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A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, tube, and many other shapes. Spherical fullerenes are also called buckyballs, and they resemble the balls used in football (soccer). 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; but they may also contain pentagonal (or sometimes heptagonal) rings.
The first fullerene molecule to be discovered, and the family's namesake, buckminsterfullerene (C60), was prepared in 1985 by Richard Smalley, Robert Curl, James Heath, Sean O'Brien, and Harold Kroto at Rice University. The name was a homage to Buckminster Fuller, whose geodesic domes it resembles. The structure was also identified some five years earlier by Sumio Iijima, from an electron microscope image, where it formed the core of a "bucky onion." Fullerenes have since been found to occur in nature. More recently, fullerenes have been detected in outer space. According to astronomer Letizia Stanghellini, "It’s possible that buckyballs from outer space provided seeds for life on Earth."
The discovery of fullerenes greatly expanded the number of known carbon allotropes, which until recently were limited to graphite, diamond, and amorphous carbon such as soot and charcoal. Buckyballs and buckytubes have been the subject of intense research, both for their unique chemistry and for their technological applications, especially in materials science, electronics, and nanotechnology.
The icosahedral C60H60 cage was mentioned in 1965 as a possible topological structure. Eiji Osawa of Toyohashi University of Technology predicted the existence of C60 in 1970. He noticed that the structure of a corannulene molecule was a subset of football shape, and he hypothesised that a full ball shape could also exist. Japanese scientific journals reported his idea, but it did not reach Europe or the Americas.
Also in 1970, R. W. Henson (then of the Atomic Energy Research Establishment) proposed the structure and made a model of C60. Unfortunately, the evidence for this new form of carbon was very weak and was not accepted, even by his colleagues. The results were never published but were acknowledged in Carbon in 1999.
Independently from Henson, in 1973 a group of scientists from the USSR, directed by Prof. Bochvar, made a quantum-chemical analysis of the stability of C60 and calculated its electronic structure. As in the previous cases, the scientific community did not accept the theoretical prediction. The paper was published in 1973 in Proceedings of the USSR Academy of Sciences (in Russian).
In mass spectrometry, discrete peaks appeared 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 molecules. C60 and other fullerenes were later noticed occurring outside the laboratory (for example, in normal candle-soot). By 1991, it was relatively easy to produce gram-sized samples of fullerene powder using the techniques of Donald Huffman, Wolfgang Krätschmer and Konstantinos Fostiropoulos. 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. Carbon nanotubes were recognized in 1991.
Minute quantities of the fullerenes, in the form of C60, C70, C76, C82 and C84 molecules, are produced in nature, hidden in soot and formed by lightning discharges in the atmosphere. In 1992, fullerenes were found in a family of minerals known as Shungites in Karelia, Russia.
In 2010, fullerenes (C60) have been discovered in a cloud of cosmic dust surrounding a distant star 6500 light years away. Using NASA's Spitzer infrared telescope the scientists spotted the molecules' unmistakable infrared signature. Sir Harry Kroto, who shared the 1996 Nobel Prize in Chemistry for the discovery of buckyballs commented: "This most exciting breakthrough provides convincing evidence that the buckyball has, as I long suspected, existed since time immemorial in the dark recesses of our galaxy." 
Buckminsterfullerene (C60) was named after Richard Buckminster Fuller, a noted architectural modeler who popularized the geodesic dome. Since buckminsterfullerenes have a shape similar to that sort of dome, the name was thought appropriate. As the discovery of the fullerene family came after buckminsterfullerene, the shortened name 'fullerene' is used to refer to the family of fullerenes. The suffix "-ene" indicates that each C atom is covalently bonded to three others (instead of the maximum of four), a situation that classically would correspond to the existence of bonds involving two pairs of electrons ("double bonds").
Since the discovery of fullerenes in 1985, structural variations on fullerenes have evolved well beyond the individual clusters themselves. Examples include:
Buckminsterfullerene is the smallest fullerene molecule containing pentagonal and hexagonal rings in which no two pentagons share an edge (which can be destabilizing, as in pentalene). It is also the most common in terms of natural occurrence, as it can often be found in soot.
The structure of C60 is a truncated icosahedron, which resembles an association football ball of the type made of twenty hexagons and twelve pentagons, with a carbon atom at the vertices of each polygon and a bond along each polygon edge.
The C60 molecule has two bond lengths. The 6:6 ring bonds (between two hexagons) can be considered "double bonds" and are shorter than the 6:5 bonds (between a hexagon and a pentagon). Its average bond length is 1.4 angstroms.
Silicon buckyballs have been created around metal ions.
A type of buckyball which uses boron atoms, instead of the usual carbon, was predicted and described in 2007. The B80 structure, with each atom forming 5 or 6 bonds, is predicted to be more stable than the C60 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 uses 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 break, yielding a puckered cage with rare Th symmetry (symmetry of a volleyball). The number of six-member rings in this molecule is 20 and number of five-member rings is 12. There is an additional atom in the center of each six-member ring, bonded to each atom surrounding it. By employing a systematic global search algorithm, later it was found that the previously proposed B80 fullerene is not global minimum for 80 atom boron clusters and hence can not be found in nature. In the same paper by Sandip De et al., it was concluded that born energy land scape is significantly different from other fullerenes already found in nature hence pure boron fullerenes are unlikely to exist in nature.
Another fairly common fullerene is C70, but fullerenes with 72, 76, 84 and even up to 100 carbon atoms are commonly obtained.
In mathematical terms, the structure of a fullerene is a trivalent convex polyhedron with pentagonal and hexagonal faces. In graph theory, the term fullerene refers to any 3-regular, planar graph with all faces of size 5 or 6 (including the external face). It follows from Euler's polyhedron formula, V − E + F = 2 (where V, E, F are the numbers of vertices, edges, and faces), that there are exactly 12 pentagons in a fullerene and V/2 − 10 hexagons.
(truncated icosahedral graph)
The smallest fullerene is the dodecahedral C20. There are no fullerenes with 22 vertices. The number of fullerenes C2n grows with increasing n = 12, 13, 14, ..., roughly in proportion to n9 (sequence A007894 in OEIS). For instance, there are 1812 non-isomorphic fullerenes C60. Note that only one form of C60, the buckminsterfullerene alias truncated icosahedron, has no pair of adjacent pentagons (the smallest such fullerene). To further illustrate the growth, there are 214,127,713 non-isomorphic fullerenes C200, 15,655,672 of which have no adjacent pentagons. Optimized structures of many fullerene isomers are published and listed on the web.
Trimetasphere carbon nanomaterials were discovered by researchers at Virginia Tech and licensed exclusively to Luna Innovations. This class of novel molecules comprises 80 carbon atoms (C
80) forming a sphere which encloses a complex of three metal atoms and one nitrogen atom. These fullerenes encapsulate metals which puts them in the subset referred to as metallofullerenes. Trimetaspheres have the potential for use in diagnostics (as safe imaging agents), therapeutics and in organic solar cells.
Nanotubes 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 heat conductivity, 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 highly speculative proposed use in the field of space technologies is to produce high-tensile carbon cables required by a space elevator.
Nanobuds have been obtained by adding buckminsterfullerenes to carbon nanotubes.
Fullerites are the solid-state manifestation of fullerenes and related compounds and materials.
"Ultrahard fullerite" is a coined term frequently used to describe material produced by high-pressure high-temperature (HPHT) processing of fullerite. Such treatment converts fullerite into a nanocrystalline form of diamond which has been reported to exhibit remarkable mechanical properties.
Materials with fullerene-like molecular structures but lacking carbon include MoS2, WS2, TiS2 and NbS2. Prof. J. M. Martin from Ecole Central de Lyon in France tested the new material under isostatic pressure and found it to be stable up to at least 350 tons/cm2.
For the past decade, the chemical and physical properties of fullerenes have been a hot topic in the field of research and development[according to whom?], and are likely to continue to be for a long time. Popular Science has discussed possible uses of fullerenes (graphene) in armor. In April 2003, fullerenes were under study for potential medicinal use: binding specific antibiotics to the structure to target resistant bacteria and even target certain cancer cells such as melanoma. The October 2005 issue of Chemistry & Biology contains an article describing the use of fullerenes as light-activated antimicrobial agents.
A common method used to produce fullerenes is to send a large current between two nearby graphite electrodes in an inert atmosphere. The resulting carbon plasma arc between the electrodes cools into sooty residue from which many fullerenes can be isolated.
There are many calculations that have been done using ab-initio quantum methods applied to fullerenes. By DFT and TD-DFT methods one can obtain IR, Raman and UV spectra. Results of such calculations can be compared with experimental results.
Researchers have been able to increase the reactivity of fullerenes by attaching active groups to their surfaces. Buckminsterfullerene does not exhibit "superaromaticity": that is, the electrons in the hexagonal rings do not delocalize over the whole molecule.
A spherical fullerene of n carbon atoms has n pi-bonding electrons, free to delocalize. These should try to delocalize over the whole molecule. The quantum mechanics of such an arrangement should be like one shell only of the well-known quantum mechanical structure of a single atom, with a stable filled shell for n = 2, 8, 18, 32, 50, 72, 98, 128, etc.; i.e. twice a perfect square number; but this series does not include 60. This 2(N + 1)2 rule (with N integer) for spherical aromaticity is the three-dimensional analogue of Hückel's rule. The 10+ cation would satisfy this rule, and should be aromatic. This has been shown to be the case using quantum chemical modelling, which showed the existence of strong diamagnetic sphere currents in the cation.
Fullerenes are stable, but not totally unreactive. The sp2-hybridized carbon atoms, which are at their energy minimum in planar graphite, must be bent to form the closed sphere or tube, which produces angle strain. The characteristic reaction of fullerenes is electrophilic addition at 6,6-double bonds, which reduces angle strain by changing sp2-hybridized carbons into sp3-hybridized ones. The change in hybridized orbitals causes the bond angles to decrease from about 120° in the sp2 orbitals to about 109.5° in the sp3 orbitals. This decrease in bond angles allows for the bonds to bend less when closing the sphere or tube, and thus, the molecule becomes more stable.
Other atoms can be trapped inside fullerenes to form inclusion compounds known as endohedral fullerenes. An unusual example is the egg shaped fullerene Tb3N@C84, which violates the isolated pentagon rule. Recent evidence for a meteor impact at the end of the Permian period was found by analyzing noble gases so preserved. Metallofullerene-based inoculates using the rhonditic steel process are beginning production as one of the first commercially-viable uses of buckyballs.
Fullerenes are sparingly soluble in many solvents. Common solvents for the fullerenes include aromatics, such as toluene, and others like carbon disulfide. Solutions of pure buckminsterfullerene have a deep purple color. Solutions of C70 are a reddish brown. The higher fullerenes C76 to C84 have a variety of colors. C76 has two optical forms, while other higher fullerenes have several structural isomers. Fullerenes are the only known allotrope of carbon that can be dissolved in common solvents at room temperature.
|1,2-dichlorobenzene||24 mg/mL||36.2 mg/mL|
|carbon disulfide||8 mg/mL||9.875 mg/mL|
|xylene||5 mg/mL||3.985 mg/mL(p-xylene)|
|toluene||3 mg/mL||1.406 mg/mL|
|benzene||1.5 mg/mL||1.3 mg/mL|
|carbon tetrachloride||0.447 mg/mL||0.121 mg/mL|
|n-hexane||0.046 mg/mL||0.013 mg/mL|
|cyclohexane||0.035 mg/mL||0.08 mg/mL|
|methanol||0.000 04 mg/mL||*|
|pentane||0.004 mg/mL||0.002 mg/mL|
|octane||0.025 mg/mL||0.042 mg/mL|
|decane||0.070 mg/mL||0.053 mg/mL|
|dodecane||0.091 mg/mL||0.098 mg/mL|
|mesitylene||0.997 mg/mL||1.472 mg/mL|
|dichloromethane||0.254 mg/mL||0.080 mg/mL|
|* : Solubility not measured|
Some fullerene structures are not soluble because they have a small band gap between the ground and excited states. These include the small fullerenes C28, C36 and C50. The C72 structure is also in this class, but the endohedral version with a trapped lanthanide-group atom is soluble due to the interaction of the metal atom and the electronic states of the fullerene. Researchers had originally been puzzled by C72 being absent in fullerene plasma-generated soot extract, but found in endohedral samples. Small band gap fullerenes are highly reactive and bind to other fullerenes or to soot particles.
Solvents that are able to dissolve buckminsterfullerene (C60 and C70) are listed at left in order from highest solubility. The solubility value given is the approximate saturated concentration. 
Solubility of C60 in some solvents shows unusual behaviour due to existence of solvate phases (analogues of crystallohydrates). For example, solubility of C60 in benzene solution shows maximum at about 313 K. Crystallization from benzene solution at temperatures below maximum results in formation of triclinic solid solvate with four benzene molecules C60·4C6H6 which is rather unstable in air. Out of solution, this structure decomposes into usual face-centered cubic (fcc) C60 in few minutes' time. At temperatures above solubility maximum the solvate is not stable even when immersed in saturated solution and melts with formation of fcc C60. Crystallization at temperatures above the solubility maximum results in formation of pure fcc C60. Millimeter-sized crystals of C60 and C70 can be grown from solution both for solvates and for pure fullerenes.
In 1999, researchers from the University of Vienna demonstrated that wave-particle duality applied to molecules such as fullerene. One of the co-authors of this research, Julian Voss-Andreae, has since created several sculptures symbolizing wave-particle duality in fullerenes (see Fullerenes in popular culture for more detail).
Some fullerenes (e.g. C76, C78, C80, and C84) are inherently chiral because they are D2-symmetric, and have been successfully resolved. Research efforts are ongoing to develop specific sensors for their enantiomers.
Two theories have been proposed to describe the molecular mechanisms that make fullerenes. The older, “bottom-up” theory proposes that they are built atom-by-atom. The alternative “top-down” approach claims that fullerenes form when much larger structures break into constituent parts.
In 2013 researchers discovered that asymmetrical fullerenes formed from larger structures settle into stable fullerenes. The synthesized substance was a particular metallofullerene consisting of 84 carbon atoms with two additional carbon atoms and two yttrium atoms inside the cage. The process produced approximately 100 micrograms.
However, they found that the asymmetrical molecule could theoretically collapse to form nearly every known fullerene and metallofullerene. Minor perturbations involving the breaking of a few molecular bonds cause the cage to become highly symmetrical and stable. This insight supports the theory that fullerenes can be formed from graphene when the appropriate molecular bonds are severed.
While past cancer research has involved radiation therapy, photodynamic therapy is important to study because breakthroughs in treatments for tumor cells will give more options to patients with different conditions. More recent experiments using HeLa cells in cancer research involves the development of new photosensitizers with increased ability to be absorbed by cancer cells and still trigger cell death. It is also important that a new photosensitizer does not stay in the body for a long time to prevent unwanted cell damage.
Fullerenes can be made to be absorbed by HeLa cells. The C60 derivatives can be delivered to the cells by using the functional groups L-phenylalanine, folic acid, and L-arginine among others. The purpose for functionalizing the fullerenes is to increase the solubility of the molecule by the cancer cells. Cancer cells take up these molecules at an increased rate because of an upregulation of transporters in the cancer cell, in this case amino acid transporters will bring in the L-arginine and L-phenylalanine functional groups of the fullerenes.
Once absorbed by the cells, the C60 derivatives would react to light radiation by turning molecular oxygen into reactive oxygen which triggers apoptosis in the HeLa cells and other cancer cells that can absorb the fullerene molecule. This research shows that a reactive substance can target cancer cells and then be triggered by light radiation, minimizing damage to surrounding tissues while undergoing treatment.
When absorbed by cancer cells and exposed to light radiation, the reaction that creates reactive oxygen damages the DNA, proteins, and lipids that make up the cancer cell. This cellular damage forces the cancerous cell to go through apoptosis, which can lead to the reduction in size of a tumor. Once the light radiation treatment is finished the fullerene will reabsorb the free radicals to prevent damage of other tissues. Since this treatment focuses on cancer cells it is a good option for patients whose cancer cells are within reach of light radiation. As this research continues into the future it will be able to penetrate deeper into the body and more effectively absorbed by cancer cells.
Moussa et al. (1996–7) studied the in vivo toxicity of C60 after intra-peritoneal administration of large doses. No evidence of toxicity was found and the mice tolerated a dose of 5 g/kg of body weight. Mori et al. (2006) could not find toxicity in rodents for C60 and C70 mixtures after oral administration of a dose of 2 g/kg body weight and did not observe evidence of genotoxic or mutagenic potential in vitro. Other studies could not establish the toxicity of fullerenes: on the contrary, the work of Gharbi et al. (2005) suggested that aqueous C60 suspensions failing to produce acute or subacute toxicity in rodents could also protect their livers in a dose-dependent manner against free-radical damage. In 2012, it was revealed that oral administration prolonged the lifespan of rats by nearly 100% without showing toxic effects. In a more recent video interview filmed in October 2012 and placed online, Professor Moussa states that pure C60 is not toxic.
A comprehensive and recent review on fullerene toxicity is given by Kolosnjaj et al. (2007). These authors review the works on fullerene toxicity beginning in the early 1990s to present, and conclude that very little evidence gathered since the discovery of fullerenes indicate that C60 is toxic.
With reference to nanotubes, a 2008 study on carbon nanotubes introduced into the abdominal cavity of mice led the authors to suggest comparisons to "asbestos-like pathogenicity". It should be noted that this was not an inhalation study, though there have been several performed in the past, therefore it is premature to conclude that nanotubes should be considered to have a toxicological profile similar to asbestos. Conversely, and perhaps illustrative of how the various classes of molecules which fall under the general term fullerene cover a wide range of properties, Sayes et al. found that in vivo inhalation of C60(OH)24 and nano-C60 in rats gave no effect, whereas in comparison quartz particles produced an inflammatory response under the same conditions. As stated above, nanotubes are quite different in chemical and physical properties to C60, i.e., molecular weight, shape, size, physical properties (such as solubility) all are very different, so from a toxicological standpoint, different results for C60 and nanotubes are not suggestive of any discrepancy in the findings.
When considering toxicological data, care must be taken to distinguish as necessary between what are normally referred to as fullerenes: (C60, C70, ...); fullerene derivatives: C60 or other fullerenes with covalently bonded chemical groups; fullerene complexes (e.g., water-solubilized with surfactants, such as C60-PVP; host-guest complexes, such as with cyclodextrin), where the fullerene is supermolecular bound to another molecule; C60 nanoparticles, which are extended solid-phase aggregates of C60 crystallites; and nanotubes, which are generally much larger (in terms of molecular weight and size) molecules, and are different in shape to the spheroidal fullerenes C60 and C70, as well as having different chemical and physical properties.
The above different molecules span the range from insoluble materials in either hydrophilic or lipophilic media, to hydrophilic, lipophilic, or even amphiphilic molecules, and with other varying physical and chemical properties. Therefore any broad generalization extrapolating for example results from C60 to nanotubes or vice versa is not possible, though technically all are fullerenes, as the term is defined as a close-caged all-carbon molecule. Any extrapolation of results from one molecule to other molecules must take into account considerations based on a quantitative structural analysis relationship study (QSARS), which mostly depends on how close the molecules under consideration are in physical and chemical properties.
Examples of fullerenes in popular culture are numerous. Fullerenes appeared in fiction well before scientists took serious interest in them. In a humorously speculative 1966 column for New Scientist, David Jones suggested that it may be possible to create giant hollow carbon molecules by distorting a plane hexagonal net by the addition of impurity atoms.
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