A family of new and novel molecules for mechanically superior two-dimensional (2D) polymers is described herein. By combining stiff carbon-containing cyclic polymer nodal units with more compliant linear polymer bridge units in an ordered, 2D repeating molecular structure it is possible to tailor the mechanical properties of 2D polymers and their assemblies to provide high stiffness, strength, and toughness. Furthermore, the inherent dimensionality of 2D polymers and their ability to be stacked into ordered and chemically interactive ensembles gives them inherent benefits in a variety of barrier and structural applications over current stiff and strong linear polymer technologies.