Buckled carbon nanotube

A few months ago, Chuang and I discovered a new type of carbon nanotubes, when we were studying how to generate the helically coiled carbon nantoubes (HCCNTs) from toroidal carbon nanotubes (TCNTs).
In the following picture, I show a beaded model for a unit cell of the BCNT (bulged or buckled CNT) which has the same molecular graph as that of T120, but with different boundary condition.



From this picture, we can see that the trick for making this type of systems is to take the inner-rim (neck) of the TCNT out, and repeat this basic unit, the resulting structure is a BCNT.

Using this trick, we can easily see that there is a one-to-one correspondence between TCNT and BCNT.

Ball of whacks

I bought this ball of whacks in the Smithsonian store at Dullus airport, Wahsington D.C. last month.
This ball is basically a rhombic triacontahedron consisted of 30 magnetic design blocks.

Paper appeared as an item in ACS homepage

My paper with Chuang on the classification of High-Genus fullerenes has appeared in ACS homepage http://portal.acs.org in July as an item in News & Research.

Comments on Sierpinski buckyball

Recently Mark left a comment on the Sierpinski's buckyball we proposed:

mark said...

That is really good and attract the Small sierpiski beaded fullerene.
butFullerenes are a family of carbon allotropes consisting of molecules composed entirely of carbon atoms arranged in the form of hollow spheres, ellipsoids, or tubes.
9/15/2009 1:41 PM

Here is my response:

You are certainly right about fullerenes. There are indeed many possible sp2 based fullerene structures. We have recently published a few papers on the systematics of toroidal CNT, helical CNT and High-Genus fullerenes.

1. Chuang, C.; Fan, Y.-C.; Jin, B.-Y. "Generalized Classification Scheme of Toroidal and Helical Carbon Nanotubes." J. Chem. Inf. 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. Inf. Model. 2009, 49, 1679-1686. DOI: 10.1021/ci900124z
3. Chuang, C.; Jin, B.-Y. "Systematics of High-Genus Fullerenes." J. Chem. Inf. Model. 2009, 49, 1664-1668. DOI: 10.1021/ci9001124, ACS News & Research, June 2009.
4. Chuang, C; Jin, B.-Y. “Hypothetical Toroidal, Cylindrical, Helical Analogs of C60.” Accepted for publication in J. Mol. Graph. Model. 2009. http://dx.doi.org/10.1016/j.jmgm.2009.07.004
5. Jin, B.-Y.; Chuang, C.; Tsoo, C.-C. "The Wonderful World of Beaded Molecules." CHEMISTRY (The Chinese Chemical Society, Taipei) 2008,66, 73-92. (in chinese).

I personally doubt the possible existence of Sierpinski fullerenes. But, mathematically speaking, it is still an interesting generalization. I have never seen any work on this possibility. As far as I know, the most popular ones are Sierpinsky tetrahedron and cube.

To see more discussion on the Sierpinski's buckyball and a simple estimation of its fractal dimension, please check several of my posts in June 2007.

http://thebeadedmolecules.blogspot.com/2007_06_01_archive.html

I still remembered that when I gave a talk on "Chemistry, Geometry and Art: The wonderful world of fullerenes" in the math department of National Taiwan University in the early July of this summer vacation, someone in the audience (an expert in the fractal geometry) was quite intrigued by the Sierpinski's buckyball I shown in one of the slides. He told me that no one has ever investigated the Siepinsky regular and semiregular polyhedra yet. I think it might be interesting if we can do something about it.