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 non-convex shape provide a promising strategy to create new porous materials, an approach that has been recently employed with cage-like molecules to form remarkable liquids with “scrabbled” porous cavities [Giri, N. et al. (2015) Nature 527:216]. 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 unique classes of geometry. By exploiting the entropic ordering characteristics of athermal colloidal particles [Allen, M. P., Evans, G. T., Frenkel, D., Mulder, B. (1993) Adv. Chem. Phys.86:1], we demonstrate that high-symmetry nonconvex rings with large internal cavities interlock within a two-dimensional layered structure leading to the formation of distinctive liquid-crystalline smectic phases. We show that these novel 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 rodor disc-like mesogenic particles.