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Century-Old Theory of Schwarzites Bought to Life with 3D Printing

Picture of Bulent Yusuf
by Bulent Yusuf
Nov 17, 2017
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Engineers at Rice University used 3D printers to make theoretical schwarzites into physical structures. Math just got real, people.

Mathletes from Rice University, Houston are using 3D printers to create super special structures that — until now — have only existed in a theory a hundred years old. These porous structures are called Schwarzites, where complex repeating patterns are fabricated from strong, light and durable materials.

Schwarzites are a century-old mathematical theory, made real thanks to 3D printing.

The schwarzites are designed with computer algorithms. The team sends data from the programs to 3D printers to make macroscale, polymer models for testing. Their samples attempt to use as little material as possible while still providing strength and compressibility.

The results have been published in Advanced Materials. These findings could soon lead to nanoscale electronic devices, catalysts, molecular sieves and battery components. Plus, on the macroscale they could become high-load-bearing, impact-resistant components for buildings, cars and aircraft.

Shooting for the moon, the team theorize that it could also one day be possible to fabricate an entire building as one schwarzite “brick”.

Schwarzites are named after the German scientist Hermann Schwarz. He first hypothesized the structures in the 1880s, mathematical marvels that have inspired a large number of organic and inorganic constructs and materials. Such structures remained theoretical until 3D printers provided the first practical way to make them.

3D Printed Schwarzites are Super Strong, Super Light

The Rice lab of materials scientist Pulickel Ajayan, in collaboration with researchers at the University of Campinas, São Paulo, investigated the bottom-up construction of schwarzites through molecular dynamics simulations and then printed those simulations in the shapes of polymer cubes.

“The geometries of these are really complex; everything is curved, the internal surfaces have negative curvature and the morphologies are very interesting,” said Rice postdoctoral researcher Chandra Sekhar Tiwary, who led an earlier study that showed how seashells protect soft bodies from extreme pressure by transferring stress throughout their structures.

“Schwarzite structures are very much the same,” he said. “The theory shows that at the atomic scale, these materials can be very strong. It turns out that making the geometry bigger with polymer gives us a material with a high load-bearing capacity.”

“You can make a whole building out of this material, and if something falls on it, it’s going to collapse slowly, so what’s inside will be protected.”

Schwarzites also displayed excellent deformation characteristics, he said. “The way a material breaks is important,” Tiwary said. “You don’t want things to break catastrophically; you want them to break slowly. These structures are beautiful because if you apply force to one side, they deform slowly, layer by layer.

“You can make a whole building out of this material, and if something falls on it, it’s going to collapse slowly, so what’s inside will be protected,” he said.

The researchers said their next step will be to refine the surfaces with higher-resolution printers and further minimize the amount of polymer to make the blocks even lighter. In the far future, they envision printing 3D schwarzites with ceramic and metallic materials on a grander scale.

“There’s no reason these have to be blocks,” said co-author and Rice graduate student Peter Owuor. “We’re basically making perfect crystals that start with a single cell that we can replicate in all directions.”

Source: Rice University

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