Helically coiled carbon nanotube derived from T140

I made one more HCCNT that was derived from parent torus, T140.

The inner part should be weaved first. Here I keep the relative position of these heptagons unchanged.

The next step is to determine the HSP (Horizontal Shift Parameter) on the outer part of the torus. The pitch of the HCCNT will depend on the magnitude of HSP. For detail, check the papers mentioned in previous post.

Helically coiled carbon nanotube derived from torus 120

I made another HCCNT (Helically coiled carbon nanotube) derived from the parent molecule, carbon nanotorus with 120 carbon atoms yesterday.

The construction of this carbon helix is quite straightforward. First we should know that this structure can be decomposed into six strips. To simplify the weaving process, one should start from the inner part of HCCNT.

To make a helical tube, one still need to finish the remaining two strips. Particularly, we need to be careful about the relative position between two neighbored pentagons. The systematic way to generate a whole family of HCCNTs from a parent TCNT is based on the concept of horizontal shift parameters (HSP). By applying a suitable HSP, one can create a whole family of HCCNTs.
The details of structural rules of HCCNTs can be found in the following three papers we published:

Chuang, C.; Fan, Y.-C.; Jin, B.-Y.* Generalized Classification of Toroidal and Helical Carbon Nanotubes J. Chem. Info. Model. 2009, 49, 361-368.
Chuang, C; Jin, B.-Y.* Hypothetical toroidal, cylindrical, helical analogs of C60 J. Mol. Graph. Model. 2009, 28, 220-225.
Chuang, C.; Fan, Y.-C.; Jin, B.-Y. On the Possible Geometries of Helically Coiled Carbon Nanotubes J. Mol. Struct. 2012, 1008, 1-7.


In fact, Chern made a bead model of the same structure a few years ago. But in the Bridges conference held in Pecs, Hungary, I met Laura Shea and gave that model to her as a souvenir. Since then, both Chern and I didn't make any new model of helically coiled carbon nanotubes.

D surface constructed from four helical strips

There is another way to build a D-type triply periodic minimal surface (TPMS) with beads. Chern has told me previously that one can not only use helical strips to build G-type TPMS, one can also use exactly the same helical strips to build D-type TPMS. If one examine two helical strips carefully, one can find that there are exactly two different ways to put them together. One gives a D-type TPMS, the other one gives a G-type surface!

The following pictures are a bead model of D-surface consisting of four helical strips. Two of them are left handed, the other two are right handed. To build a D-surface, one has to put two helical strips together in an arrangement such that two neighbored strips are mirror-symmetric to each other. So the overall structure of D-surface is not chiral.

It is useful to look at other posts with the keyword helical strip, especially the one on the G-surface created by patching two helical strips with one strip shifted by half pitch.

A single helical strip

As I discussed in the previous posts, following Chern's construction scheme, I used 16 helical strips to build the overall 2x2x2 gyroical graphitic structure. Each strip contains 8 eight-bead loops, four with blue color and four with purple color as shown in the following photos.



It is interesting note that one can easily create a kink in this helical strip on purpose. A kink in a helix changes the handedness from left to right.

Two unit cells of gyroidal graphitic surface (2x1x1)

I found that it is still difficult to identify unambiguously the boundary of gyroidal graphitic structure (GGS) if I don't pay attention to each unit cell carefully from the beginning. So I decided to use the original strategy Chern used to build this structure with helical strips. The photos below show a structure consisting of two unit cells.




In the following photo, I show part of the gyroidal structure that contains only two helical strips. It is interesting to note that one helical strip is right handed and the other one is left handed. But this two-strip unit is still chiral because one of these two strips has to be shifted a half pitch w.r.t. the other strip in order to join them together.