Three-dimensional structures of chiral membrane with free edges

We carry out Monte Carlo simulations on membranes with orientational order and multiple edges subject to external forces and also with force-free conditions. The membrane resists bending and has an edge tension, the orientational order couples with the membrane surface normal through a cost for tilting, and there is a chiral liquid crystalline interaction. For a membrane with two edges, increasing the displacement between the opposite edges requires the external force applied on the membrane to increase rapidly at first, and then gradually once the separation is sufficiently large. When the cost of tilt is small, the alignment between directors results in two parallel lines of directors perpendicular to both the local surface normal and pulling direction for achiral coupling. Increasing the chirality leads to the twisting of these lines about each other and the directors pointing towards the pulling direction. When the membrane is force-free, increasing the chiral interaction leads to multiple pi walls connecting edges and wrapping around the membrane neck, resulting in the formation of catenoid or a trinoid, depending on the number of edges.