3D axisymmetric shapes for colloidal membranes

We investigate the formation of catenoid-like colloidal membranes, fluid monolayers consisting of rod-like viruses held together by the depletion interaction. These catenoid-like membranes arise from the merging of two saddle-shaped membranes of smaller area that have been doped with shorter rods. Measurements show that the resulting structures are not true minimal surfaces but deviate slightly due to properties of the exposed edges. Using both an effective theory to describe the liquid crystal degrees of freedom by geometric properties of the edge and an explicit treatment of the liquid crystal terms, we calculate the possible axisymmetric equilibrium shapes and a phase diagram of the saddle-catenoid transition.