Shapes of fluid membranes with chiral edges

We carry out Monte Carlo simulations of a colloidal fluid membrane with a free edge and composed of chiral rodlike viruses. The membrane is modeled by a triangular mesh of beads connected by bonds in which the bonds and beads are free to move at each Monte Carlo step. Since the constituent viruses are experimentally observed to twist only near the membrane edge, we use an effective energy that favors a particular sign of the geodesic torsion of the edge. The effective energy also includes the membrane bending stiffness, edge bending stiffness, and edge tension. We find three classes of membrane shapes resulting from the competition of the various terms in the free energy: branched shapes, chiral disks, and vesicles. Increasing the edge bending stiffness smooths the membrane edge, leading to correlations among the membrane normals at different points along the edge. The normalized power spectrum for edge displacements shows a peak with increasing preferred geodesic torsion. We also consider membrane shapes under an external force by fixing the distance between two ends of the membrane and finding the shape for increasing values of the distance between the two ends. As the distance increases, the membrane twists into a ribbon, with the force eventually reaching a plateau.