Topology of naphthylenic tori

Diudea, Mircea V.

doi:10.1039/b203680k

Cited by 13 publications

(12 citation statements)

References 52 publications

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“…After the discovery of carbon nanotubes in 1991 and the subsequent theoretical construction (later followed by the experimental observation) of graphitic tori, this class of polyhedra has drawn considerable attention and many possible tessellations of the circular torus have been proposed by the community [174,175,176,177,178,179,180,181,182,183,184]. Here we review the construction of a defect-free triangulated torus and we show how the most symmetric defective triangulations can be generally grouped into two fundamental classes corresponding to symmetry groups D nh and D nd respectively.…”

Section: Geometry Of Toroidal Polyhedramentioning

confidence: 99%

“…In the past few years, alternative constructions of triangulated tori have been proposed as well as novel geometrical and graph-theoretical methods to express the coordinates of their three-dimensional structures (see for example Kirby [180], László at al [181,182], Diudea et al [183,184]). Here we choose to focus on the defect structure associated with the two most important class TPn and TAn with groups D nh and D nd .…”

Section: Geometry Of Toroidal Polyhedramentioning

confidence: 99%

See 1 more Smart Citation

Two-dimensional matter: order, curvature and defects

Bowick

Giomi

2009

Advances in Physics

334

458

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Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its Gaussian curvature. Topology dictates certain broad features of the defect structure of the ground state but curvature-driven energetics controls the detailed structured of ordered phases. Among the surprises are the appearance in the ground state of structures that would normally be thermal excitations and thus prohibited at zero temperature. Examples include excess dislocations in the form of grain boundary scars for spherical crystals above a minimal system size, dislocation unbinding for toroidal hexatics, interstitial fractionalization in spherical crystals and the appearance of well-separated disclinations for toroidal crystals. Much of the analysis leads to universal predictions that do not depend on the details of the microscopic interactions that lead to order in the first place. These predictions are subject to test by the many experimental soft and hard matter systems that lead to curved ordered structures such as colloidal particles self-assembling on droplets of one liquid in a second liquid. The defects themselves may be functionalized to create ligands with directional bonding. Thus nano to meso scale superatoms may be designed with specific valency for use in building supermolecules and novel bulk materials. Parameters such as particle number, geometrical aspect ratios and anisotropy of elastic moduli permit the tuning of the precise architecture of the superatoms and associated supermolecules. Thus the field has tremendous potential from both a fundamental and materials science/supramolecular chemistry viewpoint. Contents

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Section: Geometry Of Toroidal Polyhedramentioning

confidence: 99%

Section: Geometry Of Toroidal Polyhedramentioning

confidence: 99%

Two-dimensional matter: order, curvature and defects

Bowick

Giomi

2009

Advances in Physics

334

458

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“…1,2 The case of the nonpolyhex nanotubes is much more complicated. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] There is not yet an available general formula for the geometric and electronic structures of the nonpolyhex nanotubes when they contain pentagons and heptagons as well. 18,19 In ref 20 we presented a method for describing the geometrical structures of nonhexagonal nanotubes, nanocoils, and nanotori.…”

Section: Introductionmentioning

confidence: 99%

The Electronic Structure of Nonpolyhex Carbon Nanotubes

László

2004

J. Chem. Inf. Comput. Sci.

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Generalizing the folding method to any periodic two-dimensional planar carbon structures we have calculated the corresponding electronic structures in the framework of the one orbital one site tight-binding (BlochHückel) method by solving the eigenvalue problems in a numerical way. We discussed the metallic or the nonmetallic behavior of the nanotubes by applying the folding vectors of parameters (m, n). We extended the topological coordinate method to two-dimensional periodic planar structures as well. Nearly regular hexagonal, pentagonal, and heptagonal polygons were obtained. The curvatures of the final relaxed structures can be read from the sizes of the polygons. Thus relying only on the topological information we could describe the shape of the tubular structures and their conductivity behaviors.

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“…Their end result is the prediction of metallic or semiconductor behavior of the nanotube in terms of characteristics of the parent square lattice. This study contains further references to papers by Diudea and Kirby on this topic, including ones that allow coding of the nanotube or carbon torus structure [89][90][91][92].…”

Section: Helicity Of Nanotubesmentioning

confidence: 99%

“…Discussing the complexity of few other types of carbon nanostructures has not been included in the present chapter, but leading references will be included in the following. For carbon tori, in addition to the literature cited above [89][90][91][92], it must be mentioned that they were discussed in the literature [93][94][95] before being obtained experimentally along with nanotubes and initially called "crop circles" [96]. Coiled nanotubes [97][98][99], hyperfullerenes with negative curvature [100], and Y-junctions of carbon nanotubes [101] are closely related to nanotubes.…”

Section: Helicity Of Nanotubesmentioning

confidence: 99%