Schwarzites and Triply Periodic Minimal Surfaces: From Pure Topology Mathematics to Macroscale Applications.

Schwarzites are porous (spongy-like) carbon allotropes with negative Gaussian curvatures. They are 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. The main works on schwarzites are summarized and are available in the literature. Their unique structural, electronic, thermal, and mechanical properties are discussed. Although the synthesis of carbon-based schwarzites remains elusive, recent advances in the synthesis of zeolite-templates nanomaterials have brought them closer to reality. Atomic-based models of schwarzites are translated into macroscale ones that are 3D-printed. These 3D-printed models are exploited in many real-world applications, including water remediation and biomedical ones.

The Role of the Extrafibrillar Volume on the Mechanical Properties of Molecular Models of Mineralized Bone Microfibrils.

Bones are responsible for body support, structure, motion, and several other functions that enable and facilitate life for many different animal species. They exhibit a complex network of distinct physical structures and mechanical properties, which ultimately depend on the fraction of their primary constituents at the molecular scale. However, the relationship between structure and mechanical properties in bones are still not fully understood. Here, we investigate structural and mechanical properties of all-atom bone molecular models composed of type-I collagen, hydroxyapatite (HA), and water by means of fully atomistic molecular dynamics simulations. Our models encompass an extrafibrillar volume (EFV) and consider mineral content in both the EFV and intrafibrillar volume (IFV), consistent with experimental observations. We investigate solvation structures and elastic properties of bone microfibril models with different degrees of mineralization, ranging from highly mineralized to weakly mineralized and nonmineralized models. We find that the local tetrahedral order of water is lost in similar ways in the EFV and IFV regions for all HA containing models, as calcium and phosphate ions are strongly coordinated with water molecules. We also subject our models to tensile loads and analyze the spatial stress distribution over the nanostructure of the material. Our results show that both mineral and water contents accumulate significantly higher stress levels, most notably in the EFV, thus revealing that this region, which has been only recently incorporated in all-atom molecular models, is fundamental for studying the mechanical properties of bones at the nanoscale. Furthermore, our results corroborate the well-established finding that high mineral content makes bone stiffer.

Guided fractures in graphene mechanical diode-like structures.

The concept of a diode is usually applied to electronic and thermal devices but very rarely for mechanical ones. A recently proposed fracture rectification effect in polymer-based structures with triangular void defects has motivated us to test these ideas at the nanoscale using graphene membranes. Using fully-atomistic reactive molecular dynamics simulations we showed that robust rectification-like effects exist. The fracture can be 'guided' to more easily propagate along one specific direction than its opposite. We also observed that there is an optimal value for the spacing between each void for the rectification effect.

Devising Bone Molecular Models at the Nanoscale: From Usual Mineralized Collagen Fibrils to the First Bone Fibers Including Hydroxyapatite in the Extra-Fibrillar Volume.

At the molecular scale, bone is mainly constituted of type-I collagen, hydroxyapatite, and water. Different fractions of these constituents compose different composite materials that exhibit different mechanical properties at the nanoscale, where the bone is characterized as a fiber, i.e., a bundle of mineralized collagen fibrils surrounded by water and hydroxyapatite in the extra-fibrillar volume. The literature presents only models that resemble mineralized collagen fibrils, including hydroxyapatite in the intra-fibrillar volume only, and lacks a detailed prescription on how to devise such models. Here, we present all-atom bone molecular models at the nanoscale, which, differently from previous bone models, include hydroxyapatite both in the intra-fibrillar volume and in the extra-fibrillar volume, resembling fibers in bones. Our main goal is to provide a detailed prescription on how to devise such models with different fractions of the constituents, and for that reason, we have made step-by-step scripts and files for reproducing these models available. To validate the models, we assessed their elastic properties by performing molecular dynamics simulations that resemble tensile tests, and compared the computed values against the literature (both experimental and computational results). Our results corroborate previous findings, as Young's Modulus values increase with higher fractions of hydroxyapatite, revealing all-atom bone models that include hydroxyapatite in both the intra-fibrillar volume and in the extra-fibrillar volume as a path towards realistic bone modeling at the nanoscale.

On the structural stability and optical properties of germanium-based schwarzites: a density functional theory investigation.

Since graphene was synthesized the interest in building new 2D and 3D structures based on carbon allotropes has been growing every day. One of these 3D structures is know as carbon schwarzites. Schwarzites consist of carbon nanostructures possessing the shape of Triply-Periodic Minimal Surfaces (TPMS), which is characterized by a negative Gaussian curvature introduced by the presence of carbon rings with more than six atoms. Some examples of schwarzite families include: primitive (P), gyroid (G) and diamond (D). Previous studies considering different element species of schwarzites have investigated the mechanical, electrical and thermal properties. In this work, we investigated the stability of germanium (Ge) schwarzites using density functional theory with the GGA exchange-correlation functional. We chose one structure of each family (P8bal), (G688) and (D688). It was observed that regions usually flat in carbon schwarzites acquire buckled configurations as previously observed on silicene and germanene monolayers. The investigated structures presented a semiconducting bandgap ranging from 0.13 to 0.27 eV. We also performed calculations of optical properties within the linear regime, where it was shown that Ge schwarzite structures absorb light from infrared to ultra-violet frequencies. Therefore, our results open new perspectives of materials that can be used in optoelectronics device applications.