Nematic liquid crystals are mesogenic materials that are popular working materials for optical displays. There has been an increased interest in bistable liquid crystal devices which support two optically distinct stable equilibria. These devices typically exploit a complex geometry or anchoring conditions, which often induces defects in the equilibria. There remains a great deal to be understood about the structure of the defects and how they stabilize multiple equilibria in modern devices. This thesis focuses on four problems: the first three explore the effect of confinement and defects on nematic equilibria in simple geometries, with the aim of exploring multistability in these geometries; the fourth problem concerns the fine structure of point defects, essential for future modelling of nematic equilibria in more complex geometries. Firstly, we study nematic liquid crystals confined to two-dimensional rectangular wells using the Oseen-Frank theory. Secondly, we study equilibria within a semi-infinite rectangular domain with weak tangential anchoring on the surfaces. Thirdly, we study nematic equilibria within two-dimensional annuli. We derive explicit expressions for the director fields and free energies of equilibria within these geometries and discuss the stability of the predicted states. These three problems are motivated by the experimental work on colloidal nematic liquid crystals, which we interpret in the context of our results. Finally, we study the fine structure and stability of the radial hedgehog defect in the Landau-de Gennes theory with a sixth order bulk potential, relevant to the observability of global biaxial phases in a model with higher order potential terms.

Understanding the interaction of polyelectrolytes with oppositely charged lipid membranes is an important issue of soft matter physics, which provides an insight into mechanisms of interactions between biological macromolecules and cell membranes. Despite the fact that many (bio)macromolecules and filamentous supramolecular assemblies show semiflexible behavior, prior to this work very little was known about the conformational dynamics and Brownian motion of semiflexible particles attached to freestanding lipid membranes. In order to address these issues, diffusion and conformational dynamics of semiflexible DNA molecules and filamentous fd-virus particles electrostatically adsorbed to cationic freestanding lipid membranes were studied on the single particle level by means of optical wide-field fluorescence microscopy. Supergiant unilamellar vesicles (SGUVs) with diameters larger than 100 m represent a perfect model of a freestanding membrane. In this work, a method was developed that enabled the reliable and efficient electroformation of cationic SGUVs on ITO-coated coverslips. The utilization of SGUVs as model freestanding lipid bilayers allowed for determination of the previously unknown surface viscosity of DOPC/DOTAP membranes. In particular, the analysis of the translational diffusion coefficients of small (10, 20, 50 nm) membrane-attached anionic polystyrene beads has shown that the surface viscosity of DOPC/DOTAP membranes with CDOTAP = 1–7 mol% is independent of the DOTAP concentration and equals η = (5.9 ± 0.2) × 10−10 Pa s m. The fluorescence video-microscopy investigation of single DNA molecules attached to cationic SGUVs revealed a previously unreported conformational transition of a membrane-bound DNA molecule from a 2D random coil, the original conformation in which DNA attaches to the membrane, to a compact globule. This membrane-mediated DNA condensation is favored at high cationic lipid concentrations in the membrane and long DNA contour lengths. The DNA compaction rate in the coil–globule transition is 124 ± 46 kbp/s, and the resulting DNA globule sizes were found to be 250–350 nm at DOPC membranes containing 1 mol% DOTAP and 130–200 nm for 7 mol% DOTAP, indicating a stronger compaction for higher charge densities in the membrane. Additional experiments with freestanding cationic membranes in the gel state and supported cationic lipid membranes with gel–fluid coexistence suggest that the DNA collapse on a freestanding fluid cationic membrane may be initiated by a local lipid segregation in the membrane and is accompanied by local membrane deformations, which eventually stabilize the compact DNA globule. Furthermore, in this work single molecule studies of random-coil DNA molecules and filamentous fd-virus particles on a freestanding cationic lipid bilayer with a low charge density were carried out. The experiments revealed that these particles can be described as semiflexible chains in 2D. Taken together, DNA molecules and fd-virus particles cover a broad range of the ratio of contour length and persistence length from 0.4 to 82. The results of this work demonstrate that the mobility of such membrane-attached semiflexible particles is strongly affected by hydrodynamics in the lipid membrane and the surrounding bulk fluid, and can in essence be described using a hydrodynamics-based theory for a disk-shaped solid membrane inclusion with a characteristic size approximately equal to the radii of gyration of the particles.

Understanding the interaction of polyelectrolytes with oppositely charged lipid membranes is an important issue of soft matter physics, which provides an insight into mechanisms of interactions between biological macromolecules and cell membranes. Despite the fact that many (bio)macromolecules and filamentous supramolecular assemblies show semiflexible behavior, prior to this work very little was known about the conformational dynamics and Brownian motion of semiflexible particles attached to freestanding lipid membranes. In order to address these issues, diffusion and conformational dynamics of semiflexible DNA molecules and filamentous fd-virus particles electrostatically adsorbed to cationic freestanding lipid membranes were studied on the single particle level by means of optical wide-field fluorescence microscopy. Supergiant unilamellar vesicles (SGUVs) with diameters larger than 100 m represent a perfect model of a freestanding membrane. In this work, a method was developed that enabled the reliable and efficient electroformation of cationic SGUVs on ITO-coated coverslips. The utilization of SGUVs as model freestanding lipid bilayers allowed for determination of the previously unknown surface viscosity of DOPC/DOTAP membranes. In particular, the analysis of the translational diffusion coefficients of small (10, 20, 50 nm) membrane-attached anionic polystyrene beads has shown that the surface viscosity of DOPC/DOTAP membranes with CDOTAP = 1–7 mol% is independent of the DOTAP concentration and equals η = (5.9 ± 0.2) × 10−10 Pa s m. The fluorescence video-microscopy investigation of single DNA molecules attached to cationic SGUVs revealed a previously unreported conformational transition of a membrane-bound DNA molecule from a 2D random coil, the original conformation in which DNA attaches to the membrane, to a compact globule. This membrane-mediated DNA condensation is favored at high cationic lipid concentrations in the membrane and long DNA contour lengths. The DNA compaction rate in the coil–globule transition is 124 ± 46 kbp/s, and the resulting DNA globule sizes were found to be 250–350 nm at DOPC membranes containing 1 mol% DOTAP and 130–200 nm for 7 mol% DOTAP, indicating a stronger compaction for higher charge densities in the membrane. Additional experiments with freestanding cationic membranes in the gel state and supported cationic lipid membranes with gel–fluid coexistence suggest that the DNA collapse on a freestanding fluid cationic membrane may be initiated by a local lipid segregation in the membrane and is accompanied by local membrane deformations, which eventually stabilize the compact DNA globule. Furthermore, in this work single molecule studies of random-coil DNA molecules and filamentous fd-virus particles on a freestanding cationic lipid bilayer with a low charge density were carried out. The experiments revealed that these particles can be described as semiflexible chains in 2D. Taken together, DNA molecules and fd-virus particles cover a broad range of the ratio of contour length and persistence length from 0.4 to 82. The results of this work demonstrate that the mobility of such membrane-attached semiflexible particles is strongly affected by hydrodynamics in the lipid membrane and the surrounding bulk fluid, and can in essence be described using a hydrodynamics-based theory for a disk-shaped solid membrane inclusion with a characteristic size approximately equal to the radii of gyration of the particles.

Cette thèse porte sur la dynamique des différentes mésophases liquides cristallines et des transitions de phase d'un modèle colloïdal de particules en forme de bâtonnent: les virus fd. L'étude de l'auto-organisation des cristaux liquides colloïdaux traite des phénomènes les plus simples de formation de systèmes structurés. Dans un système où les particules anisotropes ont des interactions de noyau rigide, l'auto-organisation est purement entropique en raison de la maximisation du volume libre du système. Ainsi, il y a une modification de la dynamique qui peut être mesurée, et fournisse des informations sur le volume libre disponible et la structure de la mésophase.La dynamique des bâtonnets fd peut être mesurée avec précision à l'aide de techniques de microscopie à fluorescence. Nous quantifions la dynamique autour des transitions de phase et l'effet de la flexibilité et de la longueur en tant que mécanisme pour relâcher la contrainte de leurs voisins. En outre, dans une structure lamellaire guest-host, nous avons prouvé la pérmeation favorisée des bâtonnets longs guest à travers les couches de la matrice Smectique hast formée de plus petites particules. Dans ces conditions, la super-diffusion de la particule invitée est également observée lorsqu'elle se diffuse dans une limite de grain. Il s'agit d'un pas en avant pour comprendre la dynamique des systèmes structurés colloïdaux et aussi dans le développement des nouveaux matériaux basés sur des diffuseurs rapides avec des applications potentielles dans la biologie médicale. Les résultats expérimentaux sont très prometteurs et stimulantes. / This thesis treats the dynamics of the different liquid crystalline mesophases and phase transitions of a model colloïdal of rod-like particles: the fd viruses. The study of the self-organization of colloïdal liquid crystals treats the simplest phenomena of forming structured systems. In a system where anisotropie particles have hard core interactions, the self-organization is purely entropy driven due to the maximization of the free volume of the system. Thus, there is a change on the dynamics at single particle level that can be measured, providing information on the available free volume and the structure of the mesophase.The fd rods are a versatile colloïdal system and their self-dynamics can be accurately measured using fluorescence microscopy techniques. We quantify the relaxation of the dynamics around the phase transitions and the effect of flexibility and length as a mechanism to release the constraint of their neighbors. Moreover, in a guest-host lamellar structure we demonstrate that a big guest particle is faster than the small host, if the guest particle is not commensurate in the host energy landscape. In these conditions, also the super-diffusion of the guest particle is observed when it diffuses into a grain boundary. This is a step forward to understand the dynamics of colloïdal structured systems and also in the development the new materials based on fast diffusers with potential applications in drug delivery. The extensive experimental results are completed by a whole analysis and interpretation, being very promising and challenging.