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Physicists Solve Spherical Puzzle




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For nearly a century, scientists have been scratching their heads and reworking theories about a seemingly ho-hum problem: How does nature organize electrons, cells or other particles onto the surface of a sphere? Now a study published today in the journal Science provides experimental evidence that particles organize into a crystalline network punctuated by predictable patterns of cracks and defects. And because many things in nature are spherical in shape, the potential applications of the findings are far reaching: from viral microbiology and chemical engineering to geology.

When you rack billiard balls at the start of a game, the center ball touches exactly six other balls in a packing arrangement known as a triangular lattice, which represents the way uniformly sized crystals, cells or other same-sized particles tend to arrange on a flat surface. For decades, physicists have understood that this pattern cannot wrap seamlessly around a sphere, but they did not know how natural breaks in the network would organize. Some theorized that if the same arrangement of billiard balls were to expand around a beach ball, irregularities in the packing structure would occur such that--instead of touching the standard six balls--some balls would touch only five and others would have a seventh neighbor.

An international team of researchers led by Andreas Bausch of Munich Technical University devised an experiment to test this theory. The scientists first suspended microscopic water droplets in an oily mixture. They then added tiny, perfectly spherical, polystyrene beads and shook the liquid to create a mayonnaise-like emulsion. As the beads diffused through the liquid, the researchers recorded the process using a digital camera attached to a simple microscope. The images showed beads organizing around the water droplets into crystalline networks that fit their theory. According to the report, 12 isolated defects cropped up on spherical surfaces with diameters of about 25 microns or less. But on larger spheres, the flaws in the arrangement tended to group together forming cracks, or so-called scars, in the otherwise tightly packed crystalline shell.


Study co-author Mark Bowick of Syracuse University believes that the same predictable processes will apply to any spherical crystal, as long as it is larger than about 25 microns wide. Applications of this work may enable microbiologists to crack through the armor-like protein casings of viruses and bacteria, geologists to gleam new insights into tectonics, and chemical engineers to design new chemicals. "You could be talking about micron scale or about planets or atmospheres," Bowick says. "I'm sure there are things we haven't yet thought about."

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