in this work, two parametric l-systems have been introduced to generate the figures of two series of nanostructures. these series consist of different spherical fullerenes with various number of carbon atoms. by specifying a parameter in each series a spherical fullerene can be determined. the members of the first series are c60 , c240 , c540 , c940 ,… which can be produced by applying paramete...

If a fullerene is defined as a finite trivalent graph made up solely of pentagons and hexagons, embedding in only four surfaces is possible: the sphere, torus, Klein bottle, and projective (elliptic) plane. The usual spherical fullerenes have 12 pentagons; elliptic fullerenes, 6; and toroidal and Klein-bottle fullerenes, none. Klein-bottle and elliptic fullerenes are the antipodal quotients of ...

We explore some generalizations of fullerenes Fv (simple polyhedra with v vertices and only 5and -gonal faces) seen as (d−1)dimensional simple manifolds (preferably, spherical or polytopal) with only 5and 6-gonal 2-faces. First, finite and planar (infinite) 3-fullerenes are described. Three infinite families of spherical 4fullerenes are presented in Sections 4-6. The Construction A gives 4-poly...

In this work, two parametric L-Systems have been introduced to generate the figures of two series of nanostructures. These series consist of different spherical fullerenes with various number of carbon atoms. By specifying a parameter in each series a spherical fullerene can be determined. The members of the first series are C60 , C240 , C540 , C940 ,… which can be produced by applying paramete...

Both the eigenfunctions and the local density of states (DOS) near the pentagonal defects on the fullerenes was calculated analytically as a numerically. The results shows that the low-energy DOS has a cusp which drops to zero at the Fermi energy for any number of pentagons at the tip except three. For three pentagons, the nonzero DOS across the Fermi level is formed. Graphite is an example of ...

Like beads on a string: A synthetic method for the directional construction of strings of spherical fullerenes along stacks of planar oligothiophenes is described. The key to success was the preparation of fullerenes with two solubilizing tri(ethylene glycol) tails (bold) and an aromatic aldehyde for covalent capture by hydrazides along the oligothiophene stacks (red). BOLAG, Alatengbaolige, et...

The energetics of large-sized fullerenes and carbon nanotubes is investigated through first-principles pseudopotential calculations for the carbon cluster of CN (60<N<540). The strain energy due to the presence of pentagons, in addition to the curvature effect, makes an important contribution to the energetics of the fullerenes and nanotubes and accurately describes the N dependence of the ener...

Three surprising discoveries on the nature of matter and its properties were published in the mid-1980s. All these discoveries led to Nobel prizes. The first discovery was in 1985, when fullerenes were discovered by Robert F. Curl Jr, Sir Harold W. Kroto, and Richard E. Smalley. Fullerenes, also known as buckyballs, are spherical molecules composed of carbon atoms. The discovery of fullerenes l...

A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, or tube. Spherical fullerenes are also called buckyballs, and they resemble the balls used in Association Football. Cylindrical ones are called carbon nanotubes or buckytubes. Fullerenes are similar in structure to graphite, which is composed of stacked graphene sheets of linked hexagonal rings; ...