Renormalization group theory of banana and pizza-slice-shaped mesogens: Long-range order in 2d
Fluids and Materials Seminar
4th June 2019, 2:00 pm – 3:00 pm
Main Maths Building, SM2
It has been known that at high density, banana-shaped molecules are packed into a bent configuration locally, giving rise to interesting liquid-crystalline phases such as splay-bend and twist-bend. These spontaneous bend states can be modelled theoretically by allowing the bend elastic constant in the Frank elastic energy to become negative. Here we extend this idea to banana-shaped and pizza-slice-shaped molecules with ferro-interactions, which can display both splayed and bent states. We model this by allowing both splay and bend elastic constants in the effective Frank elastic energy to be negative. In particular, we predict two new liquid crystalline splay-bend phases. Furthermore, using renormalization group analysis, we showed that the phase transition belongs to a new constrained ferromagnet universality class. Here, unlike ordinary phase transitions, the symmetry of the system (O(n)-rotation) does not uniquely define the universality class.