How did you get interested in this research project?

The initial seed was the beautiful report by Davide Proserpio and colleagues of a novel molecular crystal framework with the topology of diamond, but a distinct threading of edges to that found in conventional diamond (L. Carlucci, G. Ciani and D. M. Proserpio, CrystEngComm., 2003, 5, 269). That work posed the irresistible challenge: how can these structures be distinguished? And what other possibilities for knottings of infinite nets are there? That led to a preliminary analysis of a simpler problem: knotted cube edge graphs. We have since explored simplest knottings of other polyhedral graphs via reticulations of the torus. That work threw up a question that occupied us for many (long) lunch-times: are all "simple" tangled graphs chiral? The answer is likely yes, provided "simple" tangled graphs contain knots or links. What seemed at first to be trivially correct resisted any proof. Then we found these strangely tangled cases, which proved our intuition wrong. So a materials chemistry report led to a theoretical analysis of entanglement, that will-we hope-in turn stimulate some real chemistry!

Figure 1.A simple knot (left) and a simple ravel (right). 

What is the most important result in the paper? 

The key underlying message in the paper is that nets can be tangled without containing any knots or links. 

What are the implications of the results you present in this paper? 

A lot of beautiful science has been based on looking at knotting at the molecular and macromolecular scales, such as polymer diffusion, topological chirality, braids and knots in DNA-protein complexes, etc. It is clear that we also need to look at other modes of entanglement beyond knotting. 

Are there any particular challenges facing future research in this area? 

The work so far is purely theoretical. In that domain, much remains to be done to classify ravels more fully. Two directions of experimental study emerge from the work: a search for ravelled structures in synthetic and natural materials and the synthesis of ravelled molecules. 

Reference 

"Ravels: Knot-free but not free. Novel entanglements of graphs in 3-space" by Toen Castle, Myfanwy E. Evans, Stephen T. Hyde, New J. Chem., 2008, 32, DOI: 10.1039/b719665b