Supramolecular structures with topologically tunable properties: circular polycatenanes and two-dimensional sheets

Supramolecular materials built of topologically interlocked polymer rings have recently gained considerable interest in supramolecular chemistry, biology, and soft matter. Two typical examples are polycatenanes, linear chains of concatenated rings, and the kDNA, a natural occuring, two dimensional surface of linked DNA rings. Here, through the use of extensive simulations, we show how one can exploit the topology of the local interlockings to store twist in circular polycatenanes, significantly altering their physical properties. By defining the twist and writhe of these ring-o-rings, we show that a relation equivalent to the Calugareanu-White-Fuller theorem for dsDNA holds for circular polycatenanes. We then extend our investigation to the case of 2D sheets of rings, showing the existence of a similar effect that leads to different global properties based on the chirality of the local interlockings. Our results suggest that supramolecular objects with storable and tunable twist can form a new category of highly designable structures with potential applications in supramolecular chemistry and material science.