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Shapes of fluid membranes with chiral edges

We carry out Monte Carlo simulations of a colloidal fluid membrane composed of chiral rod-like 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 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 normal at different points along the edge. We also consider membrane shapes under an external force by fixing the distance between two ends of the membrane, and find 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.