Deformation and orientational order of chiral membranes with free edges

Motivated by experiments on colloidal membranes composed of chiral rod-like viruses, we use Monte Carlo methods to determine the phase diagram for liquid crystalline order rods and membrane shape. We generalize Lebwohl-Lasher model a nematic with coupling curved surface edge tension resistance bending, include an energy cost tilting relative local normal. The is represented triangular mesh hard beads joined bonds, where each bead decorated director. can move, bonds reconnect directors rotate at step. When tilt small, tends be flat, only twisting near low coupling, remaining parallel normal in interior membrane. At high twist everywhere, forming cholesteric state. large, emergence state values accompanied bending into saddle Increasing flatten These results illustrate geometric frustration arising from inability have twist.