From Pure Mathematics to Macroscale Applications: The Genesis of Schwarzites

Schwarzites are porous (spongy-like) carbon allotropes with negative Gaussian curvatures. They were proposed by Mackay and Terrones inspired by the works of the German mathematician Hermann Schwarz on Triply-Periodic Minimal Surfaces (TPMS). This review presents and discusses the history of schwarzites and their place among curved carbon nanomaterials. We summarized the main works on schwarzites available in the literature. We discuss their unique structural, electronic, thermal, and mechanical properties. Although the synthesis of carbon-based schwarzites remains elusive, the recent advances in the synthesis of zeolite-templates nanomaterials bring them closer to reality. Atomic-based models of schwarzites have been translated into macroscale ones that have been 3D printed. These 3D printed models have been exploited in many real-world applications, including water remediation and biomedical ones.