2D periodic Archimedean tiling (Repost)

This is one of the eleven possibilities of Archimedean tilings of neck structures, which I've finished coding lately. Each vertex of the tiling is composed of three equilateral triangles and two squares.







The ms that I am currently working on is titled "Doubly and Triply Periodic Porous Graphitic Structures". I wonder if you have better suggestion to the title. I was first considering doubly and triply periodic quasi-minimal surfaces, since I am not sure that mathematicians would agree that these are minimal surfaces realized as graphitic structures. The paper on high-genus fullerenes that we've just published uses the word "high-genus". Although the periodic structures discussed in this new article are still made of neck structures, they may not be as high-genus as their 0D analogs since the genus value per unit cell is not-so-high.

(By Chuang on byjingroup blog, Tuesday, July 21, 2009)

A beaded model for 2-d periodic tile (Platonic tile) of graphitic structures made by Chuang a few months ago:

An icosahedral HGF (repost)

I finished extending the original code in the appendix of my thesis last night.







This particular HGF has its triangular necks with g=0, i.e. there is no carbon atoms ``at'' the neck, with three decagons per neck. And it contains 1260 carbon atoms. However since I didn't actually patch decagons on the molecule, here is the original Matlab .fig file, which may provide a better look of the molecule.

(By Chuang on byjingroup blog, Sunday, October 18, 2009)

Other uses of beads

Beads are not only useful for constructing complicated 3D structures of fullerenes, they can also be used to illustrate the surface structures and packing of liquid crystals.
I used these tricks for the general chemistry I taught last year.

1. Simply put in some beads to create a monolayer of beads.


2. By inspection, one can see there are several single crystal domains separated by grain boundary. Vacancies can occur sometimes, :-)



3. Multilayer structure can also be created easily by adding more beads. Shuffle the box slightly to make them more compact.



4. Beads with long aspect ratio can be used to model liquid crystalline structures! ;-)

More pictures of my beaded fullerenes

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)