Monday, February 4, 2013

Carbon star and other clover-shaped carbon nanotori

I recently saw a post on the clover-shaped carbon tori by my facebook friend, Tetsuaki Hirata, who is an artist from Himi, Japan and seems to be a frequent visitor of this blog. After I showed Chern about his works, Chern told me he has thought about this kind of clover-shaped carbon nanotori quite some times ago. Indeed, Chern has published a number of papers on the tubular graphitic structures. He is probably one of few people who know a lot about this kind of graphitic structures, especially on how the nonhexagons could influence the structures of a carbon nanotube. I am not surprised that he thought about this kind of structures.

1. Chuang, C.; Fan, Y.-C.; Jin, B.-Y.* Generalized Classification of Toroidal and Helical Carbon Nanotubes J. Chem. Info. Model. 2009, 49, 361-368.
2. Chuang, C; Fan, Y.-C.; Jin, B.-Y.* Dual Space Approach to the Classification of Toroidal Carbon Nanotubes J. Chem. Info. Model. 2009, 49, 1679-1686.
3. Chuang, C; Jin, B.-Y.* Hypothetical toroidal, cylindrical, helical analogs of C60 J. Mol. Graph. Model. 2009, 28, 220-225.
4. Chuang, C.; Fan, Y.-C.; Jin, B.-Y.* On the structural rules of helically coiled carbon nanotubes, J. Mol. Struct. 2012 1008, 1-7.
5. Chuang, C.; Fan, Y.-J.; Jin, B.-Y. Comments on structural types of toroidal carbon nanotubes, arXiv:1212.4567, 2013 submitted to J. Chin. Chem. Soc.

In the first two and the 5th papers, we talked about general structural rules of carbon nanotori and only touched helices briefly. In the next two papers, we discussed very generally how the horizontal and vertical shifts (HS and VS) can be exploited to change the direction of a straight carbon nanotube in order to obtain an arbitrary helically coiled carbon nanotubes. In Chern's Ms thesis, he also showed how to take advantage of HS and VS to create trefoil knots or torus knots in general, which was later summarized in a brief review we wrote, "Systematics of Toroidal, Helically-Coiled Carbon Nanotubes, High-Genus Fullerenes, and Other Exotic Graphitic Materials."  (Procedia Engineering, 2011, 14,  2373-2385).

Clover-shaped TCNTs are just a special class of more general curved carbon nanotubes we considered. A simple strategy is to introduce 180 twists along the tube direction (i.e. 180 degree VS) at suitable positions. I got a few nice figures of clover-shaped TCNTs from Chern the other days.
Among all these clover-shaped tori, I particularly like the five-fold carbon star.


Cindy Holsclaw said...

Those are cool! I agree that the star is particularly interesting.

Emilie said...

I'm wondering-- the star you show is 5 pointed, as are lots of your torus shapes. But it seems to me that the figure "wants" to be 6 sided, as you're basically working with 60 degree angles. I know beadwork, but not the chemistry of carbon. Is there something related to carbon that leads to using 5 point symmetry instead of 6 point?

Emilie said...

Actually, I meant they're 120 degree angles.

Bih-Yaw Jin said...

In principle, you can have 6 pointed star too. Chemists call this n-fold rotational symmetry. I am kind of lazy, so usually I stop at 5 fold rotational symmetry. At beginning, I want to stop at 3-fold and then decided I should keep going until it becomes a 5-pointed star. I am glad I did it.

But you can also find one or two tori with 6-fold rotational symmetry. In Chuang's thesis, he investigated the stability of TCNT with different rotational symmetry. The results he got is that carbon nanotori with n=5, 6, 7 are usually more stable than other rotational numbers. But the most stable number also depends on some other details.

Chuang Chern said...

As pointed out by Bih-Yaw, chemically speaking, the stability dependence of these molecules (if they exist) on the rotational symmetry number varies according to other specific details. In addition, there're still some intriguing differences between the microscopic forcefields and that of between beads in the macroscopic world. The dependence is even related to the methodology one uses to construct the bead structure, e.g. with fish line or elastic string (as Mr. Horibe does).