![]() ![]() “I started to put them on the symbolic plane,” she said, “and then I realized that I can’t.” By throwing out the mistakes and treating patterns as averages, it reveals a sort of ideal reality that’s normally buried beneath heaps of happenstance.īut when Regős tried to apply this method to Decurtins’ molecular pictures, she quickly ran into trouble. Rather than being an oversimplification, Domokos’ method of calculating averages is insightful, said the mathematician Marjorie Senechal of Smith College, who reviewed the new study. ![]() And on average, it still plots to a point at (3, 6) in the symbolic plane. But messy as it may be, a honeycomb is still, on average, a honeycomb. The second was the average number of polygons surrounding each vertex.īut most natural mosaics, from rock cracks to molecular monolayers, are not perfectly periodic tessellations.įor example, the cells of a real wax honeycomb are not all perfect hexagons. The first was the average number of vertices, or corners, per polygon. Then, following Domokos’ approach, she calculated two numbers for each pattern. To get started, Regős treated the 2D materials as simple polygonal tessellations - patterns that fit together with no gaps and infinitely repeat. Domokos wanted to see if Regős could use the geometry that he had originally developed to describe geological fractures to characterize the patterns in Decurtins’ images. Decurtins had sent a handful of images depicting patterns at an atomic scale - tilings of a molecule that had been designed and synthesized by his colleague Shi-Xia Liu - viewed through the eye of a powerful microscope. ![]() And this is very relaxing.” From Planets to AtomsĪfter Decurtins got in touch, Domokos tried to sell the idea to Krisztina Regős, his graduate student. And now they are just looking at formulas. “They were doing artificial intelligence, supercomputing and all this kind of jazz. “At first, they did not believe that you can do it,” Domokos said. Over the next year, Domokos and his colleagues used geometric thinking to unpack the rules of molecular self-assembly - devising a new way to constrain the mosaics that molecules can form, using only the simple geometry of tessellation. Decurtins wondered if the same geometry that describes how planets fracture could explain how molecules assemble. So Decurtins got in touch with Gábor Domokos, the study’s first author, a mathematician at the Budapest University of Technology and Economics. Forecasting self-assembly is a job for supercomputers, and the heavyweight programs required can take days or weeks to run. That’s because nature has not been especially forthcoming with her molecular design philosophy. Predicting how molecules self-assemble into 2D sheets is one of the grand challenges of materials science, said Johannes Barth, a physicist at the Technical University of Munich. So many scientists, including Decurtins and his colleagues, want to design materials that assemble themselves. It’s possible to build these 2D materials atom by atom, but doing so is expensive, difficult and time-consuming. And patterns that contain metal ions can be powerful catalysts. ![]() These 2D materials can have peculiar and practical properties that depend on how their molecular building blocks are arranged.įor example, it’s possible to arrange molecules into 2D patterns that use electrons as computational bits or to store data. “It’s just a matter of scale.”ĭecurtins’ patterns weren’t formed by cracks in the earth, but by molecules: they were mosaic-like tilings of molecules in sheets just one molecule thick. Decurtins, a chemist at the University of Bern, was reminded of the materials he had been studying. It wasn’t the unusual title that caught his eye, but the pictures on the third page - geological patterns at every scale from cracked permafrost to Earth’s tectonic plates. On a Saturday afternoon in the fall of 2021, Silvio Decurtins was leafing through a paper with a title that could have been pulled from a comic book for mathematically inclined teens: “Plato’s Cube and the Natural Geometry of Fragmentation.” ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |