Here’s an intriguing approach to self-assembly for manufacturing purposes from scientists at Brown and Johns Hopkins Universities, respectively. From the Dec. 7, 2011 news item on Nanowerk,

In a paper published in the Proceedings of National Academy of Sciences (“Algorithmic design of self-folding polyhedra”), researchers from Brown and Johns Hopkins University determined the best 2-D arrangements, called planar nets, to create self-folding polyhedra with dimensions of a few hundred microns, the size of a small dust particle. The strength of the analysis lies in the combination of theory and experiment. The team at Brown devised algorithms to cut through the myriad possibilities and identify the best planar nets to yield the self-folding 3-D structures. Researchers at Johns Hopkins then confirmed the nets’ design principles with experiments.

Here’s the magnitude of the problem these scientists were solving (from the news item),

Material chemists and engineers would love to figure out how to create self-assembling shells, containers or structures that could be used as tiny drug-carrying containers or to build 3-D sensors and electronic devices.

There have been some successes with simple 3-D shapes such as cubes, but the list of possible starting points that could yield the ideal self-assembly for more complex geometric configurations gets long fast. For example, while there are 11 2-D arrangements for a cube, there are 43,380 for a dodecahedron (12 equal pentagonal faces). Creating a truncated octahedron (14 total faces – six squares and eight hexagons) has 2.3 million possibilities.

Associate professor of applied mathematics at Brown University, Govind Menon, says (from the news item),

“The issue is that one runs into a combinatorial explosion. … How do we search efficiently for the best solution within such a large dataset? This is where math can contribute to the problem.”

Here’s how they solved the problem (from the news item),

 

“Using a combination of theory and experiments, we uncovered design principles for optimum nets which self-assemble with high yields,” said David Gracias, associate professor in of chemical and biomolecular engineering at Johns Hopkins and a co-corresponding author on the paper.

“In doing so, we uncovered striking geometric analogies between natural assembly of proteins and viruses and these polyhedra, which could provide insight into naturally occurring self-assembling processes and is a step toward the development of self-assembly as a viable manufacturing paradigm.”

“This is about creating basic tools in nanotechnology,” said Menon, co-corresponding author on the paper. “It’s important to explore what shapes you can build. The bigger your toolbox, the better off you are.” While the approach has been used elsewhere to create smaller particles at the nanoscale, the researchers at Brown and Johns Hopkins used larger sizes to better understand the principles that govern self-folding polyhedra.

The news item on Nanowerk features more details, a video of a self-assembling dodecahedron, and an image of various options for 2-D nets that can be used to create 3-D shapes.