Unconventional liquid crystal phases of helical particles

Helical particles are ubiquitous in nature. Many natural and synthetic biomolecules like polynucleotides and polypeptides; colloidal suspensions like filamentous ($fd$) virus and helical flagella and certain organic molecules are found in helical shape. Despite their abundance in nature, understanding of the phase behaviour of helical particles is poor. These helical molecules have a well known propensity to form liquid crystal phases. The chirality in the helical shapes influence their liquid crystal organization. Experimental results of the liquid crystal phases shown by these molecules are often compared to those of rods, neglecting the effect of helical shape on phase behaviour. We have undertaken an extensive investigation of the phase diagram of hard helical particles using Monte Carlo simulations. We provide evidence of new chiral phases exhibiting screw-like order. This new chiral phase is different to the cholesteric phase and is characterized by the $C_2$ symmetry axes of helices spiralling around the nematic director with periodicity equal to the particle pitch. We have used Isobaric Monte Carlo simulations to obtain a full phase diagram of helical particles. A rich polymorphism is observed exhibiting a special screw-like nematic and a number of screw-like smectic phases. The effect of helical shape on the phase diagram is studied by considering different morphologies of helix obtained by tuning the helical parameters like radius and pitch. We found a remarkable change in the phase behaviour with the change in the shape of helix. Dense packing structures of different helical shapes are found by implementing Isopointal set Structural Search Method (ISSM). The physical mechanism underlying the liquid crystal order observed in helical flagella is explained. Preliminary results on the coexistence densities using the Successive Umbrella Sampling technique are shown. Finally, some preliminary results are shown discussing the compatibility of screw-like order and cholesteric order.