Toroidal nematics: Point defects, disclination lines and walls

[eng] Confining partially order fluids can lead to frustration if the locally preferred state can not be achieved everywhere simultaneously. When this happens, the configuration of the material can not be given by the local minimum, and a plethora of compatible frustrated configurations become possible. In this case, the ground state configuration results from the minimization of the total energy. This is specially exemplified by nematic liquid crystals where the anisotropic building blocks reduce their free energy by aligning parallel to each other. Perfect parallel alignment can become impossible everywhere when the nematic is confined within different shapes while fixing the orientation at the boundaries. How this frustration is resolved and which configuration the liquid crystal acquires depends on the geometry and topology of the boundary and might require the presence of regions with no defined alignment, called defects. In this thesis we mainly focus on experimentally studying the configurations acquired by a nematic liquid crystal confined to a stable toroidal droplet with different boundary conditions. We first study the case with tangential alignment at the surface. In this case, we find stable defect populated configurations when the torus is heated to the isotropic phase and cooled back to the nematic phase. They consist mainly on defect pairs whose number and location is random and that turn out to be metastable with an energetic barrier that is high enough for them to not spontaneously annihilate. We also report the appearance of a configuration not fully elucidated that we call ”X” pattern and that can have a solitonic character. Note that all these features are observed even when there is no topological requirement for the torus to have defects. We then study the effect of applying magnetic fields on planar nematic tori with and without defect pairs and find that stable inversion walls form. In the defect free case, two splay-bend walls form, while when a defect pair is present, either one of the walls does not appear or an extra wall is formed depending on the initial location of the defect pair. Interestingly, we find that the mobility of the defects allows for the defect pair wall to reorganize into different types of walls, becoming a wall of the twist type to reduce energy. We also show how, by heating and cooling our nematic droplets in an external magnetic field, the number of defect pairs generated can be controlled. We finish our work on nematic tori by studying the case with perpendicular anchoring at the surface. We recover previous experimental results and find that the anchoring strength plays a significant role in the appearance of a configuration characterized by four dark brushes forming a spiral. Moreover, for certain conditions, stable configurations filled with disclination lines are found and experimentally studied using epifluorescence microscopy. Aside from our experimental work, from a theoretical perspective, we use the decomposition of a director field distortion into four normal modes to derive the compatibility conditions for a 2D and 3D nematic. For that, we use a simple approach based on imposing that the director field variation has to be the same when going through two different paths up to second order. This approach gives an intuitive interpretation of the different equations and provides a simple way to relate them to their counterpart in curved space through the concept of holonomy. Finally, we also discuss some side projects collaterally related to the main thesis work. We first discuss our studies on water evaporation of chitosan hydrogels. We describe the constructed setup to generate the gels and our experiments that track the mass evolution of the gels in time. Our results suggest that the evaporation rate for our hydrogels is slower than pure water due to an increase in the energy barrier for the water molecules to escape the gel, thus bringing about a kinetic character to the process. We also show the design, construction and first tests on an upscaled prototype for the production of these chitosan hydrogels. We end by briefly describing our work with thermorresponsive hydrogels that present a constant volume phase transition leading to phase coexistence between a swollen and shrunken phases when the temperature is increased rapidly. We mainly show how cylindrical gels suddenly bend due to a spontaneous polarization of the region that shrinks, which is in accordance with the current theory for this process.