Variational theory of confinement effects on cholesteric liquid crystals

This thesis is devoted to a theoretical description of the effects of confinement in cholesteric liquid crystals. The project is inspired by recent experimental works on cholesteric droplets based on amyloid fibrils. Particularly, four phase transitions were observed in droplets surrounded by isotropic fluid, at growing volumes. The complete phenomenology has to date not yet been described or predicted from a theoretical perspective. Simple scaling arguments based on bulk terms of the Frank-Oseen (FO) energy-density functional have been found only for the first three phases, so that a more thorough analysis is needed. In this thesis, we will address the issue by means of a variational approach, with particular focus on understanding how confinement affects the various terms of the FO functional, for both bulk and surface terms. This will serve to rationalize the experimental findings observed on amyloid-based systems, as well as provide a basis for more refined theoretical approaches. In this thesis we propose two models to explain the whole phenomenology presented by the system, and introduce scaling laws for the three phase transitions.