Technology Brazil São Paulo, São Paulo, Thursday, March 22 of 2018, 08:54

Ultra-strong material is produced from a nineteenth-century idea

Researchers in Brazil and US used 3D printing to produce structures with high mechanical strength based on mathematical models created by Karl Schwarz in 1880

AGÊNCIA FAPESP/DICYT - In 1880, German mathematician Karl Hermann Amandus Schwarz (1843-1921) conceived of a type of structure with complex geometry in which the surfaces are minimal and periodic (with a regular repeating pattern), and have negative curvature like a saddle.


More than 100 years later, in 1991, Mexican physicist Humberto Terrones and English crystallographer Alan Mackay proposed that including carbon rings with more than six atoms in a hexagonal graphite mesh could give rise to periodic structures with negative curvature, like those imagined by Schwarz and analogous to zeolites, porous three-dimensional minerals.


These spongy crystalline structures, called schwarzites by Terrones and Mackay as a tribute to the German mathematician, could have hundreds of atoms and porous cells, giving rise to foam-like rigid materials with unique characteristics and mechanical and electromagnetic properties. However, they only existed in theory.


Now a group of Brazilian researchers affiliated with the Center for Computational Science and Engineering (CCES), one of the Research, Innovation and Dissemination Centers (RIDCs) funded by the Sao Paulo Research Foundation – FAPESP, in collaboration with colleagues at Rice University in the United States, have found a practical way to create these materials in the real world.


The construction technique they used and the results of the experiments performed to measure compressive and impact strength are described in an article published in the journal Advanced Materials. “We succeeded in producing on the macroscopic scale materials that hitherto existed only on the atomic scale,” said Douglas Galvão, one of the authors of the article and a professor at the University of Campinas’s Gleb Wataghin Physics Institute (IFGW-UNICAMP) in São Paulo State, Brazil.


To obtain the material, the researchers first used computer algorithms to design atomic-scale models of porous structures in two different schwarzite families, primitive and gyroid.


They designed two molecular models of the primitive family, containing 48 and 192 atoms per unit cell, respectively, and two gyroid models, containing 96 and 384 atoms. The structures had minimal periodic surfaces like those originally theorized by Schwarz.


The four molecular structures were then rendered in computer modeling software to generate 3D structures and printed as cubes with faces measuring 3 sq. cm in polymer using a high-resolution 3D printer.


“The idea was to develop an atomic-scale material with exotic properties like schwarzite, build a macroscale model based on it, and produce this structure in the real world using a 3D printer to find out if it maintained those properties, including very high strength,” Galvão said.


Mechanical testing


The researchers measured the compressive and impact strength of both the atomic-scale structures (by simulation) and the models printed as 3D cubes.


The results showed high compressive and impact strength for both the atomic-scale and macroscale structures owing to a unique layered deformation mechanism.


As the load is applied, the holes start closing from the topmost layer and progress non-homogeneously into subsequent layers. As the load increases beyond the plastic region, the structure densifies but does not disintegrate because the pores in the upper layers close first, followed by the pores in subsequent layers.


“This deformation mechanism is similar to that seen in sea shells, which have a mineral matrix made of calcite and a protein layer that absorbs extreme pressure without fracturing because the stress is transferred to other parts of the structure,” Galvão said.


“What’s interesting about the schwarzite structures we created is that they’re made of only one material – the polymer PLA, used in a 3D printer – instead of two, as in sea shells, which combine a mineral matrix with organic material.”


The tests also showed that the schwarzite structures displayed outstanding resilience under mechanical compression. They could be reduced to half their original size before they underwent structural failure (fracture).


The load applied in the tests was transferred to the entire geometry of the structure regardless of which side was compressed, both in simulations with atomic-level structure and in 3D-printed models.


“We were surprised to find that some characteristics of the atomic-scale structure were preserved in the 3D-printed structures,” said Galvão, who studies nanostructures by means of molecular dynamics computer simulations.


The characteristic that most surprised the researchers, however, was impact strength. The material did not break when a structure weighing almost 10 kg was dropped from a height of 1 m.


“We’re now analyzing another schwarzite family with a structure similar to that of diamond. The results are even more impressive. The material couldn’t be broken by the strength-testing equipment available at CNPEM [the National Energy & Materials Research Center]. This high strength is due to the material’s topology,” Galvão said.


Strength and complexity


Some of the possible applications of the schwarzite structures created by the researchers are in ballistic protection, including bulletproof vests, and impact-resistant and high-load-bearing components for buildings, cars and aircraft.


“We don’t know if the polymer would melt locally if used in a bulletproof vest and hit by a bullet. We plan to conduct tests to find out,” Galvão said.


The researchers also plan to refine the surfaces of the structures using higher-resolution 3D printers and to reduce the amount of polymer to make the blocks even lighter. Another idea is to use ceramic and metallic materials on a larger scale, and not only in blocks, in order to build ultra-hard structures.


“We have a recipe now to look in the literature for interesting atomic-scale structures that have never been synthesized owing to their complexity, so as to create macroscale models of them,” Galvão said.


Rice University, headquarters for the United States-based scientists who collaborated in the research, produced a video showing schwarzite structures being made - it can be watched below and at




The Advanced Materials article “Multiscale geometric design principles applied to 3D printed schwarzites” (doi: 10.1002/adma.201704820) by Seyed Mohammad Sajadi, Peter Samora Owuor, Steven Schara, Cristiano F. Woellner, Varlei Rodrigues, Robert Vajtai, Jun Lou, Douglas S. Galvão, Chandra Sekhar Tiwary and Pulickel M. Ajayan can be retrieved from: