(192e) Shapes and Thermodynamics of Membranes with Boundaries

The shapes of blood cells, vesicles, and other topologically spherical elastic surfaces as a function of volume and surface area have been successfully described by continuum models such as that of Canham and Helfrich. Less attention, though, has been devoted to the study of membranes with boundaries, such as colloidal membranes, foams, opening phospholipid bilayers, kinetoplasts (essentially sheets of linked coils of DNA), and other 2D biological materials. In this work, we use a bespoke optimization algorithm (Locally Feasibly Projected Sequential Quadratic Programming) to find the minimum-energy shapes of membranes with boundaries under geometrical constraints. Thermal fluctuations of the sheets are simulated, and normal modes about the minimum-energy states are calculated in order to determine how geometry and curvature affect thermodynamic behavior.