanobiphenyl mesogen, whose process of parametrization and validation is reported here in detail. We have shown that this force field is a significant improvement over its previous, static charge non polarizable version in terms of density, orientational order parameter and translational diffusion.

Optimization of molecular and crystalline forms of drugs, agrochemicals, pesticides in relation to activity, bioavailability, patentability and to the fabrication of polymorphs, solvates, co-crystals with green chemistry methods

This doctorate was funded by the Regione Emilia Romagna, within a Spinner PhD project coordinated by the University of Parma, and involving the universities of Bologna, Ferrara and Modena. The aim of the project was: - Production of polymorphs, solvates, hydrates and co-crystals of active pharmaceutical ingredients (APIs) and agrochemicals with green chemistry methods; - Optimization of molecular and crystalline forms of APIs and pesticides in relation to activity, bioavailability and patentability. In the last decades, a growing interest in the solid-state properties of drugs in addition to their solution chemistry has blossomed. The achievement of the desired and/or the more stable polymorph during the production process can be a challenge for the industry. The study of crystalline forms could be a valuable step to produce new polymorphs and/or co-crystals with better physical-chemical properties such as solubility, permeability, thermal stability, habit, bulk density, compressibility, friability, hygroscopicity and dissolution rate in order to have potential industrial applications. Selected APIs (active pharmaceutical ingredients) were studied and their relationship between crystal structure and properties investigated, both in the solid state and in solution. Polymorph screening and synthesis of solvates and molecular/ionic co-crystals were performed according to green chemistry principles. Part of this project was developed in collaboration with chemical/pharmaceutical companies such as BASF (Germany) and UCB (Belgium). We focused on on the optimization of conditions and parameters of crystallization processes (additives, concentration, temperature), and on the synthesis and characterization of ionic co-crystals. Moreover, during a four-months research period in the laboratories of Professor Nair Rodriguez-Hormedo (University of Michigan), the stability in aqueous solution at the equilibrium of ionic co-crystals (ICCs) of the API piracetam was investigated, to understand the relationship between their solid-state and solution properties, in view of future design of new crystalline drugs with predefined solid and solution properties.

Fontaine modules and F-T-crystals, a dévissage

Das Hauptziel der Arbeit ist es, die Beziehung zwischen Fontaine Modulen und F-T-Kristall zu studieren. Im ersten Kapitel wird die Definition von Fontaine Modulen, die auf die inversen Cartier Transform setzt erinnern wir von Ogus und Vologodsky errichtet. Neben der Erinnerung an die urspruengliche Konstruktion des inversen Cartier Transform, eine direktere Konstruktion, die wir auch vorstellen von G.T. Lan, M. Sheng und K. Zuo. Darueber hinaus beweisen wir diernGleichwertigkeit der beiden Konstruktion.rnrnrnIm zweiten Kapitel werden wir uns daran erinnern, den Konstruktion von inversen Cartier Transform in der Log Einstellung von D. Schepler und verallgemeinern die Lan-Sheng-Zuo Konstruktion an dieser Einstellung. Darueber hinaus geben wir eine Definition von Log FontainernModulen. Im dritten Kapitel werden wir erinnern an die Definition von F-T-Kristall und beweisen das wichtigste Ergebnis dieser Arbeit: Sei $Y$ eine glatte $S_{nu}$-Schema, wobei $S_{nu}$ ist eine flache $W_{nu+1}(k)$-Schema, $nugeq1$, und $X/S_0$ seine Reduction modulo $p$ sein. Bei einem F-T-Kristall $(E,Phi,B)$ auf $Y$ der Breite von weniger als $p$ und let $(E_Y ,B_Y ,nabla_Y)$ die entsprechende gefilterte $O_Y$-modulen mit einer integrierbar Zusammenhang ausgestattet. Anschliesend wird die Reduktion dieses Objekt modulo $p$ definiert eine Fontaine Modulen auf $X/S_0$ im dem Sinnernder Ogus und Vologodsky.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

Imaging spin-filter efficiency of W(001) and Ir(001) single crystals

Während der letzten Jahre wurde für Spinfilter-Detektoren ein wesentlicher Schritt in Richtung stark erhöhter Effizienz vollzogen. Das ist eine wichtige Voraussetzung für spinaufgelöste Messungen mit Hilfe von modernen Elektronensp ektrometern und Impulsmikroskopen. In dieser Doktorarbeit wurden bisherige Arbeiten der parallel abbildenden Technik weiterentwickelt, die darauf beruht, dass ein elektronenoptisches Bild unter Ausnutzung der k-parallel Erhaltung in der Niedrigenergie-Elektronenbeugung auch nach einer Reflektion an einer kristallinen Oberfläche erhalten bleibt. Frühere Messungen basierend auf der spekularen Reflexion an einerrnW(001) Oberfläche [Kolbe et al., 2011; Tusche et al., 2011] wurden auf einenrnviel größeren Parameterbereich erweitert und mit Ir(001) wurde ein neues System untersucht, welches eine sehr viel längere Lebensdauer der gereinigten Kristalloberfläche im UHV aufweist. Die Streuenergie- und Einfallswinkel-“Landschaft” der Spinempfindlichkeit S und der Reflektivität I/I0 von gestreuten Elektronen wurde im Bereich von 13.7 - 36.7 eV Streuenergie und 30◦ - 60◦ Streuwinkel gemessen. Die dazu neu aufgebaute Messanordnung umfasst eine spinpolarisierte GaAs Elektronenquellernund einen drehbaren Elektronendetektor (Delayline Detektor) zur ortsauflösenden Detektion der gestreuten Elektronen. Die Ergebnisse zeigen mehrere Regionen mit hoher Asymmetrie und großem Gütefaktor (figure of merit FoM), definiert als S2 · I/I0. Diese Regionen eröffnen einen Weg für eine deutliche Verbesserung der Vielkanal-Spinfiltertechnik für die Elektronenspektroskopie und Impulsmikroskopie. Im praktischen Einsatz erwies sich die Ir(001)-Einkristalloberfläche in Bezug auf längere Lebensdauer im UHV (ca. 1 Messtag), verbunden mit hoher FOM als sehr vielversprechend. Der Ir(001)-Detektor wurde in Verbindung mit einem Halbkugelanalysator bei einem zeitaufgelösten Experiment im Femtosekunden-Bereich am Freie-Elektronen-Laser FLASH bei DESY eingesetzt. Als gute Arbeitspunkte erwiesen sich 45◦ Streuwinkel und 39 eV Streuenergie, mit einer nutzbaren Energiebreite von 5 eV, sowie 10 eV Streuenergie mit einem schmaleren Profil von < 1 eV aber etwa 10× größerer Gütefunktion. Die Spinasymmetrie erreicht Werte bis 70 %, was den Einfluss von apparativen Asymmetrien deutlich reduziert. Die resultierende Messungen und Energie-Winkel-Landschaft zeigt recht gute Übereinstimmung mit der Theorie (relativistic layer-KKR SPLEED code [Braun et al., 2013; Feder et al.,rn2012])

Internal characteristics, chemical compounds and spectroscopy of sapphire as single crystals

In this study more than 450 natural sapphire samples (most of basaltic type) collected from 19 different areas were examined. They are from Dak Nong, Dak Lak, Quy Chau, two unknown sources from the north (Vietnam); Bo Ploi, Khao Ploi Waen (Thailand); Ban Huay Sai (Laos); Australia; Shandong (China); Andapa, Antsirabe, Nosibe (Madagascar); Ballapana (Sri Lanka); Brazil; Russia; Colombia; Tansania and Malawi. rnThe samples were studied on internal characteristics, chemical compositions, Raman-, luminescence-, Fourier transform infrared (FTIR)-, and ultraviolet-visible-near infrared (UV-Vis-NIR)- spectroscopy. The internal features of these sapphire samples were observed and identified by gemological microscope, con focal micro Raman and FTIR spectroscopy. The major and minor elements of the samples were determined by electron probe microanalysis (EPMA) and the trace elements by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). rnThe structural spectra of sapphire were investigated by con focal Raman spectroscopy. The FTIR spectroscopy was used to study the vibration modes of OH-groups and also to determine hydrous mineral inclusions in sapphire. The UV-Vis-NIR absorption spectroscopy was used to analyze the cause of sapphire color. rnNatural sapphires contain many types of mineral inclusions. Typically, they are iron-containing inclusions like goethite, ilmenite, hematite, magnetite or silicate minerals commonly feldspar, and often observed in sapphires from Asia countries, like Dak Nong, Dak Lak in the south of Vietnam, Ban Huay Sai (Laos), Khao Ploi Waen and Bo Ploi (Thailand) or Shandong (China). Meanwhile, CO2-diaspore inclusions are normally found in sapphires from Tansania, Colombia, or the north of Vietnam like Quy Chau. rnIron is the most dominant element in sapphire, up to 1.95 wt.% Fe2O3 measured by EPMA and it affects spectral characteristics of sapphire.rnThe Raman spectra of sapphire contain seven peaks (2A1g + 5Eg). Two peaks at about 418.3 cm-1 and 577.7 cm-1 are influenced by high iron content. These two peaks shift towards smaller wavenumbers corresponding to increasing iron content. This shift is showed by two equations y(418.3)=418.29-0.53x andy(577.7)=577.96-0.75x, in which y is peak position (cm-1) and x is Fe2O3 content (wt.%). By exploiting two these equations one can estimate the Fe2O3 contents of sapphire or corundum by identifying the respective Raman peak positions. Determining the Fe2O3 content in sapphire can help to distinguish sapphires from different origins, e.g. magmatic and metamorphic sapphire. rnThe luminescence of sapphire is characterized by two R-lines: R1 at about 694 nm and R2 at about 692 nm. This characteristic is also influenced by high iron content. The peak positions of two R-lines shift towards to smaller wavelengths corresponding to increasing of iron content. This correlation is showed by two equations y(R_2 )=692.86-0.049x and y(R_1 )=694.29-0.047x, in which y is peak position (nm) of respective R-lines and x is Fe2O3 content (wt.%). Two these equations can be applied to estimate the Fe2O3 content of sapphire and help to separate sapphires from different origins. The luminescence is also applied for determination of the remnant pressure or stress around inclusions in Cr3+-containing corundum by calibrating a 0-pressure position in experimental techniques.rnThe infrared spectra show the presence of vibrations originating from OH-groups and hydrous mineral inclusions in the range of 2500-4000 cm-1. Iron has also an effect upon the main and strongest peak at about 3310 cm-1. The 3310 cm-1 peak is shifted to higher wavenumber when iron content increases. This relationship is expressed by the equation y(3310)=0.92x+3309.17, in which y is peak position of the 3310 cm-1 and x is Fe2O3 content (wt.%). Similar to the obtained results in Raman and luminescence spectra, this expression can be used to estimate the Fe2O3 content and separate sapphires from different origins. rnThe UV-Vis-NIR absorption spectra point out the strong and sharp peaks at about 377, 387, and 450 nm related to dispersed Fe3+, a broad band around 557 and 600 nm related to intervalence charge transfer (IVCT) Fe2+/Ti4+, and a broader band around 863 nm related to IVCT of Fe2+/Fe3+. rnGenerally, sapphires from different localities were completely investigated on internal features, chemical compounds, and solid spectral characteristics. The results in each part contribute for identifying the iron content and separate sapphires from different localities order origins. rn

Monte Carlo simulations of nucleation of colloidal crystals

A crystal nucleus in a finite volume may exhibit phase coexistence with a surrounding fluid. The thermodynamic properties of the coexisting fluid (pressure and chemical potential) are enhanced relative to their coexistence values. This enhancement is uniquely related to the surface excess free energy. rnA model for weakly attractive soft colloidal particles is investigated, the so called Asakura-Oosawa model. In simulations, this model allows for the calculation of the pressure in the liquid using the virial formula directly. The phase coexistence pressure in the thermodynamic limit is obtained from the interface velocity method. We introduce a method by which the chemical potential in dense liquids can be measured. There is neither a need to locate the interface nor to compute the anisotropic interfacial tension to obtain nucleation barriers. Therefore, our analysis is appropriate for nuclei of arbitrary shape. Monte Carlo simulations over a wide range of nucleus volumes yield to nucleation barriers independent from the total system volume. The interfacial tension is determined via the ensemble-switch method, hence a detailed test of classical nucleation theory is possible. The anisotropy of the interfacial tension and the resulting non-spherical shape has only a minor effect on the barrier for the Asakura-Oosawa model.

A linear O(N) model: a functional renormalization group approach for flat and curved space

In questa tesi sono state applicate le tecniche del gruppo di rinormalizzazione funzionale allo studio della teoria quantistica di campo scalare con simmetria O(N) sia in uno spaziotempo piatto (Euclideo) che nel caso di accoppiamento ad un campo gravitazionale nel paradigma dell'asymptotic safety. Nel primo capitolo vengono esposti in breve alcuni concetti basilari della teoria dei campi in uno spazio euclideo a dimensione arbitraria. Nel secondo capitolo si discute estensivamente il metodo di rinormalizzazione funzionale ideato da Wetterich e si fornisce un primo semplice esempio di applicazione, il modello scalare. Nel terzo capitolo è stato studiato in dettaglio il modello O(N) in uno spaziotempo piatto, ricavando analiticamente le equazioni di evoluzione delle quantità rilevanti del modello. Quindi ci si è specializzati sul caso N infinito. Nel quarto capitolo viene iniziata l'analisi delle equazioni di punto fisso nel limite N infinito, a partire dal caso di dimensione anomala nulla e rinormalizzazione della funzione d'onda costante (approssimazione LPA), già studiato in letteratura. Viene poi considerato il caso NLO nella derivative expansion. Nel quinto capitolo si è introdotto l'accoppiamento non minimale con un campo gravitazionale, la cui natura quantistica è considerata a livello di QFT secondo il paradigma di rinormalizzabilità dell'asymptotic safety. Per questo modello si sono ricavate le equazioni di punto fisso per le principali osservabili e se ne è studiato il comportamento per diversi valori di N.