85 research outputs found
The topology of fullerenes
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
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
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
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
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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Investigating the role of curvature on the formation and thermal transformations of soot
In this work, the role of curved polycyclic aromatic hydrocarbons (cPAH) on the initial formation mechanism and thermal transformations of soot was explored. Experimental and computational techniques were used to probe the integration, presence and impact of internal pentagonal rings on the nucleation mechanism of these particulates. A significant charge polarisation was found to occur when an internal pentagonal ring pyramidalises the aromatic network. Phase contrast transmission electron microscopy allowed for the extent of conjugation and degree of curvature to be determined in early soot nanoparticulates with 15 aromatic rings and two pentagons being the median species. The dipole moment of such a species was calculated to be 5.32 debye. The polarity was found to be persistent at flame temperatures with inversion and fluctuations being minimal. Homogeneous nucleation was considered with homodimerisation energies with one or two internal pentagonal rings within cPAH found to be comparable in energy to flat PAH (fPAH) homodimers of similar weight, with more pentagons reducing the binding energy. Ion-induced nucleation was considered with binding energies calculated between chemi-ions and cPAH suggesting small stable clusters at flame temperatures. However, physical and ion-induced nucleation of cPAH were found to be insufficient alone to explain the formation of soot. The impact of curvature on the reactivity of PAH were then studied. Strong crosslinks between σ-radicals and cPAH were found to form at their rim due to decreased aromaticity. Partially saturated rim-based pentagonal rings were also found to form localised π-radicals that allow stacked and bonded complexes to form, suggesting a covalently stabilised soot nucleation. Finally, the curved geometry of highly annealed soot, otherwise known as non-graphitising carbon, was explored using annealed molecular dynamics simulations and a discrete mesh analysis method. Analysis of the angular defect of the meshes revealed an excess of negative curvature. The coexistence of curved and layered ribbon-like structures was found to be possible due to the presence of a small number of non-sp² defects such as screw dislocations and free edges, which will impact the synthesis of novel carbon materials and the oxidation of thermally annealed soot. The incorporation of curvature and pentagonal rings is therefore considered critical for understanding the properties, formation and destruction of combustion generated carbonaceous particles and other carbon materials.This project is supported by the National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme
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