Monte Carlo simulation of fluid membranes with orientational order and free edges

Motivated by experiments on membranes composed of chiral rod-like viruses, we consider a triangular mesh of hard beads possessing directors joined by tethers. The beads, tethers and directors are free to move, reconnect or rotate at each Monte Carlo step. We model the system using the Canham-Helfrich energy in addition to a liquid crystalline energy, which include a Lebwohl-Lasher interaction, a tilt energy and a chiral energy that favors twist between neighboring directors. We find three membrane shapes: branched polymers, disks and vesicles. For the disk, we find the twist of directors is expelled to the edge of the membrane, and as the chiral coupling increases, the twist penetration depth increases until pi walls form inside the membrane. We also study the membrane shape when we pull apart two antipodal points on the membrane edge. As the distance between the antipodal points increases, the disk twists into a ribbon and the extension force increases eventually reaching a plateau.