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DIY build-a-particle kit

Self-assemblying polyhedra

By Tushna Commissariat

While the vibrant image above might, at first glance, look like a painter’s colour chart, it actually shows how different categories of polyhedral particles in a fluid would pack together as a solid. The method used to obtain the findings has been developed by Pablo Damasceno and colleagues at the University of Michigan, US, and is based on only two parameters: the shape of the particles and the number of neighbours they have in the fluid phase. What Damasceno and his team have done is run computer simulations to study how 145 different types of polyhedra pack into various structures, based on interactions driven solely by the particle shape, to come up with simple predictive criteria for the final shape that is formed. As a material’s physical properties are intrinsically dependent on its structure, understanding exactly how materials assemble and evolve is essential to designing them. The team’s calculations show that, depending on their initial shape, hard polyhedra will assemble in one of four ways: crystals, plastic crystals, liquid crystals or fully disordered structures. And these all depend only on a ratio based on the particle’s volume and surface area and on the number of neighbouring particles. In the image, the four colours depict the four assembly categories, while the shades indicate subcategories of formation. (Image courtesy of Michael Engel.) The researchers also found some abnormalities and unexpected results, with some polyhedra never assembling into any kind of structure. Take a look at the Science paper here .

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