Chiral molecules on curved colloidal membranes

Colloidal membranes, self assembled monolayers of aligned rod like molecules, offer a template for designing membranes with definite shapes and curvature, and possibly new functionalities in the future. Often the constituent rods, due to their molecular chi- rality, are tilted with respect to the membrane normal. Spatial patterns of this tilt on curved membranes result from a competition among depletion forces, nematic interac- tion, molecular chirality and boundary effects. We present a covariant theory for the tilt pattern on minimal surfaces, like helicoids and catenoids, which have been gener- ated in the laboratory only recently. We predict several non-uniform tilt patterns, some of which are consistent with experimental observations and some, which are yet to be discovered.