G. Polles, D. Marenduzzo, E. Orlandini and C. Micheletti
Self-assembling knots of controlled topology by designing the geometry of patchy templates
Nature Communications, 2015, 6 , art. no 6423
Link to online article Link to video demo of self-assembling knots out of 3D-printed templates.

Abstract
The self-assembly of objects with a set of desired properties is a major goal of material science and physics. A particularly challenging problem is that of self-assembling structures with a target topology. Here we show by computer simulation that one may design the geometry of string-like rigid patchy templates to promote their efficient and reproducible self-assembly into a selected repertoire of non-planar closed folds including several knots. In particular, by controlling the template geometry, we can direct the assembly process so as to strongly favour the formation of constructs tied in trefoil or pentafoil, or even of more exotic torus knots. Polydisperse and racemic mixtures of helical fragments of variable composition add further tunability in the topological self-assembly we discovered. Our results should be relevant to the design of new ways to synthesize molecular knots, which may prove, for instance, to be efficient cargo-carriers due to their mechanical stability.