Metal–organic frameworks (MOFs) are crystalline materials in which metal ions and organic molecules assemble into structures with built-in cavities. One can think of this as decorating a triply-periodic spatial graph (the net of the crystal) with the molecular building blocks. By varying these components and their arrangements into crystals, specific substances can be captured and stored inside the cavities.
Following pioneering work by Richard Robson, around the turn of the millenium, Omar Yaghi and Susumu Kitagawa developed more flexible and stable MOFs. This year, the Nobel Prize in Chemistry was awarded to these three researchers. MOFs have practical applications, such as harvesting water from desert air, capturing carbon dioxide, storing toxic gases, and catalyzing chemical reactions.
Mathematical models play an important role in understanding MOFs. They allow scientists to separate the effects of the underlying crystallographic net, the specific geometric embedding, and the molecular building blocks on the material’s properties. Models can also describe pore shapes, helping researchers connect structure to function. A group of VU mathematicians consisting of Senja Barthel, Hannah Rocio Santa Cruz Baur, and Riya Dogra develops topological, geometrical, and graph-theoretical methods to study and predict the properties of MOFs.