Crystallization and demixing: morphological structure analysis in many-body systems

The description and analysis of spatial data is an omnipresent task in both science and industry: In the food industry the distribution and size of pores in baked goods plays a role in their taste. In chemistry, biology and physics spatial data arises in manifold disciplines and on all length scales. On large scales one finds them in the structure of the universe or in earth surveillance data. On small scales one observes highly structured data in inner bones or on minute scales in the deformation of nucleons in nuclear pasta, which is theorized to form during the cooling of a neutron star. In particular in statistical physics many-body-systems have a tendency to collectively form complex structures by self-organization. These complex structures often allow to draw conclusions about the underlying physics. In order to formulate a quantitative relation between the physics of many-body-systems and their morphology, i.e. the spatial structure they assume, a quantitative description of this structure is essential. In this dissertation the spatial structure of phase transitions (crystallization and demixing) in many-body-systems is quantitatively described and analyzed in order to achieve an improved understanding of the physics involved. Regarding the analysis methods applied in this thesis we go beyond conventional linear measures based on two-point correlation functions or the power spectrum. Instead, the aim is a full nonlinear morphological characterization of the spatial data with measures derived from the family of Minkowski functionals and tensors. They are additive, morphological measures related to, not only geometrical concepts like volume, area and curvature, but also to topological aspects such as connectivity and are sensitive to higher order correlation. Complex plasmas (dielectric microparticles immersed in a plasma) are a well suited model system for the particle resolved investigation of many-body processes. Their optical thinness allows for the optical imaging and tracking of the fully resolved trajectories of hundreds of particle layers. Additionally interactions can be tuned over a large range allowing to manipulate the shape and magnitude of the interparticle potential. Since the gas density is typically very low, the particle motion is practically undamped resulting in a direct analogy to the atomistic dynamics in solids or fluids. Liquid-solid phase transition have been considered impossible for a long time since the Mermin-Wagner theorem forbids long-range order in two (or less) dimensions. However, Kosterlitz and Thouless (Nobel prize 2016) circumvented this by replacing the long-range order with a quasi-long-range order and by introducing a topological phase transition mediated by defects. The well accepted KTHNY theory predicts an intermediate anisotropic phase, the hexatic phase. In the first part of this thesis the KTHNY theory is tested for experiments and a simulation of the crystallization of two-dimensional complex plasma sheets. For the same experiments the hypothesis and prediction of the recently developed fractal-domain-structure (FDS) theory is tested. The FDS theory is based on the Frenkel kinetic theory of melting. It postulates a fractal relationship between crystalline domains separated by boundaries of defect lines and predicts a scale-free relation between the system energy and the defect fraction. It is found that the KTHNY theory is not applicable to the liquid-solid phase transition in complex plasmas. The FDS theory however, is validated. The other focus of this thesis is the morphological characterization of fluid-fluid demixing dynamics. The generally accepted mechanism for fluid-fluid demixing is spinodal decomposition. Spinodal decomposition is achieved by a quench deep inside the spinodal curve of the phase diagram. It is characterized by the exponential growth of longwavelength density fluctuations. However the mean-field theory predictions of spinodal decomposition are not consistent with experiments and simulations. This shows the need for particle resolved studies with tunable interactions. To this end complex plasma simulations in flat three-dimensional space and density-functional theory calculations on the two-dimensional sphere are analyzed. In both cases different stages of demixing are identified with distinct domain growth rates during spinodal decomposition. Most importantly, universal demixing behavior is found for different interaction potentials, respectively for different mixture fractions and sphere sizes. These universal features could only be resolved by applying nonlinear measures, going beyond conventional methods based on the power spectral density. This suggests that nonlinear features in the demixing kinetics play an important role and that it is crucial to address this issue in future works.Räumliche Daten zu beschreiben und zu analysieren ist eine allgegenwärtige Problemstellung sowohl in der Wissenschaft als auch in der Industrie: So spielt beispielsweise in der Nahrungsmittelindustrie die räumliche Verteilung und die Größe von Poren in Backwaren eine Rolle für deren Geschmack. In den wissenschaftlichen Gebieten der Chemie, Biologie und der Physik liefern räumlich strukturierte Systeme Grundlage vieler Forschungsbereiche und sind in allen Größenordnungen aufzufinden: Auf großen Skalen z.B. bei der Struktur des Universums oder bei Erdbeobachtungsdaten. Auf kleinen Skalen bei der Struktur im inneren von Knochen oder im kleinsten bei der Verformung von Nukleonen zu nuklearer Pasta, die z.B. beim Abkühlen von Neutronensternen entstehen soll. Insbesondere in der statistischen Physik neigen Vielteilchensysteme dazu, sich in komplexen Strukturen selbst anzuordnen. Diese komplexen räumlichen Strukturen lassen oft Rückschlüsse auf die zugrunde liegende Physik zu. Um einen quantitativen Zusammenhang zwischen der Physik von Vielteilchensystemen und ihrer Morphologie, also der Struktur die diese annehmen, herzustellen, ist eine quantitative Beschreibung dieser Struktur unerlässlich. In dieser Dissertation werden daher die räumlichen Strukturen bei Phasenübergängen (Kristallisation und Entmischung) in Vielteilchensystemen beschrieben und analysiert, um damit Rückschlüsse auf die zugrundeliegende Physik ziehen zu können. Im Hinblick auf die Methoden, die zur Analyse der in dieser Dissertation untersuchten Systeme genutzt werden, gehen wir über konventionelle Methoden, die auf dem Leistungsspektrum oder auf zwei-Punkt Korrelationsfunktionen beruhen, hinaus. Das Ziel ist es die räumlichen Daten vollständig morphologisch zu charakterisieren. Zu diesem Zweck werden Metriken basierend auf der Familie der Minkowski Funktionale und Tensoren abgeleitet. Das sind additive morphologische Maße, die auch Korrelationen höherer Ordnung detektieren können. Sie sind nicht nur mit geometrischen Konzepten wie Volumen, Fläche und Krümmung verwandt, sondern stellen auch Aspekte der Topologie wie z.B. Verbundenheit dar. Komplexe Plasmen (dielektrische Mikropartikel eingebracht in ein Plasma) stellen ein überaus geeignetes Modellsystem für die Untersuchung von Vielteilchenprozessen auf der kinetischen Ebene individueller Teilchen dar, da durch ihre optische Dünnheit die Bildgebung mehrerer hundert Lagen von Teilchen und die volle Auflösung der Teilchentrajektorien ermöglicht wird. Darüber hinaus können die Teilchenwechselwirkungen in Komplexen Plasmen auf vielfältige Art und Weise manipuliert werden. Da der Gasdruck meist sehr gering ist, sind die Teilchenbewegungen praktisch ungedämpft. Dies stellt eine direkte Analogie zur Dynamik von Atomen in Flüssigkeiten oder Festkörpern dar. Flüssig-fest Phasenübergänge in zwei-dimensionalen Systemen wurden lange Zeit als unmöglich erachtet, da das Mermin-Wagner Theorem langreichweitige Ordnung in zwei (oder weniger) Dimensionen verbietet. Kosterlitz und Thouless umgingen diese Problem jedoch, indem sie die langreichweitige Ordnung durch eine quasi-langreichweitige Ordnung ersetzten und einen topologischen Phasenübergang vorstellten, der durch Interaktionen von Kristalldefekten vonstatten geht. Diese allgemein akzeptierte KTHNY Theorie sagt eine anisotrope Zwischenphase vorher, die so genannte hexatische Phase. Im ersten Teil dieser Dissertation werden die Vorhersagen der KTHNY Theorie, anhand von Experimenten und einer Computer Simulation an einzelnen zwei-dimensionalen Komplexen Plasma Kristall-Lagen getestet. Anhand selbiger Experimente wird eine kürzlich neu entwickelte fraktale-Domänen-Struktur (FDS) Theorie getestet. Die FDS Theorie basiert auf der kinetischen Theorie des Schmelzens von Frenkel. Sie postuliert einen fraktalen Zusammenhang zwischen der eingeschlossenen Fläche von kristallinen Domänen und der Länge deren Begrenzung durch Linien aus Kristalldefekten. Es wird gezeigt, dass die KTHNY Theorie nicht auf flüssig-fest Phasenübergänge in zwei-dimensionalen Komplexen Plasmen angewandt werden kann. Die FDS Theorie wird hingegen validiert. Desweiteren wird in dieser Dissertation die morphologische Beschreibung der Entmischungsdynamik von Flüssigkeiten behandelt. Der allgemein anerkannte Mechanismus, der für die Flüssigkeitsentmischung verantwortlich ist, ist die spinodale Dekomposition. Diese wird durch das quenchen (z.B. abkühlen) in den inneren Bereich der spinodalen Kurve im Phasendiagramm ausgelöst. Das charakteristische Merkmal der spinodalen Dekomposition ist der Beginn der Entmischung durch das exponentielle Wachstum von Dichtefluktuationen mit großen Wellenlängen. Die Vorhersagen der Molekularfeldtheorie der spinodalen Dekomposition sind jedoch nicht mit experimentellen Beobachtungen und Simulationen vereinbar. Diese Tatsache zeigt den Bedarf an Studien auf, die es vermögen einzelnen Teilchen zu folgen und bei denen man die Interaktionen zwischen den Teilchen beeinflussen kann. Deshalb werden in dieser Doktorarbeit sowohl Simulationen von Komplexen Plasmen (in drei-dimensionaler Euklidscher Geometrie) als auch Dichtefunktionaltheorie Berechnungen auf der zwei-dimensionalen Sphäre untersucht. In beiden Fällen können verschiedene Stadien in der Dynamik der Entmischung unterschieden werden. Das interessanteste Ergebnis ist die Entdeckung von universellem Verhalten im Entmischungsprozess. Universalität kann in dieser Arbeit im Hinblick auf verschiedene Interaktionspotentiale, bzw. im Hinblick auf verschiedene Mischungsverhältnisse und Sphärenradien gezeigt werden. Um diese universellen Eigenschaften zu entdecken, ist die Anwendung nicht-linearer Maße zwingend erforderlich, konventionelle auf dem Leistungsspektrum basierende Maße sind hierfür unzureichend. Dies zeigt, dass die nicht-linearen Eigenschaften des Entmischungsprozesses eine wichtige Rolle spielen und ist deshalb ein Fokus künftiger Arbeitenzu diesem Thema

Entropie‐dominierte Selbstorganisationsprozesse birnenförmiger Teilchensysteme

The ambition to recreate highly complex and functional nanostructures found in living organisms marks one of the pillars of today‘s research in bio- and soft matter physics. Here, self-assembly has evolved into a prominent strategy in nanostructure formation and has proven to be a useful tool for many complex structures. However, it is still a challenge to design and realise particle properties such that they self-organise into a desired target configuration. One of the key design parameters is the shape of the constituent particles. This thesis focuses in particular on the shape sensitivity of liquid crystal phases by addressing the entropically driven colloidal self-assembly of tapered ellipsoids, reminiscent of „pear-shaped“ particles. Therefore, we analyse the formation of the gyroid and of the accompanying bilayer architecture, reported earlier in the so-called pear hard Gaussian overlap (PHGO) approximation, by applying various geometrical tools like Set-Voronoi tessellation and clustering algorithms. Using computational simulations, we also indicate a method to stabilise other bicontinuous structures like the diamond phase. Moreover, we investigate both computationally and theoretically(density functional theory) the influence of minor variations in shape on different pearshaped particle systems, including the stability of the PHGO gyroid phase. We show that the formation of the gyroid is due to small non-additive properties of the PHGO potential. This phase does not form in pears with a „true“ hard pear-shaped potential. Overall our results allow for a better general understanding of necessity and sufficiency of particle shape in regards to colloidal self-assembly processes. Furthermore, the pear-shaped particle system sheds light on a unique collective mechanism to generate bicontinuous phases. It suggests a new alternative pathway which might help us to solve still unknown characteristics and properties of naturally occurring gyroid-like nano- and microstructures.Ein wichtiger Bestandteil der heutigen Forschung in Bio- und Soft Matter Physik besteht daraus, Technologien zu entwickeln, um hoch komplexe und funktionelle Strukturen, die uns aus der Natur bekannt sind, nachzubilden. Hinsichtlich dessen ist vor allem die Methode der Selbstorganisation von Mikro- und Nanoteilchen hervorzuheben, durch die eine Vielzahl verschiedener Strukturen erzeugt werden konnten. Jedoch stehen wir bei diesem Verfahren noch immer vor der Herausforderung, Teilchen mit bestimmten Eigenschaften zu entwerfen, welche die spontane Anordnung der Teilchen in eine gewünschte Struktur bewirken. Einer der wichtigsten Designparameter ist dabei die Form der Bausteinteilchen. In dieser Dissertation konzentrieren wir uns besonders auf die Anfälligkeit von Flüssigkristallphasen bezüglich kleiner Änderungen der Teilchenform und nutzen dabei das Beispiel der Selbstorganisation von Entropie-dominierter Kolloide, die dem Umriss nach verjüngten Ellipsoiden oder "Birnen" ähneln. Mit Hilfe von geometrischen Werkzeugen wie z.B. Set-Voronoi Tessellation oder Cluster-Algorithmen analysieren wir insbesondere die Entstehung der Gyroidphase und der dazugehörigen Bilagenformation, welche bereits in Systemen von harten Birnen, die durch das pear hard Gaussian overlap (PHGO) Potential angenähert werden, entdeckt wurden. Des Weiteren zeigen wir durch Computersimulationen eine Strategie auf, um andere bikontinuierliche Strukturen, wie die Diamentenphase, zu stabilisieren. Schlussendlich betrachten wir sowohl rechnerisch (durch Simulationen) als auch theoretisch (durch Dichtefunktionaltheorie) die Auswirkungen kleiner Abweichungen der Teilchenform auf das Verhalten des kolloiden, birnenförmigen Teilchensystems, inklusive der Stabilität der PHGO Gyroidphase. Wir zeigen, dass die Entstehung des Gyroids auf kleinen nicht-additiven Eigenschaften des PHGO Birnenmodells beruhen. In ''echten'' harten Teilchensystemen entwickelt sich diese Struktur nicht. Insgesamt ermöglichen unsere Ergebnisse einen besseren Einblick auf das Konzept von notwendiger und hinreichender Teilchenform in Selbstorganistationsprozessen. Die birnenförmigen Teilchensysteme geben außerdem Aufschluss über einen ungewöhnlichen, kollektiven Mechanismus, um bikontinuierliche Phasen zu erzeugen. Dies deutet auf einen neuen, alternativen Konstruktionsweg hin, der uns möglicherweise hilft, noch unbekannte Eigenschaften natürlich vorkommender, gyroidähnlicher Nano- und Mikrostrukturen zu erklären

Entropically driven self-assembly of pear-shaped nanoparticles

This thesis addresses the entropically driven colloidal self-assembly of pear-shaped particle ensembles, including the formation of nanostructures based on triply periodic minimal surfaces, in particular of the Ia3d gyroid. One of the key results is that the formation of the Ia3d gyroid, re-ported earlier in the so-called pear hard Gaussian overlap (PHGO) approximation and confirmed here, is due to a slight non-additivity of that potential; this phase does not form in pears with true hard-core potential. First, we computationally study the PHGO system and present the phase diagram of pears with an aspect ratio of 3 in terms of global density and particle shape (degree of taper), containing gyroid, isotropic, nematic and smectic phases. We confirm that it is adequate to interpret the gyroid as a warped smectic bilayer phase. The collective behaviour to arrange into interdigitated sheets with negative Gauss curvature, from which the gyroid results, is investigated through correlations of (Set-)Voronoi cells and local curvature. This geometric arrangement within the bilayers suggests a fundamentally different stabilisation mechanism of the pear gyroid phase compared to those found in both lipid-water and di-block copolymer systems forming the Ia3d gyroid. The PHGO model is only an approximation for hard-core interactions, and we additionally investigate, by much slower simulations, pear-assemblies with true hard-core interactions (HPR). We find that HPR phase diagram only contains isotropic and nematic phases, but neither gyroid nor smectic phases. To understand this shape sensitivity more profoundly, the depletion interactions of both models are studied in two pear-shaped colloids dissolved in a hard sphere solvent. The HPR particles act as one would expect from a geometric analysis of the excluded-volume minimisation, whereas the PHGO particles show deviations from this expectation. These differences are attributed to the unusual angle dependency of the (non-additive) contact function and, more so, to small overlaps induced by the approximation. For the PHGO model, we further demonstrate that the addition of a small concentration of hard spheres ("solvent") drives the system towards a Pn3m diamond phase. This result is explained by the greater spatial heterogeneity of the diamond geometry compared to the gyroid where additional material is needed to relieve packing frustration. In contrast to copolymer systems, however, the solvent mostly aggregates near the diamond minimal surface, driven by the non-additivity of the PHGO pears. At high solvent concentrations, the mixture phase separates into “inverse” micelle-like structures with the blunt ends at the micellar centres and thin ends pointing out-wards. The micelles themselves spontaneously cluster, indicative of a hierarchical self-assembly process for bicontinuous structures. Finally, we develop a density functional for hard solids of revolution (including pears) within the framework of fundamental measure theory. It is applied to low-density ensembles of pear-shaped particles, where we analyse their response near a hard substrate. A complex orientational ordering close to the wall is predicted, which is directly linked to the particle shape and gives insight into adsorption processes of asymmetric particles. This predicted behaviour and the differences between the PHGO and HPR model are confirmed by MC simulations

Free self-assembly of spontaneously chiral, supramolecular structures

In this thesis, Molecular Dynamics simulations are used to investigate the free selfassembly of supramolecular, chiral structures. The main coarse-grained model used for this is the disc-shaped variant of the Gay-Berne potential. This is parameterised to favour face-face configurations, consistent with chromonic molecules which tend to stack due to their π − π interactions. Additionally, assemblies formed by mixtures of these discs and a second species, modelled as Lennard-Jones spheres, are investigated. Here, hot-spot zones on the rims of the discs are used to provide strong interactions with the spheres. Simulations of disc-only systems lead to self-assembly of multi-thread, chiral fibres. Depending on the choice of particle shape and face-face interaction strength, the formed fibres are reproducibly either straight or, for reasons of packing efficiency, spontaneously chiral. As they grow radially, increasing stresses cause chiral fibres to untwist either continuously or via morphological rearrangement. It is also found that, due to the kinetics of fibre initiation, the isotropic solution has to be significantly supercooled before aggregation takes place. As a result, the thermal hysteresis of the formed fibres extends to 10-20% of their formation temperatures. The kinetic barriers to the early stages of growth are investigated by the introduction of a small permanent seed. Depending on the size of the seed, monotonic fibre growth is then observed 5-10% above the normal formation temperatures. On introducing Lennard-Jones spheres and hot-spot zones at the rims of discs, twisted bilayer ribbons, sandwiching a helicoidal sphere layer, are obtained. Systematic investigation of the effects of hot-spot size on the formation and structural properties of these twisted bilayers is then performed. This shows that lateral growth of these bilayers, and the associated increases in bend stresses, lead to the development of defect lines. For relatively small hot-spot sizes, rope structures with five helical threads of discs wrapped around a sphere core self-assemble. Where such ropes aggregate, geometrical frustration leads to multi-rope structures undergoing morphological rearrangement into double-bilayers. Extending the model by giving the discs double hot-spots leads to the formation of a multi-layer twisted bundle with three different directions of growth and three modes of twist. If the sizes of the interacting particles are changed, then, further new arrangements result. For thinner discs, a different class of bilayer is found in which the threads in the two leaflets are mutually orthogonal. This is shown to provide a new pathway for formation of tubes by a rolling-up mechanism involving intermediate saddle bilayer and half-pipe structures. The dimensions of such tubes are found to be very sensitive to the extent of the hot-spot. Double-helix structures, involving two helices of discs wrapped around a central thread of sphere, are the other major class of supramolecular assembly adopted by systems involving thinner discs. Finally, the interaction of self-assembled objects, leading to behaviours such as the formation of multi-bilayer structures, is shown to be accessed on the time- and length-scales of this class of computer simulation

Crystallization and demixing: morphological structure analysis in many-body systems

The description and analysis of spatial data is an omnipresent task in both science and industry: In the food industry the distribution and size of pores in baked goods plays a role in their taste. In chemistry, biology and physics spatial data arises in manifold disciplines and on all length scales. On large scales one finds them in the structure of the universe or in earth surveillance data. On small scales one observes highly structured data in inner bones or on minute scales in the deformation of nucleons in nuclear pasta, which is theorized to form during the cooling of a neutron star. In particular in statistical physics many-body-systems have a tendency to collectively form complex structures by self-organization. These complex structures often allow to draw conclusions about the underlying physics. In order to formulate a quantitative relation between the physics of many-body-systems and their morphology, i.e. the spatial structure they assume, a quantitative description of this structure is essential. In this dissertation the spatial structure of phase transitions (crystallization and demixing) in many-body-systems is quantitatively described and analyzed in order to achieve an improved understanding of the physics involved. Regarding the analysis methods applied in this thesis we go beyond conventional linear measures based on two-point correlation functions or the power spectrum. Instead, the aim is a full nonlinear morphological characterization of the spatial data with measures derived from the family of Minkowski functionals and tensors. They are additive, morphological measures related to, not only geometrical concepts like volume, area and curvature, but also to topological aspects such as connectivity and are sensitive to higher order correlation. Complex plasmas (dielectric microparticles immersed in a plasma) are a well suited model system for the particle resolved investigation of many-body processes. Their optical thinness allows for the optical imaging and tracking of the fully resolved trajectories of hundreds of particle layers. Additionally interactions can be tuned over a large range allowing to manipulate the shape and magnitude of the interparticle potential. Since the gas density is typically very low, the particle motion is practically undamped resulting in a direct analogy to the atomistic dynamics in solids or fluids. Liquid-solid phase transition have been considered impossible for a long time since the Mermin-Wagner theorem forbids long-range order in two (or less) dimensions. However, Kosterlitz and Thouless (Nobel prize 2016) circumvented this by replacing the long-range order with a quasi-long-range order and by introducing a topological phase transition mediated by defects. The well accepted KTHNY theory predicts an intermediate anisotropic phase, the hexatic phase. In the first part of this thesis the KTHNY theory is tested for experiments and a simulation of the crystallization of two-dimensional complex plasma sheets. For the same experiments the hypothesis and prediction of the recently developed fractal-domain-structure (FDS) theory is tested. The FDS theory is based on the Frenkel kinetic theory of melting. It postulates a fractal relationship between crystalline domains separated by boundaries of defect lines and predicts a scale-free relation between the system energy and the defect fraction. It is found that the KTHNY theory is not applicable to the liquid-solid phase transition in complex plasmas. The FDS theory however, is validated. The other focus of this thesis is the morphological characterization of fluid-fluid demixing dynamics. The generally accepted mechanism for fluid-fluid demixing is spinodal decomposition. Spinodal decomposition is achieved by a quench deep inside the spinodal curve of the phase diagram. It is characterized by the exponential growth of longwavelength density fluctuations. However the mean-field theory predictions of spinodal decomposition are not consistent with experiments and simulations. This shows the need for particle resolved studies with tunable interactions. To this end complex plasma simulations in flat three-dimensional space and density-functional theory calculations on the two-dimensional sphere are analyzed. In both cases different stages of demixing are identified with distinct domain growth rates during spinodal decomposition. Most importantly, universal demixing behavior is found for different interaction potentials, respectively for different mixture fractions and sphere sizes. These universal features could only be resolved by applying nonlinear measures, going beyond conventional methods based on the power spectral density. This suggests that nonlinear features in the demixing kinetics play an important role and that it is crucial to address this issue in future works.Räumliche Daten zu beschreiben und zu analysieren ist eine allgegenwärtige Problemstellung sowohl in der Wissenschaft als auch in der Industrie: So spielt beispielsweise in der Nahrungsmittelindustrie die räumliche Verteilung und die Größe von Poren in Backwaren eine Rolle für deren Geschmack. In den wissenschaftlichen Gebieten der Chemie, Biologie und der Physik liefern räumlich strukturierte Systeme Grundlage vieler Forschungsbereiche und sind in allen Größenordnungen aufzufinden: Auf großen Skalen z.B. bei der Struktur des Universums oder bei Erdbeobachtungsdaten. Auf kleinen Skalen bei der Struktur im inneren von Knochen oder im kleinsten bei der Verformung von Nukleonen zu nuklearer Pasta, die z.B. beim Abkühlen von Neutronensternen entstehen soll. Insbesondere in der statistischen Physik neigen Vielteilchensysteme dazu, sich in komplexen Strukturen selbst anzuordnen. Diese komplexen räumlichen Strukturen lassen oft Rückschlüsse auf die zugrunde liegende Physik zu. Um einen quantitativen Zusammenhang zwischen der Physik von Vielteilchensystemen und ihrer Morphologie, also der Struktur die diese annehmen, herzustellen, ist eine quantitative Beschreibung dieser Struktur unerlässlich. In dieser Dissertation werden daher die räumlichen Strukturen bei Phasenübergängen (Kristallisation und Entmischung) in Vielteilchensystemen beschrieben und analysiert, um damit Rückschlüsse auf die zugrundeliegende Physik ziehen zu können. Im Hinblick auf die Methoden, die zur Analyse der in dieser Dissertation untersuchten Systeme genutzt werden, gehen wir über konventionelle Methoden, die auf dem Leistungsspektrum oder auf zwei-Punkt Korrelationsfunktionen beruhen, hinaus. Das Ziel ist es die räumlichen Daten vollständig morphologisch zu charakterisieren. Zu diesem Zweck werden Metriken basierend auf der Familie der Minkowski Funktionale und Tensoren abgeleitet. Das sind additive morphologische Maße, die auch Korrelationen höherer Ordnung detektieren können. Sie sind nicht nur mit geometrischen Konzepten wie Volumen, Fläche und Krümmung verwandt, sondern stellen auch Aspekte der Topologie wie z.B. Verbundenheit dar. Komplexe Plasmen (dielektrische Mikropartikel eingebracht in ein Plasma) stellen ein überaus geeignetes Modellsystem für die Untersuchung von Vielteilchenprozessen auf der kinetischen Ebene individueller Teilchen dar, da durch ihre optische Dünnheit die Bildgebung mehrerer hundert Lagen von Teilchen und die volle Auflösung der Teilchentrajektorien ermöglicht wird. Darüber hinaus können die Teilchenwechselwirkungen in Komplexen Plasmen auf vielfältige Art und Weise manipuliert werden. Da der Gasdruck meist sehr gering ist, sind die Teilchenbewegungen praktisch ungedämpft. Dies stellt eine direkte Analogie zur Dynamik von Atomen in Flüssigkeiten oder Festkörpern dar. Flüssig-fest Phasenübergänge in zwei-dimensionalen Systemen wurden lange Zeit als unmöglich erachtet, da das Mermin-Wagner Theorem langreichweitige Ordnung in zwei (oder weniger) Dimensionen verbietet. Kosterlitz und Thouless umgingen diese Problem jedoch, indem sie die langreichweitige Ordnung durch eine quasi-langreichweitige Ordnung ersetzten und einen topologischen Phasenübergang vorstellten, der durch Interaktionen von Kristalldefekten vonstatten geht. Diese allgemein akzeptierte KTHNY Theorie sagt eine anisotrope Zwischenphase vorher, die so genannte hexatische Phase. Im ersten Teil dieser Dissertation werden die Vorhersagen der KTHNY Theorie, anhand von Experimenten und einer Computer Simulation an einzelnen zwei-dimensionalen Komplexen Plasma Kristall-Lagen getestet. Anhand selbiger Experimente wird eine kürzlich neu entwickelte fraktale-Domänen-Struktur (FDS) Theorie getestet. Die FDS Theorie basiert auf der kinetischen Theorie des Schmelzens von Frenkel. Sie postuliert einen fraktalen Zusammenhang zwischen der eingeschlossenen Fläche von kristallinen Domänen und der Länge deren Begrenzung durch Linien aus Kristalldefekten. Es wird gezeigt, dass die KTHNY Theorie nicht auf flüssig-fest Phasenübergänge in zwei-dimensionalen Komplexen Plasmen angewandt werden kann. Die FDS Theorie wird hingegen validiert. Desweiteren wird in dieser Dissertation die morphologische Beschreibung der Entmischungsdynamik von Flüssigkeiten behandelt. Der allgemein anerkannte Mechanismus, der für die Flüssigkeitsentmischung verantwortlich ist, ist die spinodale Dekomposition. Diese wird durch das quenchen (z.B. abkühlen) in den inneren Bereich der spinodalen Kurve im Phasendiagramm ausgelöst. Das charakteristische Merkmal der spinodalen Dekomposition ist der Beginn der Entmischung durch das exponentielle Wachstum von Dichtefluktuationen mit großen Wellenlängen. Die Vorhersagen der Molekularfeldtheorie der spinodalen Dekomposition sind jedoch nicht mit experimentellen Beobachtungen und Simulationen vereinbar. Diese Tatsache zeigt den Bedarf an Studien auf, die es vermögen einzelnen Teilchen zu folgen und bei denen man die Interaktionen zwischen den Teilchen beeinflussen kann. Deshalb werden in dieser Doktorarbeit sowohl Simulationen von Komplexen Plasmen (in drei-dimensionaler Euklidscher Geometrie) als auch Dichtefunktionaltheorie Berechnungen auf der zwei-dimensionalen Sphäre untersucht. In beiden Fällen können verschiedene Stadien in der Dynamik der Entmischung unterschieden werden. Das interessanteste Ergebnis ist die Entdeckung von universellem Verhalten im Entmischungsprozess. Universalität kann in dieser Arbeit im Hinblick auf verschiedene Interaktionspotentiale, bzw. im Hinblick auf verschiedene Mischungsverhältnisse und Sphärenradien gezeigt werden. Um diese universellen Eigenschaften zu entdecken, ist die Anwendung nicht-linearer Maße zwingend erforderlich, konventionelle auf dem Leistungsspektrum basierende Maße sind hierfür unzureichend. Dies zeigt, dass die nicht-linearen Eigenschaften des Entmischungsprozesses eine wichtige Rolle spielen und ist deshalb ein Fokus künftiger Arbeitenzu diesem Thema

Characterization and application of fusogenic liposomes

Conventional drug delivery strategies use the endocytic pathway to introduce biomolecules like proteins, DNA, or antibiotics into living cells. The main disadvantage of endocytic uptake is the quick intercellular degradation of the cargo. Compared to this, a more promising alternative for efficient molecular delivery is the induction of membrane fusion between liposomes and mammalian cells. Therefore special liposomes with extraordinary high fusion efficiency, so-called fusogenic liposomes (FLs), have been developed for such purposes. Due to the complete fusion of the liposomal membrane and the cellular plasma membrane, the cargo molecules can be effectively released into the cell cytoplasm, avoiding their degradation. In the last decade, applications relying on FLs became more and more relevant, however, the exact fusion mechanism is still to be elucidated. Therefore the aims of this work have been to investigate those liposomes and their fusogenicity with living mammalian cells dependent on lipid composition as well as environmental conditions to elucidate the most important factors inducing fusogenic structures within the liposomes. For structural characterization of the liposomes dynamic light and neutron scattering as well as solid state-NMR, freeze-fracture-STEM, Cryo-TEM, and differential scanning calorimetry were applied. Fusion efficiency was investigated by fluorescence microscopy and flow cytometry using Chinese hamster ovary (CHO) cells as an in vitro mammalian cell model. The first results showed that fusogenic liposomes (FLs) need cationic lipids with inverted conical molecular shapes and aromatic components at a distinct concentration as well as a neutral lipid for the best fusion induction. Neutral lipids with long and unsaturated chains and a small head group (e.g., PEs) do not change the liposomal fusion ability while those with saturated short chains and a big head group (e.g., PCs) do, and in most extreme cases revert the uptake mechanism to endocytosis. Additionally, a new application of fusogenic liposomes was established. For the first time, cationic liposomes with high fusion ability were successfully used as carrier particles for the delivery of the radionuclide 131I into mammalian breast cancer cells in vitro. The FLs reached the cancer cells with high efficiency and delivered their cargo into the cell cytoplasm. The control treatment of human red blood cells did not give positive results on fusion, and in this case, the delivery of the cargo was neglectable. These results considered FLs as an appropriate tool for applications in nuclear medicine. Further results showed that as the structural reorganization of the liposomal membrane supply the total required driving force to overcome the energy barrier of the different fusion intermediate steps, like in the case of FLs, changes of the fusion conditions such as temperature, osmolality or ionic concentration of the buffer did not influence the fusion success. In the case of the endocytic liposomes (ELs), buffer conditions played a crucial role in successful fusion, however, fusion efficiency remains infinitesimal under physiological conditions. To elucidate the correlation between efficient membrane fusion and liposomal characteristics, structural investigations of FLs with the best fusion efficiency were also carried out. Here, the simultaneous presence of lipid bilayers and small micelles of around 50 to 100 nm in diameter with high surface curvatures were found. Based on the obtained results, a theoretical mechanism of membrane fusion between FLs and cellular membranes could be proposed. The positively charged lipid is necessary for establishing contact between the two membranes. The micelles are formed by the neutral, phosphoethanolamine, lipids. The lipid bilayer enclosing inverted micelles has a high positive membrane curvature, which is especially favorable for the positively charged lipid molecules. Such curvature stress usually promotes the fusion-stalk formation and subsequent membrane fusion; therefore, the proposed fusion mechanism is called a modified stalk mechanism. Moreover, traces of other three-dimensional (3D) phases with high membrane curvature such us sponge-, inverted hexagonal-, and cubic phases could not be excluded. The present structures are probably metastable precursors, such as a rhombohedral phase, that reduce bilayer stability, which is leading to the pore formation occurring. In comparison to this, ELs formed only lamellar phases shown as non-fusogenic under physiological conditions. These results give rise to the hypothesis that the predominant presence of 3D-like and 3D phases with high membrane curvatures is the most important criterion for efficient membrane fusion induction

Multi-scale metrology for automated non-destructive testing systems

This thesis was previously held under moratorium from 5/05/2020 to 5/05/2022The use of lightweight composite structures in the aerospace industry is now commonplace. Unlike conventional materials, these parts can be moulded into complex aerodynamic shapes, which are diffcult to inspect rapidly using conventional Non-Destructive Testing (NDT) techniques. Industrial robots provide a means of automating the inspection process due to their high dexterity and improved path planning methods. This thesis concerns using industrial robots as a method for assessing the quality of components with complex geometries. The focus of the investigations in this thesis is on improving the overall system performance through the use of concepts from the field of metrology, specifically calibration and traceability. The use of computer vision is investigated as a way to increase automation levels by identifying a component's type and approximate position through comparison with CAD models. The challenges identified through this research include developing novel calibration techniques for optimising sensor integration, verifying system performance using laser trackers, and improving automation levels through optical sensing. The developed calibration techniques are evaluated experimentally using standard reference samples. A 70% increase in absolute accuracy was achieved in comparison to manual calibration techniques. Inspections were improved as verified by a 30% improvement in ultrasonic signal response. A new approach to automatically identify and estimate the pose of a component was developed specifically for automated NDT applications. The method uses 2D and 3D camera measurements along with CAD models to extract and match shape information. It was found that optical large volume measurements could provide suffciently high accuracy measurements to allow ultrasonic alignment methods to work, establishing a multi-scale metrology approach to increasing automation levels. A classification framework based on shape outlines extracted from images was shown to provide over 88% accuracy on a limited number of samples.The use of lightweight composite structures in the aerospace industry is now commonplace. Unlike conventional materials, these parts can be moulded into complex aerodynamic shapes, which are diffcult to inspect rapidly using conventional Non-Destructive Testing (NDT) techniques. Industrial robots provide a means of automating the inspection process due to their high dexterity and improved path planning methods. This thesis concerns using industrial robots as a method for assessing the quality of components with complex geometries. The focus of the investigations in this thesis is on improving the overall system performance through the use of concepts from the field of metrology, specifically calibration and traceability. The use of computer vision is investigated as a way to increase automation levels by identifying a component's type and approximate position through comparison with CAD models. The challenges identified through this research include developing novel calibration techniques for optimising sensor integration, verifying system performance using laser trackers, and improving automation levels through optical sensing. The developed calibration techniques are evaluated experimentally using standard reference samples. A 70% increase in absolute accuracy was achieved in comparison to manual calibration techniques. Inspections were improved as verified by a 30% improvement in ultrasonic signal response. A new approach to automatically identify and estimate the pose of a component was developed specifically for automated NDT applications. The method uses 2D and 3D camera measurements along with CAD models to extract and match shape information. It was found that optical large volume measurements could provide suffciently high accuracy measurements to allow ultrasonic alignment methods to work, establishing a multi-scale metrology approach to increasing automation levels. A classification framework based on shape outlines extracted from images was shown to provide over 88% accuracy on a limited number of samples

Statistical analysis for longitudinal MR imaging of dementia

Serial Magnetic Resonance (MR) Imaging can reveal structural atrophy in the brains of subjects with neurodegenerative diseases such as Alzheimer’s Disease (AD). Methods of computational neuroanatomy allow the detection of statistically significant patterns of brain change over time and/or over multiple subjects. The focus of this thesis is the development and application of statistical and supporting methodology for the analysis of three-dimensional brain imaging data. There is a particular emphasis on longitudinal data, though much of the statistical methodology is more general. New methods of voxel-based morphometry (VBM) are developed for serial MR data, employing combinations of tissue segmentation and longitudinal non-rigid registration. The methods are evaluated using novel quantitative metrics based on simulated data. Contributions to general aspects of VBM are also made, and include a publication concerning guidelines for reporting VBM studies, and another examining an issue in the selection of which voxels to include in the statistical analysis mask for VBM of atrophic conditions. Research is carried out into the statistical theory of permutation testing for application to multivariate general linear models, and is then used to build software for the analysis of multivariate deformation- and tensor-based morphometry data, efficiently correcting for the multiple comparison problem inherent in voxel-wise analysis of images. Monte Carlo simulation studies extend results available in the literature regarding the different strategies available for permutation testing in the presence of confounds. Theoretical aspects of longitudinal deformation- and tensor-based morphometry are explored, such as the options for combining within- and between-subject deformation fields. Practical investigation of several different methods and variants is performed for a longitudinal AD study

Problems at the Nexus of Geometry and Soft Matter: Rings, Ribbons and Shells

There has been an increasing appreciation of the role in which elasticity plays in soft matter. The understanding of many shapes and conformations of complex systems during equilibrium or non-equilibrium processes, ranging from the macroscopic to the microscopic, can be explained to a large extend by the theory of elasticity. We are motivated by older studies on how topology and shape couple in different novel systems and in this thesis, we present novel systems and tools for gaining fundamental insights into the wonderful world of geometry and soft matter. We first look at how defects, topology and geometry come together in the physics of thin membranes. Topological constraint plays a fundamental role on the morphology of crumpling membranes of genus zero and suggest how different fundamental shapes, such as platonic solids, can arise through a crumpling process. We present a way of classifying disclinations using a generalized “Casper-Klug” coordination number. We show that there exist symmetry breaking during the crumpling process, which can be described using Landau theory and that thin membranes preserve the memory of their defects. Next we consider the problem of the shapes of Bacillus spores and show how one can understand the folding patterns seen in bacterial coats by looking at the simplified problem of two concentric rings connected via springs. We show that when the two rings loses contact, rucks spontaneous formed leading to the complex folding patterns. We also develop a simple system of an extensible elastic on a spring support to study bifurcation in system that has adhesion. We explain the bifurcation diagram and show how it differs from the classical results. Lastly, we investigate the statistical mechanics of the Sadowsky ribbon in a similar spirit to the famous Kratky-Porod model. We present a detail theoretical and numerical calculations of the Sadowsky ribbon under the effect of external force and torsion. This model may be able to explain new and novel biopolymers ranging from actin, microtubules to rod-like viruses that lies outside the scope of WLC model. This concludes the thesis.Physic