A few bead models of T120s

Here are the bead models of toroidal carbon nanotubes consisting of 120 carbon atoms students made in the second morning of this activity.

Summer camp 2011

I offered a summer camp (繽紛多彩石墨烯─結構與模型, Amazing graphitic structures or here) on creating structures and models of graphitic materials using a number of different techniques for high-school students in Taichung these few days (7/5-7/7).
Three different techniques we used in this mini-workshop are the mathematical beading (one and half days), modular origami based on PHiZZ units (half day) and zometool (half day).

1. 7/5 morning: Students learned the structures of Platonic solids and created bead models of tetrahedron, cube, dodecahedron (C20), and C24. I found that it is very useful to construct these simple trivalent Platonic solids first using beads with rod-like shape. With this, students can become familiar with the basic technique of right-angle weave.
2. The projects for the 7/5 afternoon is to construct bead models of C60 and C80. Most students can finish these projects in three hours.
3. 7/6 morning: Chern spent an hour to explain the molecular structures with jmol (a powerful program for visualizing any kind of molecular structure) first. Particularly, we use C60, T120 and so on as examples. In the next two hours, students started to make bead model of T120. All students succeeded in making their own beaded T120.
4. 7/6 afternoon: We switched to modular origami using PHiZZ units. The only project for this part is to make a dodecahedron.
5. We planned to build a giant concentered multilayer carbon onion consisting of 6 layer of icosahedral fullerenes using the Zometool tomorrow morning (7/7).



Participants:
1. TAs: Chern Chuang, Yuan-Chia Fan and Qian-Rui Huang.
2. twelve students from Taipei (2), Taichung (5), Changhua (4), and Tainan (1)..

Here are a few photos from the camp.






Two T120s that were constructed by students:

HuangShan (Mountain Huang, or Yellow Mountain)

A few pictures I took on mountain Huang (黃山) in An-Hui province after a meeting on quantum chemistry held in He-Fei last week. Mountain Huang is arguably the most beautiful mountain in China and has often been the subject of Chinese paintings and poems.




On the top of the mountain, 光明頂(GuangMingDing), I found this geodesic dome. One can easily tell this is the C180 with Goldberg vector (3,0).

A new trefoil knot

Here is a new trefoil knot by Chern. Unlike the previous trefoil knot, this new construction has much less strain and distortion. In this sense, the corresponding fullerene structure should be more stable.

(I gave this model to Prof. Qian-Er Zhang 張乾二 in Xian last August. Feb. 4, 2013)

Structural types of TCNTs

A few weeks ago, I was informed by my colleague about a paper by Beuerle et al.[1], in which they identified eight structural types of high-symmetry achiral toroidal carbon nanotubes (TCNTs) based on two of our papers in J. Chem. Inf. Model.[2,3]
These eight structural types of TCNTs are

A. Type I, Parallel Prism; outer-rim: zigzag, inner-rim: zigzag: T240, another example, detailed construction
B. Type I, Parallel Prism; outer-rim: armchair; inner-rim: armchair: Two more models
C. Type III, Parallel anti-Prism; outer-rim: zigzag; inner-rim: zigzag: T120, Another T120, T240, T240
D. Type III, Parallel anti-Prism; outer-rim: armchair; inner-rim: armchair: T140, model 2
E. Type II, Anti-parallel Prism; outer-rim: zigzag; inner-rim: armchair: T250,
F. Type II, Anti-parallel Prism; outer-rim: armchair; inner-rim: zigzag: T240
G. Type IV, anti-Parallel anti-Prism; outer-rim: zigzag; inner-rim: armchair T240, T360
H. Type IV, anti-Parallel anti-Prism; outer-rim: armchair; inner-rim: zigzag: T240, T240, detailed construction

Here, we used zigzag and armchair patterns along lattitude coordinates, instead of using chiral vectors, (1,0) and (1,1). We have all these eight structural types in our first paper without giving them names though. In addition to these TCNTs with well-defined latitudes, we also included some high-symmetry TCNTs without latitudes (not in these eight types) in our papers. They seem to ignore them. Here is an example of TCNT (with the detailed construction) that does not belong to these eight structural types. Chuang and I are working on a comment to clarify these three extra types of TCNTs and the correct relationship (transformations) among these 11 types of TCNTs.


1. F. Beuerle, C. Herrmann, A. C. Whalley, C. Valente, A. Gamburd, M. A. Ratner, J. F. Stoddart, Optical and Vibrational Properties of Toroidal Carbon Nanotubes. Chem. Eur. J. 2011, 17, 3868-3875. See also Hot topic on carbon from Wiley-VCH.


2. C. Chuang, Y.-C Fan, B.-Y Jin, "Generalized Classification Scheme of Toroidal and Helical Carbon Nanotubes." J. Chem. Inf. Model. 2009, 49, 361-368.
pdf

3. C. Chuang, Y.-C Fan, B.-Y Jin, "Dual Space Approach to the Classification of Toroidal Carbon Nanotubes." J. Chem. Inf. Model. 2009, 49, 1679-1686.
pdf

Ponytail holder

Children's day (兒童節) is celebrated today (4 April) in Taiwan. My niece made a ponytail holder with two buckyballs.