## Monday, May 7, 2007

### Triply-Stranded helix (TEM)

A few years ago, prof. L. P. Hwang discovered an interesting new family of the self-organized triply-stranded helically coiled nanoropes. These nanorope can be roughly classified into to two types according to their pitch angles. For instance, the pitch (p) and diameter (2r) of the type I nanoropes are found to be around 150 nm and 80 nm as shown below:

The width of girth is about 20 nm. It seems that the TEM figure shows many ankles similar to pentagons in the beaded model I posted in the previous blog.

By the way, just as a reminder. I remember when prof. Hwang first saw this TEM picture, he thought this was a nanobraid. He told me about this result. And asked me whether I can give an explanation to this phenomenon or not. Then I took a few hours to learn how to make a braid. After I went home that night and showed my daughter the TEM picture. Asked her what that was. She replied immediately, "That is a braid, of course." I spent some times try to find out a possible mechanism, but without success. Why? That is because the projection of a braid on the cross section of a braid is a lazy eight. Mathematically, this can be generated by a 3D curve with the parametrized form: (sin w t, cos 2 w t, p t). Note that the oscillation frequency along the y-direction is twice of that along x-direction. Why? Why not with the same frequency? If this is the case, we should have a triple-stranded helix. What kind of physical force can generate a lazy eight curve? That is beyond my imagination. Instead, I start to question the original thought of prof. Hwang. It is not hard to find that the TEMs for either a braid and a tripled-stranded helix are very similar. So result of TEM can be interpreted by both structures. Only further experiments can justify which structure is correct. With help from a technician at the TEM laboratory, we knew we can take advantage of the stereo-TEM technique to get TEM pictures at two different angles. Then reconstruct the 3D structure by merging these two pictures. The result supported the triple-stranded helix. Of course, this does not mean that the story is over. It is still an interesting problem to work out a possible mechanism for the growth and stability of this kind of triple-srtanded helices.

Su, C.-J.; Hwang, D. W.; Lin, S.-H.; Jin, B.-Y.*, Hwang, L.-P.* Self-organization of triple-stranded carbon nanoropes Phys. Chem. Comm. 2002, 5, 34. DOI: 10.1039/B110151J and pdf (open access!)