When low-molecular weight liquid crystals are confined to small cylindrical volumes of porous polymer membranes, the elastic deformation energy and surface boundary effects play an increasing role as the surface-to- volume ratio is increased. For such materials confined to micron-sized volumes the free energy associated with the surface competes with the elastic deformation part of the free energy to determine the molecular organization or director configuration within the volume. An additional contribution to the free energy occurs when external fields are applied to such a system.