Fullerene refers to a family of carbon allotropes, molecules composed entirely of carbon, in the form of a hollow sphere, ellipsoid, tube, or plane. Spherical fullerenes are also called buckyballs, and cylindrical ones are called carbon nanotubes or buckytubes. Graphene is an example of a planar fullerene sheet. Fullerenes are similar in structure to graphite, which is composed of stacked sheets of linked hexagonal rings, but may also contain pentagonal (or sometimes heptagonal) rings that would prevent a sheet from being planar.

The fullerene was discovered in 1985 by Robert Curl, Harold Kroto and Richard Smalley at the University of Sussex and Rice University, who named it after Richard Buckminster Fuller, whose geodesic domes it resembles.

In molecular beam experiments, discrete peaks were observed corresponding to molecules with the exact mass of sixty or seventy or more carbon atoms. In 1985, Harold Kroto (then of the University of Sussex), James R. Heath, Sean O'Brien, Robert Curl and Richard Smalley, from Rice University, discovered C60, and shortly thereafter came to discover the fullerenes. Kroto, Curl, and Smalley were awarded the 1996 Nobel Prize in Chemistry for their roles in the discovery of this class of compounds. C60 and other fullerenes were later noticed occurring outside the laboratory (e.g., in normal candle soot). By 1991, it was relatively easy to produce gram-sized samples of fullerene powder using the techniques of Donald Huffman and Wolfgang Krätschmer. Fullerene purification remains a challenge to chemists and to a large extent determines fullerene prices. So-called endohedral fullerenes have ions or small molecules incorporated inside the cage atoms. Fullerene is an unusual reactant in many organic reactions such as the Bingel reaction discovered in 1993. The first nanotubes were obtained in 1991.

Minute quantities of the fullerenes, in the form of C60, C70, C76, and C84 molecules, are produced in nature, hidden in soot and formed by lightning discharges in the atmosphere. Recently, Buckminsterfullerenes were found in a family of minerals known as Shungites in Karelia, Russia.

The existence of C60 was predicted in 1970 by Eiji Osawa of Toyohashi University of Technology. He noticed that the structure of a corannulene molecule was a subset of a soccer-ball shape, and he made the hypothesis that a full ball shape could also exist. His idea was reported in Japanese magazines, but did not reach Europe or America.

Buckminsterfullerene (C60 buckyball) was named after Richard Buckminster Fuller, a noted architectural modeler who popularized the geodesic dome. Since buckminsterfullerenes have a similar shape to that sort of dome, the name was thought to be appropriate. As the discovery of the fullerene family came after buckminsterfullerene, the shortened name 'fullerene' was used to refer to the family of fullerenes.

A new type of buckyball utilizing boron atoms instead of the usual carbon has been predicted and described by researchers at Rice University. The B-80 structure is predicted to be more stable than the C-60 buckyball. One reason for this given by the researchers is that the B-80 is actually more like the original geodesic dome structure popularized by Buckminster Fuller which utilizes triangles rather than hexagons. However, this work has been subject to much criticism by quantum chemists as it was concluded that the predicted Ih symmetric structure was vibrationally unstable and the resulting cage undergoes a spontaneous symmetry breaking yielding a puckered cage with rare Th symmetry (symmetry of the Volleyball)

Nanotubes (buckytubes) are cylindrical fullerenes. These tubes of carbon are usually only a few nanometres wide, but they can range from less than a micrometer to several millimeters in length. They often have closed ends, but can be open-ended as well. There are also cases in which the tube reduces in diameter before closing off. Their unique molecular structure results in extraordinary macroscopic properties, including high tensile strength, high electrical conductivity, high ductility, high resistance to heat, and relative chemical inactivity (as it is cylindrical and "planar"—that is, it has no "exposed" atoms that can be easily displaced). One proposed use of carbon nanotubes is in paper batteries, developed in 2007 by researchers at Rensselaer Polytechnic Institute. Another proposed use in the field of space technologies and science fiction is to produce high-tensile carbon cables required by a space elevator.

Nanobuds have been obtained by adding Buckminsterfullerenes to carbon nanotubes.

Ultrahard fullerite (C60) is a form of carbon synthesized under high pressure high temperature conditions. It is believed that fullerene molecules are three-dimensionally polymerized in this material.

Examples of fullerenes in popular culture are numerous. Fullerenes appeared in fiction well before scientists took serious interest in them. In New Scientist there used to be a weekly column called "Daedalus" written by David Jones, which contained humorous descriptions of unlikely technologies. In 1966 the columnist included a description of C60 and other forms of graphite. This was meant as pure entertainment. Fullerenes are part of the plot in a science fiction novel named Decipher written by Stel Pavlou and published in 2001. Bucky Balls were also mentioned in A&E's 2008 remake of The Andromeda Strain, which is based on the Michael Crichton novel of the same name; other novels to make mention of them include Kim Stanley Robinson's Mars Trilogy; Iron by Poul Anderson and Neal Stephenson's The Diamond Age. The buckyball is the state molecule of Texas.

Since the discovery of fullerenes in 1985, structural variations on fullerenes have evolved well beyond the individual clusters themselves. Examples include:

• buckyball clusters: smallest member is C 20 (unsaturated version of dodecahedrane) and the most common is C 60;
• nanotubes: hollow tubes of very small dimensions, having single or multiple walls; potential applications in electronics industry;
• megatubes: larger in diameter than nanotubes and prepared with walls of different thickness; potentially used for the transport of a variety of molecules of different sizes;
• polymers: chain, two-dimensional and three-dimensional polymers are formed under high pressure high temperature conditions
• nano"onions": spherical particles based on multiple carbon layers surrounding a buckyball core; proposed for lubricants;
• linked "ball-and-chain" dimers: two buckyballs linked by a carbon chain;
• fullerene rings

The potential applications of carbon nanotubes are varied. Carbon nanotubes, a type of fullerene, have potential in fields such as nanotechnology, electronics, optics, materials science, and architecture. Over the years new discoveries have led to new applications, often taking advantage of their unique electrical properties, extraordinary strength, and efficiency in heat conduction.

Among others: high tensile strength fibers, strong building materials (concrete and steel), solar cells, Acoustics (loudspeakers), water and air filters, fastest known electronic oscillators (> 50 GHz), electrical and electronics circuits (semiconductors and transistors).

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