Gyroidal graphitic structure

Gyroidal graphitic structure (GGS) is complicated and confusing. Although Chern has worked out the rules for relative positions among nonhexagons on a graphene sheet with computer already, it is still hard to create a real physical model of this structure with beads. The many GGS bead models I posted in this blog are either incomplete or still containing some mistakes. This includes the bead model of GGS, made by Chern early this year. I believe, this is because only a single color of beads (pink) for octagons is used. So it is hard to distinguish the relative position of octagons.

From the pink model, one can find that these octagons can be classified into three classes. The relative positions of these three types of octagons can be easily identified. So in order to minimize the chance of making mistakes, one should use three different colors for octagons. The photos shown below is the bead model of GGS I made last weekend. Using three different kinds of colors, the relative positions of these octagons are vividly displayed. The hard part I have now is to find a way to terminate this structure.

1. At the beginning: every octagon is surrounded by four other octagons belonging to the other two classes. You may be able to see other local rules for these octagons in this photo. Global rule is more complicated to be described here without a schematic plot.



2. Monkey saddle: Here is an interesting direction to view the GGS. One can see a coronene located right at the position of a monkey saddle. Surrounding a coronene, there are six octagons.


3. View it from x-direction

4. View it from y-direction


The normal of every octagon with the same color is lying along the same coordination axis of the three dimensional Cartesian coordinate system.

Network of perpendicular carbon nanotubes

I am working on a structure consisting of a network of inter-penetrating carbon nanotubes that are perpendicular to each other. Only four unit cells are done currently. Hopefully I can finish the next four unit cells in next few weeks.




This structure is very similar to the one posted in
"Pseudo P-type carbon Schwartzite", except that I inserted a segment of carbon nanotubes in between each two nearest-neighbored junctions. Three mutually perpendicular carbon nanotubes meet at a junction that contains 24 heptagons. Moreover, one can also easily identify eight monkey saddles at each junction.

Two tiny T120 made by Laura Shea

Laura Shea showed me these two beautiful T120 made of tiny crystal beads in the Bridges conference. They are so small. You can really wear these two carbon nanotori as earrings.

Buckyball made of 60 dodecadedra

I made this structure with beads last weekend. Still unfinished. The finished structure should have 60 dodecahedra arranged like a buckball. One has two ways to interpret this structure:
1. If every dodecahedron represents a carbon atom, we have a standard C₆₀.
2. If we still use beads to represent CC bonds, then we have a giant molecule, C₇₅₀. In this molecule, 450 carbon atoms are sp³ hybridized or tetra-valent and 300 atoms are sp² hybridized or trivalent. But I suspect these sp² hybridized carbon atoms are not energetically favorable, so it is better to have hydrogen atoms connected to these sp2-carbons. Then we get C₇₅₀H₃₀₀!



The bead model of this structure (see here) might be first constructed by Emilie. She asked me to comment about this structure in my blog long time ago (I couldn't find the exact location though).

I decided to make one from beads after I saw the same structure made by a toy designer, Dick Esterle, who actually invented this kind of toys, in the Bridges conference last week.