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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.
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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.
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Graphynes and graphdiynes are generic names for families of two-dimensional carbon allotropes, where acetylenic groups connect benzenoid-like hexagonal rings, with the coexistence of sp and sp2 hybridized carbon atoms. The main differences between graphynes and graphdiynes are the number of acetylenic groups (one and two for graphynes and graphdiynes, respectively). Similarly to graphene nanoscrolls, graphyne and graphdiynes nanoscrolls are nanosized membranes rolled into papyrus-like structures. In this work we studied through molecular dynamics simulations, using reactive potentials, the structural and thermal (up to 1000 K) stability of α,ß,γ-graphyne and α,ß,γ-graphdiyne scrolls. Our results demonstrate that stable nanoscrolls can be created for all the structures studied here, although they are less stable than corresponding graphene scrolls. This can be elucidated as a result of the higher graphyne/graphdiyne structural porosity in relation to graphene, and as a consequence, the π-π stacking interactions decrease.
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We analyzed the impact of the complex channel network of donor and acceptor domains in nanostructured solar cells on the mobility of the charge carriers moving by thermally activated hopping. Particular attention was given to the so called intermixed phase, or interface roughness, that has recently been shown to promote an increase in the cell efficiency. The domains were obtained from a Monte Carlo simulation of a two-species lattice gas. We generated domain morphologies with controllable channel size and interface roughness. The field and density dependence of the carrier hopping mobility in different morphologies was obtained by solving a master equation. Our results show that the mobility decreases with roughness and increases with typical channel sizes. The deleterious effect of the roughness on the mobility is quite dramatic at low carrier densities and high fields. The complex channel network is shown to be directly responsible for two potentially harmful effects to the cell performance: a remarkable decrease of the mobility with increasing field and the accumulation of charge at the domains interface, which leads to recombination losses.
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We develop a simple continuum model for the current voltage characteristics of a material as measured by the conducting atomic force microscopy, including space charge effects. We address the effect of the point contact on the magnitude of the current and on the transition voltages between the different current regimes by comparing these with the corresponding expressions obtained with planar electrodes.
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We have reformulated a traditional model used to describe the current-voltage dependence of low mobility materials sandwiched between planar electrodes by using the quasi-electrochemical potential as the fundamental variable instead of the local electric field or the local charge carrier density. This allows the material density-of-states to enter explicitly in the equations and dispenses with the need to assume a particular type of contact. The diffusion current is included and as a consequence the current-voltage dependence obtained covers, with increasing bias, the diffusion limited current, the space-charge limited current, and the injection limited current regimes. The generalized Einstein relation and the field and density dependent mobility are naturally incorporated into the formalism; these two points being of particular relevance for disordered organic semiconductors. The reformulated model can be applied to any material where the carrier density and the mobility may be written as a function of the quasi-electrochemical potential. We applied it to the textbook example of a nondegenerate, constant mobility material and showed how a single dimensionless parameter determines the form of the I(V) curve. We obtained integral expressions for the carrier density and for the mobility as a function of the quasi-electrochemical potential for a Gaussianly disordered organic material and found the general form of the I(V) curve for such materials over the full range of bias, showing how the energetic disorder alone can give rise, in the space-charge limited current regime, to an IâV(n) dependence with an exponent n larger than 2.