Tiling the plane with noncongruent toric focal conic domains

This paper deals with regular arrays of macroscopic defects (focal conic domains) observed when a slab of lamellar phase is sandwiched between two substrates imposing different orientational anchorings. We report, in particular, detailed observations of the texture of a lyotropic lamellar phase in contact with a glass substrate and a lyotropic sponge phase. We consider several models for the defects depending on the material and the substrate parameters. Their energy has a common form, and the main features of the textures are explained in the framework of a simple model where disks of different sizes tile a plane in order to minimize a particular interface energy.