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In this work, we propose a new methodology for obtaining 3D carbon allotrope structures from 2D ones through topological mapping. The idea is to select a 3D target structure and 'slice' it along different structural directions, creating a series of 2D structures. As a proof of concept, we chose the Tubulane structure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based on cross-linked carbon nanotubes. One of obtained 2D 'sliced' structures was mapped into the biphenylene carbon (BPC). We showed that compressing BPC along different directions can generate not only the target Tubulane 12-hexa(3,3) but at least two other structures, bcc-C6 and an unreported member of the Tubulane family, which we called Tubulane X. The methodology proposed here is completely general, it can be used coupled with any quantum method. Considering that new 2D carbon allotropes, such as the biphenylene carbon network, which is closely related to BPC, have been recently synthesized, the approach proposed here opens new perspectives to obtain new 3D carbon allotropes from 2D structures.

Hydrogen is a promising element for applications in new energy sources like fuel cells. One key issue for such applications is storing hydrogen. And, to improve storage capacity, understanding the interaction mechanism between hydrogen and possible storage materials is critical. This work uses DFT simulations to comprehensively investigate the adsorption mechanism of H/H$_2$ on the 2D metallic porphyrins with one transition metal in its center. Our results suggest that the mechanism for adsorption of H (H$_2$) is chemisorption (physisorption). The maximum adsorption energy for atomic hydrogen was $-3.7$ eV for 2D porphyrins embedded with vanadium or chromium atoms. Our results also revealed charge transfer of up $-0.43$ e to chemisorbed H atoms. In contrast, the maximum adsorption energy calculated for molecular hydrogen was $-122.5$ meV for 2D porphyrins embedded with scandium atoms. Furthermore, charge transfer was minimal for physisorption. Finally, we also determined that uniaxial strain has a minimal effect on the adsorption properties of 2D metallic porphyrins.

Schwarzites are porous structures that present negative Gaussian curvatures. Although initially proposed for carbon, in principle, schwarzites of other elements are possible. In this work, we have carried out a detailed investigation of the effect of element composition (C, Ge, Si, SiC, and BN) on the structural, electronic and optical properties of a gyroid schwarzite structure, the so-called G688. The DFT simulations were carried out using the well-known SIESTA code. Our results showed that formation energy values are in similar range of other related allotrope structures and are thermally stable (up to 1000~K). From the electronic analyses, our results indicate that all structures, except the carbon one, present semiconductor characteristics. From the optical properties, except for the infrared region where only silicon and germanium show some absorption, the other structures exhibit optical activity only in the visible and ultra-violet regions, and all of them have large refractive index values. For reflectivity, except for Si and Ge schwarzites that reflect almost 40\% of light, the other schwarzites exhibit low reflectivity. These characteristics make them good candidates for optoelectronic applications, such as infrared/ultraviolet absorbers, and ultraviolet blockers.

In this work, we investigated the effect of knots in the thermal transport of graphene nanoribbons through non-equilibrium molecular dynamics simulations. We considered the cases of one, two, and three knots are present. Temperature jumps appear in the temperature profile where the knots are located, which indicates that they introduce thermal resistances in the system, similar to interfacial Kapitza resistance present between two different materials and/or single materials with defects and/or lattice distortions. We found that the thermal resistance introduced by each individual knot is essentially the same as the overall resistance increase linearly with the number of knots, as they behave as thermal resistances associated in series. Also, the relative position between each knot in the arrangement does not strongly affect the thermal current produced by the temperature gradient, showing a weak thermal rectification effect.

The concept of the 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 voids 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 easier 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.

In this work, We combined fully atomistic molecular dynamics and finite elements simulations with mechanical testings to investigate the mechanical behavior of atomic and 3D-printed models of pentadiamond. Pentadiamond is a recently proposed new carbon allotrope, which is composed of a covalent network of pentagonal rings. Our results showed that the stress-strain behavior is almost scale-independent. The stress-strain curves of the 3D-printed structures exhibit three characteristic regions. For low-strain values, this first region presents a non-linear behavior close to zero, followed by a well-defined linear behavior. The second regime is a quasi-plastic one and the third one is densification followed by structural failures (fracture). The Young's modulus values decrease with the number of pores. The deformation mechanism is bending-dominated and different from the layer-by-layer deformation mechanism observed for other 3D-printed structures. They exhibit good energy absorption capabilities, with some structures even outperforming kevlar. Interestingly, considering the Ashby chart, 3D-printed pentadiamond lies almost on the ideal stretch and bending-dominated lines, making them promising materials for energy absorption applications.

Pentadiamond is a recently proposed new carbon allotrope consisting of a network of pentagonal rings where both sp$^2$ and sp$^3$ hybridization are present. In this work we investigated the mechanical and electronic properties, as well as, the thermal stability of pentadiamond using DFT and fully atomistic reactive molecular dynamics (MD) simulations. We also investigated its properties beyond the elastic regime for three different deformation modes: compression, tensile and shear. The behavior of pentadiamond under compressive deformation showed strong fluctuations in the atomic positions which are responsible for the strain softening at strains beyond the linear regime, which characterizes the plastic flow. As we increase temperature, as expected, Young's modulus values decrease, but this variation (up to 300 K) is smaller than 10\% (from 347.5 to 313.6 GPa), but the fracture strain is very sensitive, varying from $\sim$44\% at 1K to $\sim$5\% at 300K.

Free-standing monolayer amorphous carbon (MAC) is a pure carbon structure composed of randomly distributed atom rings with different sizes, which was recently synthesized. In this work, we carried out ab initio and tight-binding calculations to investigate the optoelectronic properties of MAC and its derived nanotube and nanoscroll configurations. Our results show MAC, tube, and scrolls exhibit similar electronic behavior. All structures absorb from infrared to ultraviolet, with maximum absorption peaks the visible-ultra violet ($\sim 3.2$ eV). The maximum and minimum reflectivity values are in the range 0.3-0.5 (infrared) and 0.1-0.0 (ultraviolet), making these materials good candidates to ultraviolet filters.

Schwarzites are porous crystalline structures with Gaussian negative curvature. In this work, we investigated the mechanical behavior and energy absorption properties of two carbon-based diamond schwarzites (D688 and D8bal). We carried out fully atomistic molecular dynamics (MD) simulations. The optimized MD atomic models were used to generate macro-scale models for 3D-printing (PolyLactic Acid (PLA) polymer filaments) through Fused Deposition Modelling (FDM). Mechanical properties under uniaxial compression were investigated for both the atomic models and the 3D-printed ones. Mechanical testings were performed on the 3D-printed schwarzites where the deformation mechanisms were found to be similar to those observed in MD simulations. These results are suggestive of a scale-independent mechanical behavior that is dominated by structural topology. The structures exhibit high specific energy absorption and crush force efficiency ~0.8, which suggest that the 3D-printed diamond schwarzites are good candidates as energy-absorbing materials.

Since graphene was synthesized the interest for building new 2D and 3D structures based on the 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 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 acquires 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 schwarzites structures absorb light from infrared to ultra-violet frequencies. Therefore, our results open new perspectives of materials that can be used in optelectronics devices application., Comment: 23 pages, 6 figures

Recently (C.-T. Toh et al., Nature 577, 199 (2020)), the first synthesis of free-standing monolayer amorphous carbon (MAC) was achieved. MAC is a pure carbon structure composed of five, six, seven and eight atom rings randomly distributed. MAC proved to be surprisingly stable and highly fracture resistant. Its electronic properties are similar to boron nitride. In this work, we have investigated the mechanical properties and thermal stability of MAC models using fully-atomistic reactive molecular dynamics simulations. For comparison purposes, the results are contrasted against pristine graphene (PG) models of similar dimensions. Our results show that MAC and PG exhibit distinct mechanical behavior and fracture dynamics patterns. While PG after a critical strain threshold goes directly from elastic to brittle regimes, MAC shows different elastic stages between these two regimes. Remarkably, MAC is thermally stable up to 3600 K, which is close to the PG melting point. These exceptional physical properties make MAC-based materials promising candidates for new technologies, such as flexible electronics., Comment: 5 figures and 10 pages

Schwarzites are 3D crystalline porous materials exhibiting the shape of Triply Periodic Minimal Surfaces (TPMS). They possess negative Gaussian curvature, created by the presence of rings with more than six sp2-hybridized carbon atoms. Recently, new routes to their synthesis have been proposed. Due to its foam-like structure, schwarzites are interesting for mechanical energy absorption applications. In this work, we investigate through fully atomistic reactive molecular dynamics the mechanical response under ballistic impacts of four structures from primitive (P) and gyroid (G) families (two structures within each family). The two structures in the same family differ mainly by the ratio of hexagons to octagons, where this ratio increases the 'flatness' of the structures. Although the penetration depth values are higher in the 'flatter' structures (P8bal and G8bal), the absorbed kinetic energy by them is considerably higher, which yields them a better energy-absorption performance.

Triply Periodic Minimal Surfaces (TPMS) possess locally minimized surface area under the constraint of periodic boundary conditions. Different families of surfaces were obtained with different topologies satisfying such conditions. Examples of such families include Primitive (P), Gyroid (G) and Diamond (D) surfaces. From a purely mathematical subject, TPMS have been recently found in materials science as optimal geometries for structural applications. Proposed by Mackay and Terrones in 1991, schwarzites are 3D crystalline porous carbon nanocrystals exhibiting the shape of TPMS. Although their complex topology poses serious limitations on their synthesis with conventional nanoscale fabrication methods, such as Chemical Vapour Deposition (CVD), TPMS can be fabricated by Additive Manufacturing (AM) techniques, such as 3D Printing. In this work, we used an optimized atomic model of a schwarzite structure from the D family (D8bal) to generate a surface mesh that was subsequently used for 3D-printing through Fused Deposition Modelling (FDM). This D schwarzite was 3D-printed with thermoplastic PolyLactic Acid (PLA) polymer filaments. Mechanical properties under uniaxial compression were investigated for both the atomic model and the 3D-printed one. Fully atomistic Molecular Dynamics (MD) simulations were also carried out to investigate the uniaxial compression behavior of the D8bal atomic model. Mechanical testings were performed on the 3D-printed schwarzite where the deformation mechanisms were found to be similar to those observed in MD simulations. These results are suggestive of a scale-independent mechanical behavior that is dominated by structural topology.

We investigated through fully atomistic molecular dynamics simulations, the mechanical behavior (compressive and tensile) and energy absorption properties of two families (primitive (P688 and P8bal) and gyroid (G688 and G8bal)) of carbon-based schwarzites. Our results show that all schwarzites can be compressed (with almost total elastic recovery) without fracture to more than 50%, one of them can be even remarkably compressed up to 80%. One of the structures (G8bal) presents negative Poisson's ratio value (auxetic behavior). The crush force efficiency, the stroke efficiency and the specific energy absorption (SEA) values show that schwarzites can be effective energy absorber materials. Although the same level of deformation without fracture observed in the compressive case is not observed for the tensile case, it is still very high (30-40%). The fracture dynamics show extensive structural reconstructions with the formation of linear atomic chains (LACs).