Biological & Soft Matter Seminar: Mechanics of Colloidal Membranes
Prof. Thomas Powers, Brown University, USA
Colloidal membranes consist of a monolayer of rod-like viruses held together by osmotic pressure. They share many properties with lipid bilayers, such as in-plane fluidity and resistance to bending. However, they also display distinctive properties, such as a propensity to have exposed edges and to take on shapes with negative Gaussian curvature. In this talk I will study edge fluctuations of large, mostly flat membranes.
We use an effective theory to account for liquid crystalline degrees of freedom near the edge by geometric quantities such as the length, curvature, and geodesic torsion of the edge. I will also describe theoretical work on a variant of the classic problem of the axisymmetric shape of a soap film held between two circular rings. Motivated by the properties of colloidal membranes, we consider a membrane of fixed area and a resistance to bending connecting two circular rings. We find a critical area, below which there is a maximum separation of the rings, just as in the soap film problem. However, above the critical area, the membrane is able to connect the rings at any separation by forming a tether.