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Using magnetic toys as inspiration, researchers tease out structures of self-assembled clusters
Date:1/28/2010

ten than the octahedron.

"The only possible explanation was entropy," says Manoharan. "Most people are familiar with entropy as a measure of 'disorder', but the most useful definition of entropy is simply the number of different ways a bunch of particles can arrange themselves."

Natalie Arkus, a former applied mathematics graduate student who worked with Brenner, Glover Professor of Applied Mathematics and Applied Physics, provided a hint to solving the puzzle, as she discovered a method to calculate all the possible structures that could be formed using geometric magnetic toys (composed of magnetic metal rods and silver ball bearings).

As there are more ways for the complicated tri-tetrahedron structure to form (something that can be directly seen by labeling the toy spheres and counting the ways they can be put together) the shape appears far more frequently than the octahedron. In general, among clusters with the same potential energy, highly symmetric structures are less likely to arise.

The researchers also found that when the number of particles reaches nine or higher, entropy plays another important role.

Because the number of possible structures with nine or more particles is vast, the team focused on what are called non-rigid, or flexible structures. Non-rigidity occurs when a cluster has half-octahedra that share at least one vertex, allowing the cluster to twist without breaking or forming another bond (something also easily seen with the toys).

"Because they can move flexibly, the non-rigid clusters have high vibrational entropy," explains Manohran. "In cases with nine or more particles, symmetric clusters do not appear as often due to rotational entropy. The ability to rotate is useful, as it allows clusters to have extra bonds."

As a general rule, the team found that for all clusters up to 8 particles and a select number of structures with up to 12, the most symmetric structures occurred the l
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Contact: Michael Patrick Rutter
mrutter@seas.harvard.edu
617-496-3815
Harvard University
Source:Eurekalert  

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