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

Pomelo, a tool for computing Generic Set Voronoi Diagrams of Aspherical Particles of Arbitrary Shape

We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to granular materials. A generalization of the conventional Voronoi diagram for points or monodisperse spheres is the Set Voronoi diagram, also known as navigational map or tessellation by zone of influence. In this construction, a Set Voronoi cell contains the volume that is closer to the surface of one particle than to the surface of any other particle. This is required for aspherical or polydisperse systems. Pomelo is designed to be easy to use and as generic as possible. It directly supports common particle shapes and offers a generic mode, which allows to deal with any type of particles that can be described mathematically. Pomelo can create output in different standard formats, which allows direct visualization and further processing. Finally, we describe three applications of the Set Voronoi code in granular and soft matter physics, namely the problem of packings of ellipsoidal particles with varying degrees of particle-particle friction, mechanical stable packings of tetrahedra and a model for liquid crystal systems of particles with shapes reminiscent of pearsComment: 4 pages, 9 figures, Submitted to Powders and Grains 201

Complex motion of steerable vesicular robots filled with active colloidal rods

While the collective motion of active particles has been studied extensively, effective strategies to navigate particle swarms without external guidance remain elusive. We introduce a method to control the trajectories of two-dimensional swarms of active rod-like particles by confining the particles to rigid bounding membranes (vesicles) with non-uniform curvature. We show that the propelling agents spontaneously form clusters at the membrane wall and collectively propel the vesicle, turning it into an active superstructure. To further guide the motion of the superstructure, we add discontinuous features to the rigid membrane boundary in the form of a kinked tip, which acts as a steering component to direct the motion of the vesicle. We report that the system's geometrical and material properties, such as the aspect ratio and Peclet number of the active rods as well as the kink angle and flexibility of the membrane, determine the stacking of active particles close to the kinked confinement and induce a diverse set of dynamical behaviors of the superstructure, including linear and circular motion both in the direction of, and opposite to, the kink. From a systematic study of these various behaviors, we design vesicles with switchable and reversible locomotions by tuning the confinement parameters. The observed phenomena suggest a promising mechanism for particle transportation and could be used as a basic element to navigate active matter through complex and tortuous environments.Comment: 11 pages, 5 figure

Purely entropic self-assembly of the bicontinuous Ia3̅d gyroid phase in equilibrium hard-pear systems

We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia3d structure by entropic self-assembly, extending the previous observations of Barmes et al. (2003 Phys. Rev. E 68, 021708. (doi:10.1103/PhysRevE.68.021708)) and Ellison et al. (2006 Phys. Rev. Lett. 97, 237801. (doi:10.1103/PhysRevLett.97.237801)). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression–decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedo

Universal hidden order in amorphous cellular geometries

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties

Universal hidden order in amorphous cellular geometries

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties

Complex motion of steerable vesicular robots filled with active colloidal rods

Abstract While the collective motion of active particles has been studied extensively, effective strategies to navigate particle swarms without external guidance remain elusive. We introduce a method to control the trajectories of two-dimensional swarms of active rod-like particles by confining the particles to rigid bounding membranes (vesicles) with non-uniform curvature. We show that the propelling agents spontaneously form clusters at the membrane wall and collectively propel the vesicle, turning it into an active superstructure. To further guide the motion of the superstructure, we add discontinuous features to the rigid membrane boundary in the form of a kinked tip, which acts as a steering component to direct the motion of the vesicle. We report that the system’s geometrical and material properties, such as the aspect ratio and Péclet number of the active rods as well as the kink angle and flexibility of the membrane, determine the stacking of active particles close to the kinked confinement and induce a diverse set of dynamical behaviors of the superstructure, including linear and circular motion both in the direction of, and opposite to, the kink. From a systematic study of these various behaviors, we design vesicles with switchable and reversible locomotions by tuning the confinement parameters. The observed phenomena suggest a promising mechanism for particle transportation and could be used as a basic element to navigate active matter through complex and tortuous environments

Rationalizing Euclidean Assemblies of Hard Polyhedra from Tessellations in Curved Space

Entropic self-assembly is governed by the shape of the constituent particles, yet a priori prediction of crystal structures from particle shape alone is non-trivial for anything but the simplest of space-filling shapes. At the same time, most polyhedra are not space-filling due to geometric constraints, but these constraints can be relaxed or even eliminated by sufficiently curving space. We show using Monte Carlo simulations that the majority of hard Platonic shapes self-assemble entropically into space-filling crystals when constrained to the surface volume of a 3-sphere. As we gradually decrease curvature to "flatten" space and compare the local morphologies of crystals assembling in curved and flat space, we show that the Euclidean assemblies can be categorized either as remnants of tessellations in curved space (tetrahedra and dodecahedra) or non-tessellation-based assemblies caused by large-scale geometric frustration (octahedra and icosahedra)