Engineering Rings in Network Materials

Network materials can be crystalline or amorphous solids, or even liquids, where typically directional interactions link the building blocks together, resulting in a physical representation of a mathematical object, called a graph or equivalently a network. Rings, which correspond to a cyclic path in the underlying network, consisting of a sequence of vertices and edges, are medium-range structural motifs in the physical space. This Perspective presents an overview of recent studies, which showcase the importance of rings in the emergence of crystalline order as well as in phase transitions between two liquid phases for certain network materials, comprised of colloidal or molecular building blocks. These studies demonstrate how the selection of ring sizes can be exploited for programming self-assembly of colloidal open crystals with an underlying network and elucidate rings as a vehicle for entanglement that distinguishes the two liquid phases of different densities involved in liquid–liquid phase transitions of network liquids with local tetrahedral order. In this context, an outlook is presented for engineering rings in network materials composed of colloidal and molecular building blocks, with implications also for metal-organic frameworks, which have been extensively studied as porous crystals, but, more recently, as network-forming liquids and glasses as well.