Beaded model of Carbon Nanotube Trefoil Knot

Trefoil knot is one of the most beautiful geometric shapes that intrigue both mathematicians and artists alike. Previously Chuang and I have shown that one can in fact tile on trefoil knot with graphitic sheet. By introducing non-hexagons on the suitable position, the resulting carbon nanotube trefoil knots can be very stable.

The problem is whether we can really build a beaded model for this new family of carbon compounds. Previously, we have tried to create a beaded model for CNTTK by weaving the girth first and then the axial direction of the tubule. Based on this strategy, we realize that the intrinsic curvature introduced by the non-hexagons is too large, so it seems that the construction of trefoil knot with beads is not possible unless large deformation is applied.

Last weekend, Chuang gave me a figure of CNTTK 504 with only one strip of polyacene is shown (see previous post). This suggested that one may weave along the axial direction first. So construction of a beaded CNTTK 504 amounts to weaving 6 strips of polyacenes. Using this weaving algorithm, one may be able to adjust the intermediate structures more easily since they are more flexible. The extra deformation that has to be introduced can then be distributed more evenly over a larger area. This is quite different from the previous weaving algorithm we adopted. The extra deformation created in the previous method is concentrated on particular segment of the tubule. The final structure may look quite distorted. Thus, the new algorithm has better potential for making a CNTTK.

This is indeed the case. I finally made one beaded CNTTK 504. The resulting beaded structure as shown in the following figure looks great. The overall shape of this structure looks quite similar to the optimized structure we obtained before. With closer inspection, we can also see the distortion away from the intrinsic curvatures created with non-hexagons.