PROVIDENCE, R.I. [Brown University] -- 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.
"The issue is that one runs into a combinatorial explosion," said Govind Menon, associate professor of applied mathematics at Brown University. "How do we search efficiently for the best solution within such a large dataset? This is where math can contribute to the problem."
In a paper published in the Proceedings of National Academy of Sciences, 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.
"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 ass
|Contact: Richard Lewis|