Membranes in Rod Solutions: A System with Spontaneously Broken Symmetry

We consider a dilute solution of infinitely rigid rods near a curved, perfectly repulsive surface and study the contribution of the rod depletion layer to the bending elastic constants of membranes. We find that a spontaneous curvature state can be induced by exposure of BOTH sides of the membrane to a rod solution. A similar result applies for rigid disks with a diameter equal to the rod's length. We also study the confinement of rods in spherical and cylindrical repulsive shells. This helps elucidate a recent discussion on curvature effects in confined quantum mechanical and polymer systems.