A few bead models of diamondoid molecules

Mathematical beading can be used to construct any diamondoid molecule, also known as nanodiamonds or condensed adamantanes. Here, I show three such molecular systems:

Adamantane (C₁₀H₁₆);
Diamantane (C₁₄H₂₀) also diadamantane, two face-fused cages;
One of 9 isomers of Pentamantane with chemical formula C₂₆H₃₂.

Ping-Pong Valence Sphere Model

Valence sphere models, a qualitative chemical bond model that includes the influence of the electron pair repulsion among valence electron pairs and attraction between positive atomic core and negative electron pairs, can be constructed with Ping-Pong balls easily. Here, I made three pairs of linked ping-pong balls and used them to create a tetrahedral sp³-hybridized AX₄ system and a octahedral d²sp³ hybridized AX₆ system.

Another dodecahedrane

I made one more valence sphere model (VSM) of dodecadrane (C₂₀H₂₀) yesterday. Although this model looks simple compared to other bead models I have made, I still feel satisfied every time I made a bead model of this molecule.

Styrofoam ball/rubber band model of ethylene

I posted a bead model of ethylene made by Qing Pang, a high-school student in TFG school. I don't like the way double bond is handled in her model because the channel (hole) orientations of two beads that used to model double bond is perpendicular to the bond orientation. I would prefer to have a bead valence model in which channel of each bead lies exactly along a particular bond. In the sense, to describe a double bond by beads, we need to use the banana bond representation of double bond proposed by Linus Pauling. This also means that, to construct a correct bead valence bond model of a double bond, we have to use a bead with a curved channel with an angle about 71 degree. I don't think one can get commercial beads which have channels with this particular angle.

But to illustrate the idea of banana bond, here I try to make a styrofoam ball/rubber band model of ethylene by carefully puncturing a channel with approximately this angle (see the styrofoam ball in the center). The resulting styrofoam model of ethylene looks just great!

It is straightforward to construct valence sphere model of acetylene with five styrofoam balls. Three of these balls represent triple bond and the remaining two balls represent single C-H bonds. Using the elementary geometry, one can show that the angle of the curved channel for the ball representing triple bond is about 38 degrees.

workshop for ICCE/ECRICE

I had a workshop for joint meeting of the 22nd International Conference on Chemistry Education and the European Conference for Research in Chemical Education yesterday in Rome, Italy. My collaborator and I prepared materials for 40 people. But only around 10 people participated the event.

Before participants to make their bead models in this hands-on workshop, I gave a 30-min introductory talk about what can done with beads and particularly the connection of the bead model to the valence sphere model (VSM). I tried to emphasize that bead model is the best method to realize the VSM for both fullerenes and other molecules with sp3, dsp3 and d2sp3 hybridization.

Prismane

Prismane with 3-, 4-, and 5-fold rotational symmetry:

Bead VSM of cubane

I just made a bead VSM (valence sphere model) of cubane (C₈H₈) by myself. The structure looks neat to me. Every valence electron pair is faithfully represented by a big bead, purple for CC bond and pink for CH bond. Small beads which have no chemical meaning are used to bind the pink beads to the central carbon cube. I didn't distinguish CC bonds from CH bonds. In principle, electron pairs responsible for these two types of chemical bonds should have different momenta. So they should have different sizes of charge clouds.

Advantages of beaded models

Compared with other methods for building physical models of fullerenes, the beaded molecules have many advantages:
1. The hard-sphere interactions among beads correctly mimic the microscopic valence-shell repulsion.

2. The only information needed to build a particular fullerene with a spiral is completely encoded in its spiral code.

3. The resulting shape of a beaded fullerene is in good agreement with the real geometry of the corresponding fullerene.

4. The mechanical response of a beaded molecule is related to that of a true fullerene molecule under pressure.

5. The beaded molecule can be made quite compact by using beads with small diameters. The sizes of the beaded molecules for fullerenes with even several hundreds of carbon atoms are less than 10 cm, which can be held in hand easily; while using the commercial models for the same fullerene, the sizes are typically much larger.

6. The resulting beaded molecules are aesthetically pleasing.

7. The structures of beaded molecules are stable, robust, and durable.