Fullerene

Buckminsterfullerene C60 (left/top) and carbon nanotubes (right/below) are two examples of structures in the fullerene family.

C60a
Carbon nanotube zigzag povray cropped

A fullerene is an allotrope of carbon in the form of a hollow sphere, ellipsoid, tube, and many other shapes and sizes. Spherical fullerenes, also referred to as Buckminsterfullerenes or buckyballs, resemble the balls used in association football. Cylindrical fullerenes are also called carbon nanotubes (buckytubes). Fullerenes are similar in structure to graphite, which is composed of stacked graphene sheets of linked hexagonal rings. Unless they are cylindrical, they must also contain pentagonal (or sometimes heptagonal) rings.[1]

The first fullerene molecule to be discovered, and the family's namesake, buckminsterfullerene (C60), was manufactured in 1985 by Richard Smalley, Robert Curl, James Heath, Sean O'Brien, and Harold Kroto at Rice University. The name was an 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".[2] Fullerenes have since been found to occur in nature.[3] More recently, fullerenes have been detected in outer space.[4] According to astronomer Letizia Stanghellini, "It’s possible that buckyballs from outer space provided seeds for life on Earth."[5]

The discovery of fullerenes greatly expanded the number of known carbon allotropes, which had previously been limited to graphite, graphene, diamond, and amorphous carbon such as soot and charcoal. Buckyballs and buckytubes have been the subject of intense research, both for their chemistry and for their technological applications, especially in materials science, electronics, and nanotechnology.[6]

History

Fullerene c540
The icosahedral fullerene C540, another member of the family of fullerenes

The icosahedral C60H60 cage was mentioned in 1965 as a possible topological structure.[7] Eiji Osawa of Toyohashi University of Technology predicted the existence of C60 in 1970.[8][9] He noticed that the structure of a corannulene molecule was a subset of an association football shape, and he hypothesised that a full ball shape could also exist. Japanese scientific journals reported his idea, but neither it nor any translations of it reached 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.[10][11]

In 1973, independently from Henson, a group of scientists from the USSR 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).[12]

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 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.[13] Kroto, Curl, and Smalley were awarded the 1996 Nobel Prize in Chemistry[14] 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 1990 it was relatively easy to produce gram-sized samples of fullerene powder using the techniques of Donald Huffman, Wolfgang Krätschmer, Lowell D. Lamb, 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 first discovered and synthesized in 1991.[15][16]

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.[17] In 1992, fullerenes were found in a family of minerals known as Shungites in Karelia, Russia.[3]

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."[18]

Naming

The discoverers of the Buckminsterfullerene (C60) allotrope of carbon named it after Richard Buckminster Fuller, a noted architectural modeler who popularized the geodesic dome. Since buckminsterfullerenes have a similar shape to those of such domes, they thought the name appropriate.[19]
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").

Types of fullerene

Since the discovery of fullerenes in 1985, structural variations on fullerenes have evolved well beyond the individual clusters themselves. Examples include:[20]

  • 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[21]
  • polymers: chain, two-dimensional and three-dimensional polymers are formed under high-pressure high-temperature conditions; single-strand polymers are formed using the Atom Transfer Radical Addition Polymerization (ATRAP) route[22]
  • nano"onions": spherical particles based on multiple carbon layers surrounding a buckyball core[23] proposed for lubricants;[24]
  • linked "ball-and-chain" dimers: two buckyballs linked by a carbon chain[25]
  • fullerene rings[26]

Buckyballs

C60 isosurface
C60 with isosurface of ground state electron density as calculated with DFT
C60 Buckyball
Rotating view of C60, one kind of fullerene

Buckminsterfullerene

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 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 van der Waals diameter of a C60 molecule is about 1.1 nanometers (nm).[27] The nucleus to nucleus diameter of a C60 molecule is about 0.71 nm.

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.

Boron buckyball

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.[28] One reason for this given by the researchers is that B80 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[29][30] 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).[29] 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.[31] In the same paper by Sandip De et al., it was concluded that boron's energy landscape is significantly different from other fullerenes already found in nature hence pure boron fullerenes are unlikely to exist in nature.

Other buckyballs

Another fairly common fullerene is C70,[32] 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.

Graph of 20-fullerene w-nodes Graph of 26-fullerene 5-base w-nodes Graph of 60-fullerene w-nodes Graph of 70-fullerene w-nodes
20-fullerene
(dodecahedral graph)
26-fullerene graph 60-fullerene
(truncated icosahedral graph)
70-fullerene graph

The smallest fullerene is the dodecahedral C20. There are no fullerenes with 22 vertices.[33] The number of fullerenes C2n grows with increasing n = 12, 13, 14, ..., roughly in proportion to n9 (sequence A007894 in the 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.[34]

Heterofullerenes have heteroatoms substituting carbons in cage or tube-shaped structures. They were discovered in 1993[35] and greatly expand the overall fullerene class of compounds. Notable examples include boron, nitrogen (azafullerene), oxygen, and phosphorus derivatives.

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[36] and in organic solar cells.[37]

Carbon nanotubes

Kohlenstoffnanoroehre Animation
This rotating model of a carbon nanotube shows its 3D structure.

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.[38] Another highly speculative proposed use in the field of space technologies is to produce high-tensile carbon cables required by a space elevator.

Carbon nanobuds

Nanobuds have been obtained by adding buckminsterfullerenes to carbon nanotubes.

Fullerite

C60-Fulleren-kristallin
The C60 fullerene in crystalline form

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.[39]

Inorganic fullerenes

Materials with fullerene-like molecular structures but lacking carbon include MoS2, WS2, TiS2 and NbS2. Under isostatic pressure, these new materials were found to be stable up to at least 350 tons/cm2 (34.3 GPa).[40]

Properties

In the early 2000s, the chemical and physical properties of fullerenes were a hot topic in the field of research and development. Popular Science discussed possible uses of fullerenes (graphene) in armor.[41] 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 contained an article describing the use of fullerenes as light-activated antimicrobial agents.[42]

In the field of nanotechnology, heat resistance and superconductivity are some of the more heavily studied properties.

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.

Aromaticity

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.[43]

As a result, C60 in water tends to pick up two more electrons and become an anion. The nC60 described below may be the result of C60 trying to form a loose metallic bond.

Chemistry

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.[44] Recent evidence for a meteor impact at the end of the Permian period was found by analyzing noble gases so preserved.[45] Metallofullerene-based inoculates using the rhonditic steel process are beginning production as one of the first commercially viable uses of buckyballs.

Solubility

C60 Fullerene solution
C60 in solution
Carbon 60 Olive Oil Solution
C60 in extra virgin olive oil showing the characteristic purple color of pristine C60 solutions

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.

Solvent C60
mg/mL
C70
mg/mL
1-chloronaphthalene 51 ND
1-methylnaphthalene 33 ND
1,2-dichlorobenzene 24 36.2
1,2,4-trimethylbenzene 18 ND
tetrahydronaphthalene 16 ND
carbon disulfide 8 9.875
1,2,3-tribromopropane 8 ND
chlorobenzene 7 ND
p-xylene 5 3.985
bromoform 5 ND
cumene 4 ND
toluene 3 1.406
benzene 1.5 1.3
carbon tetrachloride 0.447 0.121
chloroform 0.25 ND
n-hexane 0.046 0.013
cyclohexane 0.035 0.08
tetrahydrofuran 0.006 ND
acetonitrile 0.004 ND
methanol 4.0×10−5 ND
water 1.3×10−11 ND
pentane 0.004 0.002
heptane ND 0.047
octane 0.025 0.042
isooctane 0.026 ND
decane 0.070 0.053
dodecane 0.091 0.098
tetradecane 0.126 ND
acetone ND 0.0019
isopropanol ND 0.0021
dioxane 0.0041 ND
mesitylene 0.997 1.472
dichloromethane 0.254 0.080
ND, not determined

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,[46] 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.[47][48][49][50][51]

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.[52][53]

Quantum mechanics

In 1999, researchers from the University of Vienna demonstrated that wave-particle duality applied to molecules such as fullerene.[54]

Chirality

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.

Construction

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.[55]

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.[55]

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.[55][56]

Production technology

Fullerene production processes comprise the following five subprocesses: (i) synthesis of fullerenes or fullerene-containing soot; (ii) extraction; (iii) separation (purification) for each fullerene molecule, yielding pure fullerenes such as C60; (iv) synthesis of derivatives (mostly using the techniques of organic synthesis); (v) other post-processing such as dispersion into a matrix. The two synthesis methods used in practice are the arc method, and the combustion method. The latter, discovered at the Massachusetts Institute of Technology, is preferred for large scale industrial production.[57][58]

Applications

Fullerenes have been extensively used for several biomedical applications including the design of high-performance MRI contrast agents, X-ray imaging contrast agents, photodynamic therapy and drug and gene delivery, summarized in several comprehensive reviews.[59]

Tumor research

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. 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.[60]

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.[61] Functionalizing the fullerenes aims 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.[62]

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.[63]

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.[64] 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, the treatment may penetrate deeper into the body and be absorbed by cancer cells more effectively.[60]

Safety and toxicity

Lalwani et al. published a comprehensive review on fullerene toxicity in 2013.[59] 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. The toxicity of these carbon nanoparticles is not only dose- and time-dependent, but also depends on a number of other factors such as:

  • type (e.g.: C60, C70, M@C60, M@C82
  • functional groups used to water-solubilize these nanoparticles (e.g.: OH, COOH)
  • method of administration (e.g.: intravenous, intraperitoneal)

The authors therefore recommend assessing the pharmacology of every new fullerene- or metallofullerene-based complex individually as a different compound.

Popular culture

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.[65]

On 4 September 2010, Google used an interactively rotatable fullerene[66] C60 as the second 'o' in their logo to celebrate the 25th anniversary of the discovery of the fullerenes.[67][68]

See also

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External links

26-fullerene graph

In the mathematical field of graph theory, the 26-fullerene graph is a polyhedral graph with V = 26 vertices and E = 39 edges. Its planar embedding has three hexagonal faces (including the one shown as the external face of the illustration) and twelve pentagonal faces. As a planar graph with only pentagonal and hexagonal faces, meeting in three faces per vertex, this graph is a fullerene. The existence of this fullerene has been known since at least 1968.

Bingel reaction

The Bingel reaction in fullerene chemistry is a fullerene cyclopropanation reaction to a methanofullerene first discovered by C. Bingel in 1993 with the bromo derivative of diethyl malonate in the presence of a base such as sodium hydride or DBU. The preferred double bonds for this reaction on the fullerene surface are the shorter bonds at the junctions of two hexagons (6-6 bonds) and the driving force is relief of steric strain.

The reaction is of importance in the field of chemistry because it allows the introduction of useful extensions to the fullerene sphere. These extensions alter their properties, for instance solubility and electrochemical behavior, and therefore widen the range of potential technical applications.

Buckminsterfullerene

Buckminsterfullerene is a type of fullerene with the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) that resembles a soccer ball (football), made of twenty hexagons and twelve pentagons, with a carbon atom at each vertex of each polygon and a bond along each polygon edge.

C70 fullerene

C70 fullerene is the fullerene molecule consisting of 70 carbon atoms. It is a cage-like fused-ring structure which resembles a rugby ball, made of 25 hexagons and 12 pentagons, with a carbon atom at the vertices of each polygon and a bond along each polygon edge. A related fullerene molecule, named buckminsterfullerene (C60 fullerene), consists of 60 carbon atoms.

It was first intentionally prepared in 1985 by Harold Kroto, James R. Heath, Sean O'Brien, Robert Curl and Richard Smalley at Rice University. Kroto, Curl and Smalley were awarded the 1996 Nobel Prize in Chemistry for their roles in the discovery of cage-like fullerenes. The name is a homage to Buckminster Fuller, whose geodesic domes these molecules resemble.

Carbon monofluoride

Carbon monofluoride (CF, CFx, or (CF)x), also called polycarbon monofluoride (PMF), polycarbon fluoride, poly(carbon monofluoride), and graphite fluoride, is a material formed by high-temperature reaction of fluorine gas with graphite, charcoal, or pyrolytic carbon powder. It is a highly hydrophobic microcrystalline powder. Its CAS number is 51311-17-2. In contrast to graphite intercalation compounds it is a covalent graphite compound.

Carbon is stable in a fluorine atmosphere up to about 400 °C, but between 420-600 °C a reaction takes place to give substoichiometric carbon monofluoride, CF0.68 appearing dark grey. With increasing temperature and fluorine pressure stoichiometries up to CF1.12 are formed. With increasing fluorine content the colour changes from dark grey to cream white indicating the loss of the aromatic character. The fluorine atoms are located in an alternating fashion above and under the former graphene plane, which is now buckled due to formation of covalent carbon-fluorine bonds. Reaction of carbon with fluorine at even higher temperature successively destroys the graphite compound to yield a mixture of gaseous fluorocarbons such as tetrafluorocarbon, CF4, and tetrafluoroethylene, C2F4.In a similar fashion the recently found carbon allotrope fullerene, C60 reacts with fluorine gas to give fullerene fluorides with stoichiometries up to C60F48.A precursor of carbon monofluoride is the fluorine-graphite intercalation compound, also called fluorine-GIC.

Other intercalation fluorides of carbon are

poly(dicarbon fluoride) ((C2F)n);

tetracarbon monofluoride (TCMF, C4F).Graphite fluoride is a procursor for preparation of graphene fluoride by a liquid phase exfoliation.

Carbon nanobud

In nanotechnology, a carbon nanobud is a material that combines carbon nanotubes and spheroidal fullerenes, both allotropes of carbon, in the same structure, forming "buds" attached to the tubes. Carbon nanobuds were discovered and synthesized in 2006.

In this material, fullerenes are covalently bonded to the outer sidewalls of the underlying nanotube. Consequently, nanobuds exhibit properties of both carbon nanotubes and fullerenes. For instance, the mechanical properties and the electrical conductivity of the nanobuds are similar to those of corresponding carbon nanotubes. However, because of the higher reactivity of the attached fullerene molecules, the hybrid material can be further functionalized through known fullerene chemistry. Additionally, the attached fullerene molecules can be used as molecular anchors to prevent slipping of the nanotubes in various composite materials, thus modifying the composite’s mechanical properties.Owing to the large number of highly curved fullerene surfaces acting as electron emission sites on conductive carbon nanotubes, nanobuds possess advantageous field electron emission characteristics. Randomly oriented nanobuds have already been demonstrated to have an extremely low work function for field electron emission. Reported test measurements show (macroscopic) field thresholds of about 0.65 V/μm, (non-functionalized single-walled carbon nanotubes have a macroscopic field threshold for field electron emission ~2 V/μm) and a much higher current density as compared with that of the corresponding pure single-walled carbon nanotubes. The electron transport properties of certain nanobud classes have been treated theoretically. The study shows that electrons indeed pass to the neck and bud region of the nanobud system.

Canatu Oy, a Finnish company, claims the intellectual property rights for nanobud material, its synthesis processes, and several applications.

Endohedral fullerene

Endohedral fullerenes, also called endofullerenes, are fullerenes that have additional atoms, ions, or clusters enclosed within their inner spheres. The first lanthanum C60 complex was synthesized in 1985 and called La@C60. The @ (at sign) in the name reflects the notion of a small molecule trapped inside a shell. Two types of endohedral complexes exist: endohedral metallofullerenes and non-metal doped fullerenes.

Endohedral hydrogen fullerene

Endohedral hydrogen fullerene (H2@C60) is an endohedral fullerene containing molecular hydrogen. This chemical compound has a potential application in molecular electronics and was synthesized in 2005 at Kyoto University by the group of Koichi Komatsu. Ordinarily the payload of endohedral fullerenes are inserted at the time of the synthesis of the fullerene itself or is introduced to the fullerene at very low yields at high temperatures and high pressure. This particular fullerene was synthesised in an unusual way in three steps starting from pristine C60 fullerene: cracking open the carbon framework, insert hydrogen gas and zipping up by organic synthesis methods.

Fullerene chemistry

Fullerene chemistry is a field of organic chemistry devoted to the chemical properties of fullerenes. Research in this field is driven by the need to functionalize fullerenes and tune their properties. For example, fullerene is notoriously insoluble and adding a suitable group can enhance solubility. By adding a polymerizable group, a fullerene polymer can be obtained. Functionalized fullerenes are divided into two classes: exohedral fullerenes with substituents outside the cage and endohedral fullerenes with trapped molecules inside the cage.

This article covers the chemistry of these so-called "buckyballs," while the chemistry of carbon nanotubes is covered in carbon nanotube chemistry.

Gallery of named graphs

Some of the finite structures considered in graph theory have names, sometimes inspired by the graph's topology, and sometimes after their discoverer. A famous example is the Petersen graph, a concrete graph on 10 vertices that appears as a minimal example or counterexample in many different contexts.

Higher fullerenes

Higher fullerenes are fullerene molecules consisting of more than 70 carbon atoms. They adopt cage-like structures made up of the fusion of hexagons and pentagons, with a carbon atom at the vertices of each polygon and a bond along each polygon edge. They are all black solids that dissolve sparingly in organic solvents to give deeply colored solutions.

List of graphs by edges and vertices

This sortable list points to the articles describing various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number) and χ' (chromatic index) are also sortable, allowing to search for a parameter or another.

See also Graph theory for the general theory, as well as Gallery of named graphs for a list with illustrations.

Lower fullerenes

Lower fullerenes are fullerene molecules consisting of fewer than 60 carbon atoms. They are cage-like fused-ring structures made of hexagons and pentagons, with a carbon atom at the vertices of each polygon and a bond along each polygon edge.

Nanocar

The nanocar is a molecule designed in 2005 at Rice University by a group headed by Professor James Tour. Despite the name, the original nanocar does not contain a molecular motor, hence, it is not really a car. Rather, it was designed to answer the question of how fullerenes move about on metal surfaces; specifically, whether they roll or slide (they roll).

The molecule consists of an H-shaped 'chassis' with fullerene groups attached at the four corners to act as wheels.

When dispersed on a gold surface, the molecules attach themselves to the surface via their fullerene groups and are detected via scanning tunneling microscopy. One can deduce their orientation as the frame length is a little shorter than its width.

Upon heating the surface to 200 °C the molecules move forward and back as they roll on their fullerene "wheels". The nanocar is able to roll about because the fullerene wheel is fitted to the alkyne "axle" through a carbon-carbon single bond. The hydrogen on the neighboring carbon is no great obstacle to free rotation. When the temperature is high enough, the four carbon-carbon bonds rotate and the car rolls about. Occasionally the direction of movement changes as the molecule pivots. The rolling action was confirmed by Professor Kevin Kelly, also at Rice, by pulling the molecule with the tip of the STM.

Organic compound

In chemistry, an organic compound is generally any chemical compound that contains carbon. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. Study of the properties and synthesis of organic compounds is the discipline known as organic chemistry. For historical reasons, a few classes of carbon-containing compounds (e.g., carbonates and cyanides), along with a handful of other exceptions (e.g., carbon dioxide), are not classified as organic compounds and are considered inorganic. No consensus exists among chemists on precisely which carbon-containing compounds are excluded, making the definition of an organic compound elusive. Although organic compounds make up only a small percentage of the Earth's crust, they are of central importance because all known life is based on organic compounds. Most synthetically produced organic compounds are ultimately derived from petrochemicals consisting mainly of hydrocarbons.

Organic solar cell

An organic solar cell or plastic solar cell is a type of photovoltaic that uses organic electronics, a branch of electronics that deals with conductive organic polymers or small organic molecules, for light absorption and charge transport to produce electricity from sunlight by the photovoltaic effect. Most organic photovoltaic cells are polymer solar cells.

The molecules used in organic solar cells are solution-processable at high throughput and are cheap, resulting in low production costs to fabricate a large volume. Combined with the flexibility of organic molecules, organic solar cells are potentially cost-effective for photovoltaic applications. Molecular engineering (e.g. changing the length and functional group of polymers) can change the band gap, allowing for electronic tunability. The optical absorption coefficient of organic molecules is high, so a large amount of light can be absorbed with a small amount of materials, usually on the order of hundreds of nanometers. The main disadvantages associated with organic photovoltaic cells are low efficiency, low stability and low strength compared to inorganic photovoltaic cells such as silicon solar cells.

Compared to silicon-based devices, polymer solar cells are lightweight (which is important for small autonomous sensors), potentially disposable and inexpensive to fabricate (sometimes using printed electronics), flexible, customizable on the molecular level and potentially have less adverse environmental impact. Polymer solar cells also have the potential to exhibit transparency, suggesting applications in windows, walls, flexible electronics, etc. An example device is shown in Fig. 1. The disadvantages of polymer solar cells are also serious: they offer about 1/3 of the efficiency of hard materials, and experience substantial photochemical degradation.Polymer solar cells inefficiency and stability problems, combined with their promise of low costs and increased efficiency made them a popular field in solar cell research. As of 2015, polymer solar cells were able to achieve over 10% efficiency via a tandem structure.

Spherical aromaticity

In organic chemistry, spherical aromaticity is formally used to describe an unusually stable nature of some spherical compounds such as fullerenes, polyhedral boranes.

In 2000, Andreas Hirsch and coworkers in Erlangen, Germany, formulated a rule to determine when a fullerene would be aromatic. They found that if there were 2(n+1)2 π-electrons, then the fullerene would display aromatic properties. This follows from the fact that an aromatic fullerene must have full icosahedral (or other appropriate) symmetry, so the molecular orbitals must be entirely filled. This is possible only if there are exactly 2(n+1)2 electrons, where n is a nonnegative integer. In particular, for example, buckminsterfullerene, with 60 π-electrons, is non-aromatic, since 60/2 = 30, which is not a perfect square.In 2011, Jordi Poater and Miquel Solà, expanded the rule to determine when a fullerene species would be aromatic. They found that if there were 2n2+2n+1 π-electrons, then the fullerene would display aromatic properties. This follows from the fact that a spherical species having a same-spin half-filled last energy level with the whole inner levels being fully filled is also aromatic. It is similar to Baird's rule.

Transition metal fullerene complex

A transition metal fullerene complex is a coordination complex wherein fullerene serves as a ligand. Fullerenes are typically spheroidal carbon compounds, the most prevalent being buckminsterfullerene, C60.One year after it was prepared in milligram quantities in 1990, C60 was shown to function as a ligand in the complex [Ph3P]2Pt(η2-C60).Since this report, a variety of transition metals and binding modes were demonstrated. Most transition metal fullerene complex are derived from C60, although other fullerenes also coordinate to metals as seen with C70Rh(H)(CO)(PPh3)2.

Truncated icosahedron

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.

It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.

It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces.

This geometry is associated with footballs typically patterned with white hexagons and black pentagons. Geodesic domes such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 ("buckyball") molecule.

It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated order-5 dodecahedral honeycomb.

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