85 research outputs found

    The topology of fullerenes

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    Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website

    Graphene as a quantum surface with curvature-strain preserving dynamics

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    We discuss how the curvature and the strain density of the atomic lattice generate the quantization of graphene sheets as well as the dynamics of geometric quasiparticles propagating along the constant curvature/strain levels. The internal kinetic momentum of Riemannian oriented surface (a vector field preserving the Gaussian curvature and the area) is determined.Comment: 13p, minor correction

    Molecular Dynamics Studies Of The Annealing Of Carbon Peapods

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    In the past 30 years, carbon kept surprising the scientific community given the previous assumption that all carbon structures are already known. Apart from graphite, diamond and amorphous; new carbon allotropes including fullerenes, carbon nanotubes (CNT) and graphenes were discovered in year 1985, 1991 and 2004 respectively. Carbon peapod is a hybrid carbon nanostructure in which fullerenes such as C60 are encapsulated in an outer carbon nanotube. Carbon peapod can be transformed into a double-walled carbon nanotube (DWCNT) through annealing process. In essence, the fullerenes will fuse and form a smaller CNT in the outer CNT which acts as a mold/container. However there are a few research gaps in the simulations of the annealing process, e.g., potential was not applied to the outer CNT of the peapod and long range (van der Waals) interactions was ignored. In this thesis, the structures of three carbon peapods with different diameters are first constructed based on experimentally measured data. The peapods in the study are 13C60@CNT(13, 5), 13C60@CNT(14, 7) and 13C60@CNT(12, 12), where there are 13 C60 molecules in each peapod. Classical molecular dynamics (MD) simulations are performed to study the morphological transition of carbon peapods into DWCNT for the whole annealing process which lasted for 1 ns. All MD simulations are done with LAMMPS and AIREBO is chosen as the potential to simulate the inter- and intra-molecular interactions among the carbon atoms. From the simulated results it is observed that increased reactivity of the carbon peapod is associated with increasing annealing temperature

    Generating carbon schwarzites via zeolite-templating

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    Zeolite-templated carbons (ZTCs) comprise a relatively recent material class synthesized via the chemical vapor deposition of a carbon-containing precursor on a zeolite template, followed by the removal of the template. We have developed a theoretical framework to generate a ZTC model from any given zeolite structure, which we show can successfully predict the structure of known ZTCs. We use our method to generate a library of ZTCs from all known zeolites, to establish criteria for which zeolites can produce experimentally accessible ZTCs, and to identify over 10 ZTCs that have never before been synthesized. We show that ZTCs partition space into two disjoint labyrinths that can be described by a pair of interpenetrating nets. Since such a pair of nets also describes a triply periodic minimal surface (TPMS), our results establish the relationship between ZTCs and schwarzites-carbon materials with negative Gaussian curvature that resemble TPMSs-linking the research topics and demonstrating that schwarzites should no longer be thought of as purely hypothetical materials

    Magnetically Induced Current Densities in Toroidal Carbon Nanotubes

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    Molecular structures of toroidal carbon nanotubes (TCNTs) have been constructed and optimized at the density functional theory (DFT) level. The TCNT structures have been constrained by using point groups with high symmetry. TCNTs consisting of only hexagons (polyhex) with armchair, chiral, and zigzag structures as well as TCNTs with pentagons and heptagons have been studied. The employed method for constructing general polyhex TCNTs is discussed. Magnetically induced current densities have been calculated using the gauge-including magnetically induced currents (GIMIC) method. The strength of the magnetically induced ring currents has been obtained by integrating the current density passing a plane cutting the ring of the TCNT. The main pathways of the current density have been identified by visualizing the current density. The calculations show that the strength of the diatropic ring current of polyhex TCNTs with an armchair structure generally increases with the size of the TCNT, whereas TCNTs with a zigzag structure sustain very weak diatropic ring currents. Some of the TCNTs with pentagons and heptagons sustain a strong diatropic ring current, whereas other TCNT structures with pentagons and heptagons sustain paratropic ring currents that are, in most cases, relatively weak. We discuss the reasons for the different behaviors of the current density of the seemingly similar TCNTs.Peer reviewe
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