#8 Liquid crystals with split personality

Liquid crystals (LCs) are a state of matter intermediate between solid and liquid; they retain some of the order of a solid, but are free to flow as a liquid. In particular, their (non-spherical) constituent particles all point, on average, in the same direction, termed the director. LC behaviour can be driven by temperature (thermotropic LCs made of organic molecules) or by concentration in a solvent (lyotropic LCs made of micron-sized colloids). Recently, Smalyukh and co-workers were able to stabilise a hybrid molecular-colloidal LC which exhibits preferential alignment along two mutually-perpendicular directors. This biaxial nematic (NB) phase is very exciting because of both ts fundamental interest and its potential applications, such as faster bistable displays or devices. In this project we propose to study this by Monte Carlo simulation of a two-dimensional (2D) lattice model in which both colloidal nanorods and molecules are assumed to be long and short rods, respectively, that can only point along the axes of a 2D lattice and may not overlap. Two neighbouring short rods attract each other when they are parallel, whereas a long and a short rod attract when they are perpendicular.

The figure shows a numerical simulation, performed by us using Python, of a system with periodic boundary conditions at fixed temperature. The long colloidal rods are coloured green, every other site is occupied by a small molecule, in a horizontal (yellow) or vertical (purple) orientation.