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From Pure Mathematics to Functional Materials: The case of Schwarzites

In 1880 the German mathematician Karls Schwarz proposed a serie of structures with negative Gaussian curvatures (triply periodic minimal surfaces (TPMS)). More than a hundred years later, Mackay and Terrones [1] proposed new carbon crystalline structures containing rings with more than six atoms, which produce positive and negative curvatures. These structures were known as Shwarzites. These structures are predicted to present exceptional electronic and mechanical properties, with many potential technological applications. However, there are indirect experimental evidences for their existence [3]. We proposed a different approach [3] to study these structures building macroscale structural models from atomic scale ones that can be 3D printed. Interestingly, some properties observed at nanoscale (such 50% compression without fracture and high resistance to ballistic impacts) are also present at macroscale. They also exhibit a unique layer-by-layer deformation mechanism. Our proposed approach is completely general and opens new perspectives in materials science for structures that have been proven to be impossible or very difficult to be synthesised. We will also discuss some modelling cases of Archimedean-like structures [4] and relationship between prime numbers and cicagas [5].

[1] A. L. Mackay, H. Terrones, Nature 1991, v352, 762.

[2] R. S. Ruoff, MRS Bull. 2012, v37, 1314.

[3] S. M. Sajadi, P. S. Owuor, S. Schara, C. F. Woellner, V. Rodrigues, R. Vajtai, J. Lou, D. S. Galvao, C. S. Tiwary, and P. M. Ajayan, Adv. Mater. 2017, 1704820.

[4] M. D. Lima et al., Science 2012, v338, 6109.

[5] P. R. A. Campos, V. M. de Oliveira, R. Giro e D. S. Galvão, Phys. Rev. Lett. 2004, v93, 098107.

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