- © 2014 by the Mineralogical Society of America
Fullerenes, carbon nanotubes, and graphene are nanometer-sized forms of carbon with the properties of almost ideal low-dimensional systems. These systems have been at the center of exceptionally intense scientific interest. They have been considered not only as objects of fundamental research but also as components in a wide range of possible applications. In popular science, their names are synonymous with nanotechnology.
Nowadays, we can create entirely new materials thanks to our ability to manipulate matter at the atomic level. In condensed matter, typical atom–atom distances are of the order of tenths of a nanometer (nm). The term nanotechnology refers to the study and exploitation of these new materials. The properties of nanometer-sized objects can be qualitatively different from those of ordinary matter because they result from a more direct expression of the laws of quantum mechanics. Indeed, the physics of these systems is said to be mesoscopic, in contrast to macroscopic, which applies to micrometer (μm)-sized objects.
In the last twenty years, carbon has come to play a leading role in materials science because of nanometer-sized systems known as fullerenes, carbon nanotubes (CNTs), and graphene. These systems have been the topic of a huge amount of scientific work owing to their potential for technological applications. Here, we will try to clarify the context and motivations behind this great excitement, focusing only on certain selected aspects.
THE ALLOTROPES OF CARBON
The two most common crystalline forms (allotropes) of carbon are diamond and graphite. Graphite is a stack of graphene layers weakly bonded to each other. Within a graphene layer, however, bonding is strong and results from sp2 hybridization (see later): each atom is coordinated to three atoms, resulting in a honeycomb planar lattice. Besides forming diamond and graphite, carbon atoms can aggregate in many different ways: as whiskers, carbon filaments, different kinds of amorphous carbon, glassy carbon, nanoporous carbon, etc. (see Beyssac and Rumble 2014 and Buseck and Beyssac 2014, both in this issue). It is unexpected that an element with only two stable, crystalline allotropes would give rise to such an astounding variety of systems. Indeed, starting in 1985, the discovery of previously unknown classes of nanometer-sized carbon allotropes—fullerenes and CNTs— changed the perspective. More recently, the isolation of one-atom-thick graphene membranes initiated a flurry of research.
Fullerenes, CNTs, and graphene are, basically, very stable macromolecules of sp2-hybridized carbon atoms (Fig. 1). The sp2 coordination is common in organic chemistry, and graphene can be seen as a giant polycyclic aromatic molecule. A CNT is a seamless tube formed by a rolled graphene ribbon, ideally forming a one-dimensional crystal. In fullerenes, the sp2 bond is further distorted, and the presence of twelve pentagonal rings (within the carbon hexagons of the honeycomb) allows the formation of a closed cage structure. The simplest fullerene is the C60 molecule. Note that, here, we use the term fullerene to denote only small cage structures, while CNTs and graphene are also referred to as fullerenes in the literature.
Kroto et al. (1985) discovered the C60 fullerene while studying carbon clusters produced by vaporization of graphite after laser heating. They were surprised to discover from their work with mass spectrometry that clusters consisting of exactly 60 atoms were, by far, the dominant species. It was hypothesized (and later confirmed) that the carbon atoms were arranged in a closed cage structure resembling the seams in a soccerball (football). Besides C60, other closed cage structures are possible; for example, C70 is relatively common. R. F. Curl, H. W. Kroto, and R. E. Smalley were awarded the 1996 Nobel Prize in Chemistry for their discovery of fullerenes. The 1985 discovery thrilled the scientific community. However, fullerenes remained mainly a curiosity until Krätschmer et al. (1990) found fullerenes in the soot produced by an electric-arc discharge from graphite electrodes. Indeed, the arc-discharge approach allowed the production of macroscopic quantities of fullerenes by means of an accessible and simple technique.
Since then, fullerenes have been studied thoroughly in several different contexts (see, for example, Dresselhaus et al. 1996), ranging from low-temperature superconductors to photovoltaic materials and from high-pressure physics to biological applications. They have a huge surface area per gram of material (~103 m2/g), and their chemistry has been extensively studied. Their cage-like structure has been used to encapsulate other materials, such as metals and molecular complexes. Different experimental conditions can lead to the growth of different kinds of fullerenes. However, in conditions favoring the formation of small carbon clusters, the C60 fullerene is generally the most abundant species. Various formation mechanisms have been proposed (Harris 2011), and the high yield of C60 is usually attributed to its particular geometrical structure. Indeed, graphene consists of hexagonal rings in a planar arrangement, and the incorporation of pentagons mandates curvature, while maintaining the three-fold connection of each atom. It can be demonstrated that twelve pentagons are required to obtain a closed structure and that C60 is the smallest structure containing twelve pentagons not adjacent to each other.
Fullerenes have been reported from various terrestrial and extraterrestrial sources, as reviewed by Buseck (2002). Fullerenes have been found in terrestrial shungites (enigmatic carbon-rich rocks with a complex metamorphic history), in rocks from impact structures, and from major stratigraphic boundaries, like the Cretaceous–Tertiary. Fullerenes have also been reported in carbonaceous chondrites. Most of these occurrences have been questioned, and there is as yet no explanation for the processes generating fullerenes in geological samples. Fullerenes should not be confused with various spherical and onion-ring structures, which are widespread in both geological and environmental samples derived from partial combustion of carbon materials (soots and charcoals) and from graphitization during burial of specific carbon precursors (see Buseck and Beyssac 2014).
CARBON FIBERS AND FILAMENTS BEFORE 1991
Before discussing CNTs, we need to remind the reader that carbon fibers and filaments have been studied since the 19th century. The modern era of carbon fibers started in 1956 when R. Bacon realized that by using an arc-discharge apparatus (similar to the one later used by Krätschmer et al. 1990) one could grow carbon fibers resembling cat's whiskers (Bacon 1960). Bacon's “whiskers” were up to 3 cm long and on the scale of a micrometer in diameter. Whiskers have amazing properties: they are 10 times stronger than steel in traction and, at the same time, can be bent without breaking. Whiskers are macroscopic fibers of graphitic carbon in which graphene layers are rolled parallel to the fiber axis. They are usually interpreted as scrolls, similar to the chrysotile fibers of the serpentine mineral group. Although they never became a commercial product, whiskers stimulated research in carbon fibers and remained a benchmark for the mechanical and thermal properties of carbon fibers developed and commercialized in the 1960s and 1970s. These macroscopic fibers are usually obtained after the carbonization (not necessarily graphitization) of filaments made from polymer precursors, such as rayon, polyacrilonitrile (PAN), and polymerized pitch.
The synthesis of carbon filaments from chemical reactions was developed well before the 1990s. Indeed, it has been known since the end of the 19th century that carbon filaments can be grown from the thermal decomposition of organic molecules. The first evidence of hollow, nanometersized carbon filaments was found in the 1950s (as discussed in Monthioux and Kuznetsov 2006). Systematic studies started in the 1970s with the work of R. T. K. Baker, M. Endo, and others. They were motivated by the need to avoid the growth of filaments in certain reactions and were generally focused on micrometer-diameter fibers. The study of these “vapor-grown fibers” continued through the 1980s and laid the basis for the chemical vapor-deposition methods used nowadays to grow CNTs (Harris 2011) and to synthesize diamonds. Chemical processing requires the interaction of a molecular precursor with a catalyst, usually, but not always, a metal. Precursors may be hydrocarbons, such as acetylene, but filaments can also be obtained from the disproportionation reaction of CO to CO2.
The “gold rush” of research on carbon nanotubes was triggered by a publication by Iijima (1991). Inspired by Krätschmer et al. (1990) and using a similar arc-discharge approach, Iijima found CNTs in the solid deposit formed on the negative electrode after the electric discharge (on the contrary, fullerenes were found in the soot collected from the apparatus walls). Carbon needles consisting of concentric, coaxial graphene tubes, more perfect and of smaller diameter than previously observed carbon filaments, were identified (Fig. 2a). These multiwall CNTs measured from a few to a few tens of nanometers in diameter and up to one micron in length. The smallest tube had a diameter of 2.2 nm, which corresponds to a ring of 30 carbon hexagons. The radial separation of the rolled graphene sheets matched the graphite interlayer distance. After a short time, CNTs consisting of a one-atom-thick wall (single-wall CNTs) were produced by introducing a metallic catalyst in the arc-discharge apparatus (Bethune et al. 1993; Iijima and Ichihashi 1993). These single-wall CNTs had diameters as small as 1.2 nm. The birth of CNT science was also accompanied by an increasing interest in other nanometer-sized carbon structures, such as carbon onions, nanocones, and nanoscrolls.
Since the turning point in 1991, CNTs have been at the center of an unprecedented research effort. This revolution was due to a change in attitude on the part of investigators: while in the 1980s researchers were mainly focused on finding improved macroscopic carbon filaments, from the 1990s attention turned towards the special properties related to the nanometric structure of the filaments.
NANOELECTRONICS AND OTHER APPLICATIONS
CNTs are 10 times stronger than steel and, at the same time, are lighter and more flexible. Considered as molecules, CNTs have the highest of all length-to-diameter ratios. Although current commercial applications are primarily based on the use of multiwall CNTs embedded in other materials, the properties of isolated single-wall CNTs are considered the most fascinating. As an example, specialists in nanodevice fabrication have been able to put metallic contacts at the two ends of a single-wall CNT and study how an electric current flows through the tube. CNTs are considered unique in this context. Let us compare a CNT with a small-diameter wire. In a wire, when the diameter is at least micron-sized, the electrons behave as point-like classical particles and, even when they are forced to flow along the wire by an electric field, they can move in all three spatial directions. Electrons are confined to move along the wire by collisions with its walls. In a CNT, however, the diameter is namometer-sized and, at these length scales, electrons cannot be considered point-like classical particles. Electrons are intrinsically confined by their quantum-mechanical nature to flow in the almost one-dimensional channel of the CNT, unconstrained by lateral collisions.
Electron transport can be very different depending on the CNT type. For example, a CNT can behave as a metallic wire or as a semiconducting wire, depending on the orientation of the graphene hexagons with respect to the tube axis. Semiconducting materials are the building blocks of microelectronics, and scientists have tried to build new kinds of electronic devices based on CNTs. Indeed, semiconducting CNTs have been used as the active component in transistors, which are the fundamental switches in electronic devices. The first CNT-based transistors were built by Tans et al. (1998) and Martel et al. (1998), and after a few years it was possible to construct CNT transistors with better properties than the standard silicon-based ones. Unfortunately, commercial applications of CNTs in nanoelectronics are unlikely in the near future given the absence of device-fabrication techniques that can be used in mass production.
The use of CNTs as field-effect emitters is an example of an application more likely to be available in the medium term. The principle of operation is simple: by applying an electrostatic voltage between two electrodes, one can induce the emission of electrons from the negative electrode. Sharply pointed electrodes are particularly efficient electron emitters; thus CNTs are ideal for this purpose. Macroscopic electron emitters are basic components of X-ray generators, which are commonly used in medical radiography and cathode ray televisions. CNTs can be used to make miniaturized X-ray sources and flat-panel displays in which an array of CNT emitters fire electrons towards luminescent pixels. Moreover, the chemistry of CNTs is well known. Nowadays, almost any desired chemical species can be attached to a CNT (functionalization), allowing, for example, the enhancement of the species' solubility in water and its biocompatibility. CNTs are also used as components in electrochemical “sensors” and “biosensors” (systems used to detect a certain molecule or a biological process and to convert the chemical event into a detectable signal).
A plethora of different methods have been developed to produce multiwall and single-wall CNTs, which can be single or aggregated in bundles. Current methods allow a good control of quality, characterized by high purity and an absence of defects. On the other hand, catalyzer-assisted fabrication techniques can be used, for example, to grow ensembles of parallel CNTs of similar length (the “nano carpets” used in field-effect devices) and to grow a single CNT at a specific location in a nanoelectronic device. However, in spite of these successes, the present lack of methods for mass production of tubes of the same length, diameter, and structure is the major obstacle to their commercial use.
Finally, we leave the quest for technological applications and consider CNTs simply as scientific “toys.” Automated, nanometer-sized machines are, of course, science fiction objects. However, CNTs have been used to build mechanical components of nanomachines. Barreiro et al. (2008; 2011) fabricated a nanoscale motor by using two coaxial CNTs that slide with respect to each other (Fig. 2b). The inner tube is long, is supported between two fixed points, and is shown in Figure 2b. The outer tube (which is shorter and has a larger diameter) can rotate and/or translate along the inner tube. A cargo can be attached to the outer tube (the outer tube is hidden by the cargo and is not visible in Figure 2b), and an electrical signal drives the motion, producing subnanometer displacements.
The graphene lamellae that make up graphite can easily be separated. Graphite has been “intercalated” and “exfoliated” into lamellae by chemical methods since the 19th century. Intercalation means that small molecules or atoms are inserted between the graphene layers. Graphite intercalated compounds (GICs) were the object of intense study in the 1970s, because GICs can display superconductivity and are used as negative electrodes in rechargeable lithium-ion batteries. On the other hand, chemists have known since the 19th century that the treatment of graphite with strong oxydizers can lead to layered compounds called graphite oxydes (GOs). The interlayer bonding of GOs is even weaker than in graphite; consequently, their layers can be dispersed in solution to yield molecular sheets. These sheets can be used as precursors for making graphene. In the 1970s, monolayer graphene and graphene composed of a few layers were obtained as a result of procedures such as (1) the reaction of organic molecules on a surface, (2) the segregation of carbon at the surface of a metal (segregation results from phase separation of the carbon dissolved in a metallic alloy upon changing temperature), and (3) growth on a silicon carbide surface after thermally induced sublimation of silicon (Dreyer et al. 2010). These methods, among others, are still used to produce graphene (Bonaccorso et al. 2012).
Starting in the late 1990s, several groups studied very thin graphitic films in the context of devices operating in the realm of mesoscopic physics. The ultimate goal of the research was to study electron transport. Since graphite can be exfoliated into extremely thin lamellae, the lamellae offered a system in which the electrons are confined in two dimensions (2-D). R. S. Ruoff, W. de Heer, P. Kim, C. Dekker, and others worked on these systems using different approaches. The turning point came when A. K. Geim and K. S. Novoselov showed that one-atom-thick graphene sheets could be easily obtained by peeling highly oriented pyrolitic graphite with sticky cellophane tape (Novoselov et al. 2004). This extremely simple method is known as the “Scotch tape” technique (Fig. 3a). Scotch tape was already being utilized to cleave the surface of graphite samples for use as a reference material in scanning tunnel microscopy experiments. Geim and Novoselov reversed the idea and used Scotch tape to obtain graphene sheets. The exfoliated, thin graphite sheets were deposited on an SiO2 substrate (an electrical insulator) and metallic contacts were applied to the graphene. It was clear from the beginning that the electrical conducting properties of the obtained devices were exceptional. This kind of experiment led to the observation of the “relativistic” quantum Hall effect (Novoselov et al. 2005; Zhang et al. 2005), the most striking demonstration of the pure 2-D nature of graphene electrons. Meyer et al. (2007) reported individual graphene sheets freely suspended on a microfabricated scaffold. Keim and Novoselov were awarded the 2010 Nobel Prize in Physics for their work on graphene.
After 2005, the number of scientific investigations devoted to graphene exploded. This excitement can be explained by several factors. Graphene was the first monoatomic membrane to be isolated. It is very stable. Its electrons behave as if they were in an almost ideal 2-D crystal. Indeed, graphene is considered the most ideal 2-D system studied so far. While the typical devices showing mesoscopic physics operate at extremely low temperatures, the quantum effects in graphene are robust and can survive at room temperature. Graphene's properties are among the most encouraging for research. Besides having a mechanical strength comparable to that of CNTs, electron “mobility” in graphene is very good and may reach record values (mobility quantifies how fast the electrons can travel under an applied electric field). As a membrane, graphene does not suffer from the geometrical limitation of CNTs. Once deposited on a substrate, it can be cut and patterned with electron beam lithography to make any desired device configuration (Fig. 3c, d). The popularity of graphene among scientists is also related to practical aspects. The Scotch tape technique is a very easy, accessible, and cheap way to produce good-quality and reproducible samples. By comparison, other known 2-D systems are obtained by building semiconductor heterostructure devices using complex and expensive techniques, such as molecular beam epitaxy. Although not suitable for mass production, the Scotch tape technique is still considered one of the best choices for laboratory production. Moreover, graphene samples can be characterized using easy and nondestructive techniques. For example, for a sample composed of several graphene flakes, one can single out, without ambiguity, one layer from the multilayer flakes simply by using an optical microscope (Fig. 3b).
We will mention just two examples of the many contexts in which graphene has been studied. Graphene is a very resistant membrane, and it is impermeable to other molecules. By drilling nanopores of a selected diameter, it is possible to use graphene as a molecular sieve (efficient sieves have to be thin, and graphene is the thinnest-possible membrane) for gas purification and even water desalination. Moreover, graphene may become the key component in a new kind of electric storage battery—a supercapacitor that can be recharged in seconds rather than in hours. Small supercapacitors have existed since the 1970s, and they usually need components with a high surface area, such as porous carbon. Graphene has a much higher surface area and may, indeed, revolutionize the field (El-Kady and Kaner 2013).
GRAPHENE'S ELECTRONIC PROPERTIES
In a solid, the state of an electron is determined by its momentum, p, and energy, ε. According to quantum mechanics, for a given momentum p, an electron can have a set of discrete energy levels, called electronic bands. In standard conditions, electrons tend to remain in the lowest energy states: below a certain energy, εF (Fermi level), the bands are occupied by electrons; above it they are empty. The bands immediately below and above εF are called valence and conduction bands, respectively. In general, the bands with energy near εF play a special role. For example, only electrons near εF can induce an electric current.
The electronic gap is the difference between the energy of the lowest empty state and that of the highest occupied one. The great majority of materials can be classified into three groups. Metals are materials in which the gap is zero. Because of this, even the application of a small voltage induces a current flow. In semiconductors and insulators the gap is not zero. In semiconductors, such as silicon, the gap is relatively small and current can be induced above a certain voltage threshold; in insulators, however, the gap is too big and no current can be induced. Graphite, which has an electronic structure similar to graphene's, belongs to a fourth category, called semimetal: in graphite the gap is zero, but the number of electronic states near εF is very small and, thus, graphite does not conduct electricity as well as a metal. Graphene is an even more extreme case than graphite. Indeed, in graphene, the gap is zero but, at the same time, the number of electronic states at εF (in an ideal sample) is exactly zero (Fig. 4b).
In actual samples, εF can be shifted, for example, by introducing charged impurities (dopants). In semiconductors this can induce significant modifications of the system, and this is the reason why semiconductors are so important in electronics. Indeed, by increasing εF, one increases the number of electrons that can conduct electricity; by decreasing εF, one can partially deplete the valence band in such a way that the electrical current appears as the result of the flux of positively charged particles (holes). Another way to change εF is to use an external electrostatic potential. Given a planar geometry one can put an electrode below or above the material. This electrode is called the “gate,” and it is separated from the material by an insulator. By applying a voltage to the gate, εF can be changed systematically (field-effect device configuration). In graphene, the gap is zero. Tuning the voltage on the gate electrode makes it possible to move continuously from a system in which electricity is carried by electrons to a system in which electricity is carried by “holes” (Novoselov et al. 2004).
ULTRARELATIVISTIC QUANTUM PHYSICS IN GRAPHENE
Graphene's electronic bands retain certain characteristics of the orbitals of an isolated carbon atom. An isolated carbon atom has six electrons, which are arranged in the orbitals called 1s, 2s, and 2p. The p orbitals can be distinguished into px, py, pz (z is the direction perpendicular to the graphene plane). The 2s orbitals together with the px and py orbitals form the sp2 hybridization and are associated with the bands that determine the strong in-plane covalent bond. The energy of these bands is well below the Fermi level, εF. On the other hand, the pz orbitals are associated with the bands nearest to εF. These bands do not directly participate in the covalent bond and are called π (occupied) and π* (empty). The π and π* bands have the same energy only for one particular value of the momentum, p0. In the vicinity of p0, the π and π* bands have a conic shape, which is commonly called the Dirac cone of graphene (Fig. 4a). In particular, the energy of the π* bands is ε = VF|p–p0|, while the energy of the π bands is ε = −VF|p–p0|, where vF is the slope of the cone (ε = 0 corresponds to εF in undoped samples). Although the overall shapes of graphite (or graphene composed of a few layers) bands have some similarities, the actual Dirac cone is present only in single-layer graphene.
The conic shape of the graphene π and π* bands has attracted much attention (Katsnelson 2012). To explain this, we must remember that the relation between energy and momentum, ε(p) (which is called “dispersion”), of a particle determines its dynamics. In the case of a particle traveling in a vacuum, when the particle velocity is much smaller than or near the speed of light, c, one distinguishes between nonrelativistic and relativistic motion. The term ultrarelativistic applies to zero-mass particles, which travel at the speed of light. In semiconductors, the conduction band dispersion near the gap is parabolic: ε = p2/(2m*). This energy–momentum relation is the same as that of an isolated electron with mass m* moving in a vacuum in nonrelativistic conditions. Even though m* is a parameter that is not equal to the mass of the electron, the movements of the two particles (in the solid and in the vacuum) are completely analogous. On the other hand, the conic dispersion of the graphene π and π* bands is the same as that of a massless particle moving in a vacuum in ultrarelativistic conditions. Even though graphene electrons travel at a speed much smaller than c, the movements of the graphene electrons and that of the massless particle are completely analogous. To understand why this fact has captured the imagination of so many scientists, we can mention that semiconductor heterostructures have been extensively used to build mesoscopic devices such as quantum wells and potential barriers (Mitin et al. 1999). These systems have been studied for several practical reasons. However, one of their most fascinating characteristics is that, in these structures, the electrons behave as if they were moving in the idealized conditions encountered in the classical textbook exercises in nonrelativistic quantum mechanics, (Landau and Lifshitz 1965). Indeed, semiconductor heterostructures have allowed the most direct implementation, in actual devices, of the principles learned by generations of physics students. Graphene has played an analogous role in providing a platform for implementing certain idealized experiments of high-energy physics (Katsnelson et al. 2006: Young and Kim 2009).
Carbon nano-objects have been studied in a wide range of contexts, and they have also been considered as components in many different technological applications. The study of the interaction of carbon nano-objects with the environment is receiving growing attention at various levels. On the one hand, carbon nano-objects may offer new solutions to various pollution problems; for example, they have been proposed for the removal of oil from contaminated water (Hashim et al. 2012) and as heavy-metal absorbers. On the other hand, their toxicity in the environment and to humans remains a major concern (Hyung et al. 2007; Chowdhury et al. 2013).
We acknowledge reviews by M. Hochella, P. Burns, D. Rumble, and O. Beyssac, and discussions with P. Kim and E. Balan. AB acknowledges financial support from a Beatriu de Pinós fellowship from the Generalitat de Catalunya.