Materials comprising porous structures, often in the form of interconnected concave cavities, are typically assembled from convex molecular building blocks. The use of nanoparticles with a characteristic nonconvex shape provides a promising strategy to create new porous materials, an approach that has been recently used with cagelike molecules to form remarkable liquids with "scrabbled" porous cavities. Nonconvex mesogenic building blocks can be engineered to form unique self-assembled open structures with tunable porosity and long-range order that is intermediate between that of isotropic liquids and of crystalline solids. Here we propose the design of highly open liquid-crystalline structures from rigid nanorings with ellipsoidal and polygonal geometry. By exploiting the entropic ordering characteristics of athermal colloidal particles, we demonstrate that high-symmetry nonconvex rings with large internal cavities interlock within a 2D layered structure leading to the formation of distinctive liquid-crystalline smectic phases. We show that these smectic phases possess uniquely high free volumes of up to ∼ 95%, a value significantly larger than the 50% that is typically achievable with smectic phases formed by more conventional convex rod-or disklike mesogenic particles.nanorings | porous liquid crystals | self-assembly S elf-assembly of particles ranging in size from the nanometer to the micrometer scales can be used to fabricate structures in the mesoscale regime (1-5), otherwise difficult to achieve with traditional methods of chemical synthesis. Strategies to produce functional materials from the self-assembly of relatively simple nonspherical (anisotropic) building blocks have undergone unprecedented growth as a result of recent advances in experimental techniques to fashion colloidal and nanoparticles of arbitrary shape and well-defined sizes (6-9). An appealing feature of colloidal particles is that the repulsive and attractive contributions of the interaction between the particles can be modulated by controlling the properties of both the particle surface and the solvent medium to induce different types of forces, including short-range repulsions approaching hard-core (athermal) interactions (10).Colloidal particles are commonly represented using simplified coarse-grained convex geometries including ellipsoids, spherocylinders, polyhedra, and cut spheres (11, 12). The phase behavior of these convex models has been studied extensively by theory and simulation (13,14). Nonconvex (NC) models have received significantly less attention. NC particles offer new possibilities for the fabrication of functional materials as a result of the self-assembly of unique structures driven by interlocking and entanglement (15)(16)(17)(18)(19)(20). As featured in our current paper, NC rings can be packed into exotic highly open (low density) structures. Self-assembled NC framelike arrays are of particular interest due to their unusual optical, electrical, and mechanical properties, as a consequence of the large surface-to-...