Resumen de Confinement and polydispersity in granular systems and liquid crystals
In this thesis we delve into the study of liquid crystals, both through a theoretical approach as well as through experiments on granular systems of which the steady states resemble liquid-crystalline structures. We model different systems with particular shapes and under specific conditions, aiming to understand how they affect phase stability and behaviour.
The experiments were performed on a vertically vibrated monolayer of cylindrical rods restricted to an annulus (circular cavity with a mid circular obstacle) and between two parallel plates that don't allow for particle overlap on the vertical axis. We observed that the introduction of the obstacle produces "domain walls" with tetratic and isotropic configurations separating regions with strong smectic ordering, as opposed to experiments where no obstacle was present that showed strong tetratic ordering with four point-like defects.
For the theoretical approach we modelled a two-dimensional system formed of particles shaped like hard isosceles triangles and studied both the one-component case as well as some particular mixtures. We found stable triatic configurations for both the one component case and for certain symmetric mixtures. Also our results yielded, as far as we can tell, the first evidence of a Nematic-Nematic transition on one-component hard particle systems. We also studied the effects of polydispersity in a two-dimensional system of hard rectangles. We obtained that polydispersity has an important effect on the phase diagram, strengthening the 1st order Isotropic-Nematic transition and decreasing the stability of the tetratic phase. Also we found that polydispersity induces strong fractionation between the coexisting phases.
Finally we studied the effects of confinement on a system of hard plate-like particles restricted to lie between two parallel hard walls. We were able to obtain stable homeotropic configurations for particular aspect ratios and specific values of wall separation and packing fraction. Also considering biaxial particles produced a rich phase diagram that merits a more dedicated analysis. We explained the obtained behaviour by looking at how entropy is maximized as the system approaches close packing.
