Saturday, July 31, 2010

Slides of my talk at Bridges 2010

I just uploaded the slides of my talk to google doc for anyone who is interested in this subject: pdf.

Friday, July 23, 2010

Wednesday, July 14, 2010

Structural rules of high-genus fullerenes

Some people asked me about the pattern for making a high-genus fullerene. It is quite difficult to explain. Previously, I have posted two series pictures for creating two types of high-genus fullerenes: one consisting of octagon necks and the other for pentagon necks. They should be clear enough for anyone who try to create one.

If you want to create high-genus fullerenes in addition to these two HG-fullerenes. You have to follow more general structural rules. C. Chuang has worked out very general structural rules for constructing high-genus fullerenes belonging to tetrahedral, octahedral and icosahedral groups last year. The details have been described in this paper:

1. "Systematics of High-Genus Fullerenes." J. Chem. Inf. Model. 2009, 49, 1664-1668. DOI: 10.1021/ci9001124, ACS News & Research, July 2009.

Interestingly, this paper on the classification of High-Genus fullerenes has appeared in the "News & Research" session of ACS homepage in July 2009.

Tuesday, July 13, 2010

Two articles on the beaded molecules

I have written an article in English for the beaded molecules. In the paper, I describe in details the connection between bead models and fullerenes. But only structures without holes, i.e. genus=0, are discussed in this paper. I submitted this paper to J. Chem. Edu. two years ago. Unfortunately some reviewers do not seem to appreciate that the advantage and flexibility of using beads to represent microscopic structures of fullerenes. One of the reviewers said that he got totally confused when I said that spherical beads represent chemcal bonds, instead of atoms. Another reviewer doubted the pedagogical value of this approach. So, I was asked by the editor to make major revision for this paper. I didn't do it and submitted this paper to the J. Chin. Chem. Soc. instead.

Here is the paper:

1. Jin, B.-Y.*; Chuang, C.; Tsoo, C.-C. "Construction of Physical Models for Arbitrary Fullerenes with Beads: Realization of Tangent-Sphere Model" J. Chin. Chem. Soc. 2010, 57, 316-324.

A similar paper in Chinese has also been published two years ago:

2. 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 am thinking about writing two more papers on tubular (toroidal structures, helical structures, and toroidal knots) and high-genus structures (periodic minimal surfaces, extended structures, high-genus fullerenes), respectively, later this year.

Wonder How To

WonderHowTo site has said something about us: Mathematical Beading: Accessories to Thought.

Carnival of Mathematics #67

My site has been mentioned in Carnival of Mathematics #67.

Another set of beaded T240

Chuang and I are particularly interested in toroidal shape of graphitical structures or carbon donuts. Systematic structural rules of this type of molecules have been worked out by us. The details were presented in these two articles:

1. "Generalized Classification Scheme of Toroidal and Helical Carbon Nanotubes." J. Chem. Inf. Model. 2009, 49, 361-368.

2. "Dual Space Approach to the Classification of Toroidal Carbon Nanotubes." J. Chem. Inf. Model. 2009, 49, 1679-1686.

We have made many bead models for carbon donuts. Here are a few models for isomers of TCNT (Toroidal carbon nanotube) with 240 carbon atoms. Since beads stand for carbon-carbon bonds (edge of the graph), one need 360 beads to create one such structure. The basic construction procedure is basically the same for all TCNTs. The difference is where and when to put a heptagons and pentagons for a particular TCNT.

(Constructed by Chuang)