Weaire-Phelan structure

The Weaire-Phelan structure is a complex 3-dimensional structure. In 1993, Denis Weaire and Robert Phelan, two physicists based at Trinity College Dublin found that in computer simulations of foam, this structure was a better solution of the Kelvin problem than a foam of truncated octahedra.^[1]

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  In 1887, Lord Kelvin asked how space could be partitioned into cells of equal volume with the least area of surface between them, i.e., what was the most efficient soap bubble foam?^[2] He proposed a 14-sided space-filling polyhedron (a tetrakaidecahedron) with 6 square sides and 8 hexagonal sides (or truncated octahedron) with slightly curved faces because of Plateau's laws which govern the structures of foams. The Kelvin structure was believed to be the optimal solution for more than 100 years.

The Weaire-Phelan structure uses two kinds of cells of equal volume; an irregular pentagonal dodecahedron and a tetrakaidecahedron with 2 hexagons and 12 pentagons, again with slightly curved faces. The surface area is 0.3% less than the Kelvin structure, quite a large difference in this context. It has not been proved that the Weaire-Phelan structure is optimal, but it is generally believed to be likely.

A related chemical structure

A closely related structure may be obtained by flattening the faces and straightening the edges. This is also often, though slightly incorrectly, referred to as the Weaire-Phelan structure. It is found as a crystal structure in chemistry where it is usually known as the 'Type I clathrate structure'. Gas hydrates formed by methane, propane and carbon dioxide at low temperatures have a structure in which water molecules lie at the nodes of the Weaire-Phelan structure and are hydrogen bonded together, and the larger gas molecules are trapped in the polyhedral cages. Some alkali metal silicides and germanides also form this structure (Si/Ge at nodes, alkali metals in cages), as does the silica mineral melanophlogite (silicon at nodes, linked by oxygen along edges). Melanophlogite is a metastable form of SiO₂ that is stabilized in this structure because of gas molecules trapped in the cages. The International Zeolite Association uses the symbol MEP to indicate the framework topology of melanophlogite.

The Weaire-Phelan structure is the inspiration for the design of the aquatic centre for the 2008 Olympics in Beijing in China.

See also

• Minimal surface
• Soap bubble
• Beijing National Aquatics Centre

References

1. ^ Weaire D and Phelan R, "A counterexample to Kelvin's conjecture on minimal surfaces", Phil. Mag. Lett. 69, 107-110 (1994)
2. ^ On the Division of Space with Minimum Partitional Area, By Lord Kelvin (Sir William Thomson),Philosophical Magazine, Vol. 24, No. 151, p. 503 (1887)