Workshop at Taichung

I gave a one-day workshop on the beaded molecules for some junior high school students this summer (7/2-7/3/2009) at Taichung, Taiwan. Here is a picture about the workshop.



In the morning, after a brief introduction on the chemical bonding and a few simple molecular structures, I then started to teach student the platonic solids and basic weaving techniques by asking them to make a C20 (a dodecahedron). I simply asked students follow my instructions step by step without too much explanation. This is because, I think, it is important to have some hands on experience for constructing beaded fullerenes first. Some students can get the basic rules of weaving just after a few steps, others may take a longer time and kept asking me how to do the next step. But it took about an hour for all students to get the first project done. I also found that it is better to use larger beads around 10mm to 12 mm for students who have no experience in beading. To create a C20, one need 30 beads. So it is not too expensive even for a group of 50 students.

The next project in the afternoon was to construct a C60. Of course, before we started to do that, I explain the icosahedron, truncated icosahedron and a few background information on fullerenes to them. Unlike C20, where all atoms and bonds are equivalent, here we have two different bond types, 5-6 and 6-6 bonds, so it is natural to use two different color of beads for the construction. In fact, this is not a burden for weaving. Instead, color of beads can be used as a mnemonic aid for denoting the place of pentagons. One needs 90 beads to represent chemical bonds in a C60. Since students have some experience in the morning for making a C20, I find it convenient and more cost effective to use 6mm beads with two different colors for students to work on in this project. It took about 2 hours for most of students to construct his or her C60.


The picture shown below is the C60 I made in this workshop. At the end, I gave it to one of students in this workshop as a souvenir.

New P-Type surface

I created a new P-surface with eight unit cells (2x2x2) using white and red beads last weekend. In total, 2880 beads are used. (Note that 90 beads are needed to create a C60.) Unlike previous two P-surfaces, I use red beads for octagons this time. The weaving process for creating a large beaded structure usually takes a long time and is prone to error.

Since the whole weaving process is essentially serial, the beads have to be added one by one along a single string of thread. So, once an error was made in the past, it is difficult to correct it without untieing all the beads up to that point the error was made.

The errors I made are usually something like using 9 beads to create an octagons (3 or 4 times out 128 octagons in the structure) and using 7 beads for hexagon (only 1 times). It is easy to understand why these errors occur more frequently for octagons, since it is more difficult to distinguish octagon and nonagon.

The first P-type structure Chuang and I made together has been given away to Bob Silbey as a gift in the summer of 2008. I made the remaining two P-surfaces by myself.




Silbey's 65 Birthday Symposium. I was in the second row far left.

(photo taken from http://web.mit.edu/newsoffice/2005/silbey.html)

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.