I would like to thank Bernadette Bensaude Vincent for her help in improving this text, Jean-Noël Rouzaud and Kostas Kostarelos for their carbon lessons. A tribute is due to the memory of Millie Dresselhauss (1930-2017).

1The nanoscale science and technology funding initiatives launched in the 2000s were supported by grand narratives and slogans such as “there’s plenty of room at the bottom” or “shaping the world atom by atom” (IWGN, 1999). After the conquest of space, here is the conquest of the “nanoworld”. Populated with objects the size of few billionth of a meter in principle inaccessible to our senses, a distant world becomes a land of promises.

2In this dizzying world, carbon is king. Fullerenes, nanotubes and graphene (figure 1) are the star materials of nanotechnologies, the stuff their dreams are made of. These all-carbon molecules with iconic shapes have the power to attract thousands of researchers and millions of dollars and to dangle miraculous solutions to all kinds of engineering problems from health to environment and from electronics to mechanics (Pugno, 2006).

4This chapter argues that carbon nanomaterials are the product of a shift in the pattern of existential relations or “modes of existence” that defines them as objects that matter. This notion of “modes of existence” belongs traditionally to the philosophical field of ontology. This field aims at explaining change by what persists through time so that we can hold true beliefs about the world. It usually considers that there is first, being (substance, reality, nature, or whatever) and, only then, modalization of being, i.e. different ways of saying something about the same existing thing. For instance, for Aristotle I can speak of the same substance according to the category of quality, quantity, locus, relation, etc. I can even vary the degree of existence of that thing from the potential to the actual, but without ever going so far as to change the being of this thing, which is assigned to a well-defined identity. So in classical ontology the notion of “modes of existence” is usually taken in a weak sense. It refers to modifications of dictum, not of being.

5Here the notion of “modes of existence” is taken in a strong sense along the lines of French philosopher of art Etienne Souriau (1943), who advocated a “muti-realism”, which has recently been taken over by Bruno Latour (2010). Under this usage the modality attributes another way of being to that which it modifies. Carbon can be apprehended both as a chemical element, as a range of materials, of fossil fuels, as a tool for measuring our ecological impact (“carbon footprint”), etc. Its multiplicity of modes is nicely suggested by the chemical concept of “allotropy” (“different ways”), but it goes well beyond that of different chemical objects. Each mode typifies a different ontology for carbon, a different way of being in connection with writing (graphein in Greek, from which the word “graphite” is formed), a different way for carbon to write itself (through us) (Loeve & Bensaude Vincent, 2017). So instead of ontology this perspective lends itself better to what can be called “ontography” (Lynch, 2013).

6Between biography and ontology, ontography sets into narratives the modes of existence of singular things by focusing on the various inscriptions they afford to our material and symbolic practices. So for nanocarbons: they afforded a language of graphemes, surfaces of inscription, geometric structures, operations, and schemes that enabled multiple deterritorializations between bench and brand.

7The first three parts retrace the separate life-stories of the turbulent carbon filaments, the academic graphene, and the speculative carbon balloon. The final three parts recount their nano-renaissance in a world of low dimensions: 0D fullerene, 1D nanotubes, and 2D graphene. The conclusion draws an analogy between them and the three basic figures composing the world of painting according to Kandinsky (1929): point, line, and plane.

1. Doomed to Oblivion: Carbon Filaments

8In 1826, Dr. Hugh Colquhoun (1826, p. 2) writes an enthusiastic notice introducing the discovery of “several highly interesting states of aggregation of carbon, one of which is not only of a very singular structure, but also an entirely new form”.

10However, carbon filaments resurfaced in two different and independent contexts. First, in the course of bench experiments on “azotocarbures” (nitrocarbons), Alsatian chemist Paul Schützenberger, director of the École municipale de physique et de chimie de la ville de Paris and his son Léon, a chemical engineer graduated from the same school, observed “certain facts worthy of interest that pertain to the chemical history of carbon” (Schützenberger & Schützenberger, 1890, p. 774). To achieve full decomposition of cyanogene (N≡C−C≡N), they used a refractory vessel made of almost pure carbon (charbon de cornue) powdered with cryolite, a powerful dissolvent. The resulting carbon clogged the tube in a blackish felting presenting long thin filaments. Rubbed onto a sheet of paper, the substance leaves a dark trace reminiscent of “plumbago” (i.e. pencil lead: graphite). But which form of graphite was this “cyanogene coal”? Its oxidation products did not match with any graphite forms identified in the literature. So they cautiously concluded: “the filamentous carbon formed by the pyrolytic decomposition of cyanogene in the presence of cryolitic vapours constitutes a particular variety of carbon, neighbouring but not identical to electric graphite” (p. 777). But if the bench experiments on nitrocarbons were connected to the Schützenbergers’ views on organic pigments and artificial cellulose, filamentous carbon was not. Presenting no commercial value in a school and at a time when applications prevailed, the matter ends there.

11Carbon filaments reappeared later on in coke ovens. A communication by two industrialists, Constant and Henri Pélabon (1903, p. 706-709), read at the Académie des sciences de Paris by Henri Moissan reports the meticulous observation of “certain deposits with a threadlike appearance and constituting, through the entanglement of their wires, a genuine wool of carbon”. This “filamentary carbon” (carbone filiforme) forms in the part of the oven exposed most directly to the highest temperatures. It is “generally cylindrical”, sometimes with “very thin and tight packages of wires that seem to have arisen in some points of other wires of larger diameter” and “some wires that seem formed of a succession of rings”. Their length varies from 5 to 8 centimeters and their thickness between 1 and 15 microns. For the two industrialists the formation of such filiform carbon is undesirable because it is a sign that “the pace of the oven is pushed too far”.

12Although the Pelabon’s report quotes the Schützenbergers’ report, neither of them refer to the carbon filaments that Thomas A. Edison was exploiting with relative success in his incandescent light bulbs. A surprising silence since Edison’s invention had famously lighted the Paris World’s Fair in 1889. Carbon filaments were selected by Edison at the end of an extensive research program where he spent $40,000 testing 6,000 natural substances over the world before choosing a naturally fibrous organic material containing a large amount of cellulose, bamboo. In 1879, Edison filed a patent describing the processes for obtaining “metallized” carbon filaments by “flash carbonization” of bamboo, i.e., by means of the electric arc previously used for illumination in the first street lamps. “Metallization” also involved repeated electric arc treatment to get very pure (“metallic”) carbon. Consisting of twists of several wires measuring about ten microns in diameter, these carbon filaments were featured in the first brand of “Ediswan” light bulbs commercialized in the 1880s and were also used in street lamps.

13Thus, at the turn of the 20th century carbon filaments lived two parallel lives in two different technical systems. In coal and steel-making, where they could occasionally be transferred to the chemist’s bench, their formation was undesirable, a sign that something went wrong. In early lightbulbs they had a luminous and widely public “brand” existence (Ediswan, General Electric, Shelby…). Electric light was the star of the celebrations of technical progress. But their success was ephemeral. During the interwar period they were supplanted by tungsten on the ground that overheated carbon is sublimed and blackens the bulb after thirty hours of use.

14Carbon filaments fell into oblivion for a few decades before being recalled on stage thanks to Transmission Electron Microscope. TEM brought key information about their genesis not only because it is a powerful instrument (TEM provides rather static information) but because carbons bear the traces of their forming events (Rouzaud et al., 2015). However, using TEM did not change the mode of existence of the filaments: it provided knowledge about their conditions of formation so as to avoid it. In the 1950s British ceramic chemists studying the wear of blast-furnace brickworks reported TEM observations of helical carbon “vermicules” and pointed out the catalytic origin of this “unusual form of carbon” (Davis et al., 1953). The vermicules’ growth was catalyzed by iron particles and a clear relationship was established between the initial particles’ distribution and the growth and form of the filaments. A single metallic “speck” gives rise to a single carbon thread measuring as little as 10 nanometers, while a collection of “points” gives rise to many twisted threads forming a bigger “rope” of several microns so tough that it can penetrate deeply in the brick and provoke its rupture. The metal particles often stay attached to the filaments as a mark of their catalytic origin, as visible as black points in another TEM study (figure 2) published in Russian at about the same time (Radushkevitch & Lukyanovich, 1952). The paper went unnoticed by Western scientists. In retrospect, many have claimed that the micrograph, which shows a 50-nm wide inner cavity, is the first image of multi-wall nanotubes ever seen (Monthioux & Kuznetsov, 2006).

15“Filamentary growth of graphite has recently been rediscovered” reads a 1958 crystallography paper (Hillert & Lange, 1958). Focusing an entire instrumental arsenal on the filaments (TEM, polarized light microscopy, X-ray and electron diffraction), the crystallographers make clear that the filaments are hollow, built up of lamellar units bent into cylinders, single or multi-wall, with thicker threads formed by radial growth. They display a variety of shapes while having all the same crystalline structure, graphite. The thicker threads are produced by a two-step mechanism: first, catalyzed growth of an individual filament; second, catalyst-free pyrolytic carbon deposition thickening the fiber.

17Actually, these retrospective readings highlight less some obscure forgotten precursors prone to reduce the revolutionary claims of nanotechnologists than the obscuring effects of research programs. Indeed, in the 1950s catalytically-grown carbon filaments could have become a research field in its own right if the thin filaments had not been eclipsed by the bigger carbon fibers.

19One can observe without discovering. The famous Archimedean eureka does not proceed from mere visual evidence obtained through powerful instruments but from a context-dependent disposition of mind. Unlike chemists who examined the formation of the turbulent filaments in blast furnaces in order to get rid of them, Bacon was working for a chemical company producing high-volume polymer commodities, Union Carbide. These filaments, which could bend and kink while remaining unbroken, could serve to make bigger and even more robust materials.

20Yet reinforcing fibers became strategic during the Cold War period when major space and military programs required the manufacture of materials combining the lightness of plastics with the hardness of steel and the strength of ceramics. Bacon’s whiskers served right away as precursors of the “carbon fibers” industrially mass-developed since 1963 as a reinforcing structure for composite materials. Dubbed “the new steel”, carbon fibers won the competition among materials hands-down: with their high elastic modulus and low density and rigidity, when inserted in epoxy or polyamide resins they offered performance five or six times higher than aluminum or titanium alloys. Supersonic planes, helicopter tails and blades, rockets, Formula One cars, sports equipment… carbon fibers were strategic, high-performance and capitalistic – relatively expensive – materials for a proud industry employing armadas of materials scientists and engineers (Bensaude Vincent, 1998, p. 178-180).

21The success of carbon fibers increased the clandestine status of their precursors, the carbon filaments. Hitherto encountered as anomalous by-products of steel production, they were now eclipsed by “the new steel”. When found once again on carbon arc anodes (Wiles & Abrahamson, 1978), they were identified as “carbon fibers from about 4 nm to about 100 nm”. They were not different objects, but smaller objects of the same kind. Of course, they kept on popping up, but in rather old-fashioned fields such as Soviet “metallic science” (Nesterenko et al., 1982) or marginal research such as heterogeneous atmospheric chemistry (Buseck & Bradley, 1982). Again, they were quickly forgotten.

2. An Academic Material: Graphene

22By the mid-20th century graphite was a highly strategic material for the nuclear industry, with no less than 11 uranium-graphite-gas reactors built in France in the 1950-60s. While nuclear graphite occupied the forefront of the technomilitary scene (Walker, 1962), a more discrete but no less strategic existence opened up to graphite in the fabrication of intercalation compounds (Teissier, 2014, p. 253-254).

23Graphite is made of stacked layers held together by weak van der Waals forces, each layer constituted of hexagonally-arranged carbon atoms linked by strong covalent bonds. Because of its lamellar structure, graphite is able to take up atoms, ions, molecules, or even metallic alloys by expanding the space between the planes while maintaining its structure unchanged. Due to its chemical properties (both oxidizing and reducing) graphite exchanges electrons with its intercalated guest. These intercalation compounds are used in the manufacture of electrodes and batteries, such as the lithium-graphite compounds forming the negative electrode of lithium-ion batteries in our mobile phones and laptops.

25Boehm forged the term “graphene” (from graphite + benzene) in the 1980s for denoting a single layer of hexagonal carbon (Boehm et al., 1986). His definition was formally adopted in a 1994 IUPAC nomenclature for graphite intercalated compounds and officially endorsed in the 1997 Compendium of Chemical Terminology (McNaught & Wilkinson, 1997).

26Carbon filaments had no proper chemical name but were designated by a compound term (“graphite filaments”, “fibrils”, “vermicules”, or “whiskers”). On the contrary the IUPAC Compendium stressed that “it is not correct to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure”, and consequently that “the term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed”. Thanks to Boehm, the two-dimensional plane composing three-dimensional graphite had a name and a material identity of its own. “Graphene” became a common term to refer to the single sheet of graphite in the well-established and industrially-relevant field of carbon intercalation. Naming matters.

27Moreover, the name denoted something that many solid-state chemists and physicists were familiar with: the perfect chicken-wire monolayer structure they were trained to draw for decades. Thus, before earning a name of its own graphene pre-existed as a theoretical paper model for understanding the chemistry and physics of graphite. It was used to calculate the band structure of graphite from the 1940s onwards and provided a paradigmatic case study to teach band theory (Pisanty, 1991). It was a “paper material”, a structural component virtually involved in higher-dimensional graphite and an abstract model used for many scientific purposes, but materialized only in paper drawings.

28This did not prevent researchers from getting graphene crystals at the bench, either as “overlayers” grown by epitaxy on a metallic substrate, “pancakes on a plate” etched or sliced into individual layers, or in the form of rolls, cones, or folded like an origami, which minimizes their surface energy – each time in a particular disposition or supported by a surface, never in its free state. Thus academic graphene lived a kind of dual or Platonic existence as an intelligible form and an imperfect copy.

3. A Speculative Molecule: The Carbon Balloon

29If graphene was an academic material, the nanomaterial known today as “fullerene” (C₆₀) was first a speculative molecule. Structurally, C₆₀ is a truncated icosahedron, a semi-regular polyhedron belonging to the class of the Archimedean solids, which grants it interesting mathematical properties and makes it resonate with an entire esoteric tradition devoted to mathematical cosmography. The figure appears in particular in the illustrations realized by Leonardo de Vinci in 1509 for the De Divina Proportione of Luca Pacioli and in Kepler’s treatise Harmonices Mundi.

31In addition to Daedalus’ speculations, C₆₀ and bigger polyhedral carbon clusters were repeatedly postulated and subjected to theoretical calculations. Japanese computational chemist Eiji Osawa predicted that carbon’s structure would then be “superaromatic” (i.e., a conjugated aromatic structure that goes on and on and wraps back to itself) and thus probably stable (Osawa, 1970). He displayed a football image in the publication’s front page. Soviet researchers D. A. Bochvar and E. G. Gal’pern (1972) presented the first Hückel calculation on C₆₀ and came independently to the same conclusions as Osawa. Several other calculations followed (Davidson, 1981), including a paper entitled “Footballene: a theoretical prediction for the stable, truncated icosahedral molecule C₆₀” (Haymet, 1985). None of these theoreticians cited one another.

32Thus, kicked off by the erudite speculations of a fictitious inventor, there was a strange football world cup involving mutually ignorant players. But the carbon balloon, theoretically possible and stable, also represented a synthetic challenge that many chemists believed would soon be at hand. As Cyrus Mody (2008, p. 166) reports, Orville Chapman set several generations of UCLA graduate students to “futile attempts to synthesize ‘socchorene’ [sic] (I_h-C₆₀)”.

33Footbalene, soccerbalene, carbon balloon, soccerane, socchorene… Could we not find a more appropriate name for a molecule on the threshold of existence? In a brainstorming exercise in nomenclature, chemists Josep Castells and Felix Serratosa (1983) attempted to forge a tentative IUPAC name for the hydrogenated species C₆₀H₆₀: Hentriacontacyclo[29. 29. 0. 0^2,14. 0^3,12. 0^4,59. 0^5,10. 0^6,58. 0^7,55. 0^8,53. 0^9,21. 0^11,20. 0^13,18. 0^15,30. 0^16,28. 0^17,25. 0^19,24. 0^22,52. 0^23,50. 0^26,49. 0^27,47. 0^29,45. 0^32,44. 0^33,60. 0^34,57. 0^35,43. 0^36,56. 0^37,41. 0^38,54. 0^39,51. 0^40,48. 0^42,46]hexacontane!

34But the quest for the synthesis of the carbon balloon never gave any result, until others simply fell upon it.

4. Fullerene: The Third Allotrope Fallen from the Sky

35As an astrochemist, Kroto got interested in the mysterious new diffuse interstellar bands (“the DIBs”) detected in the 1970s by radiospectroscopy in the dark clouds of interstellar space. The molecular carrier of the DIBs was – and is still – an astrochemical enigma. From the DIB’s spectra it was hypothesized that they might be long acetylic carbon-chained molecules ([−C≡C−]_n) known for their controversial ability to form “carbine”, a hypothetical linear “third carbon allotrope” also known as chaoite or “white carbon” (Kasatochkin, 1967). The existence of carbyne as a solid was dubious because the longer these molecules are, the more unstable and even explosive they become. Kroto thought it was pure “carbon’s myth” (Kroto, 2010).

36However, in a 1977 study using the Algonquin (Ontario) radio telescope in which he participated, the team managed to successfully detect the vibration frequency of polyynylcyanides HC₅N (H−C≡C−C≡C−C≡N), HC₇N (H−C≡C−C≡C−C≡C−C≡N), and HC₉N, “the largest molecule yet detected in interstellar space” (Kroto et al., 1978). Kroto conjectured that their synthesis might originate from red giant carbon stars. To test this hypothesis he travelled in 1985 to Texas to work with Richard Smalley at Rice University. Smalley and his team had just built an apparatus that, Kroto thought, could nicely simulate the extreme plasma chemistry of carbon stars.

37The machine, dedicated to the production and study of metallic and semiconductor clusters (crystals of the size of a few atoms), had no proper name. It was referred to as the AP2, “the second-generation apparatus, a supersonic nozzle in which a high-energy laser strikes a rotating disc of graphite. A chaotic plasma forms at the graphite surface, provoking the vaporization of carbon atoms into a dense and high-speed helium flow. The carbon time-of-flight mass spectroscopy detection of the helium gas emitted by the machine showed very neat spikes indicating the presence of “something” very stable made of 60 carbon atoms and other residual carbon clusters. In 1984, another group at Exxon got the same spikes in a larger spectrum with a similar apparatus, built at Rice (Rohlfing et al., 1984). They were trying to understand the undesirable accumulation of carbon on catalysts. But they did not focus on these specific spikes.

38Kroto et al. (1985) disclosed the newcomer in Nature. Instead of proposing a structural formula or a molecular model like any chemistry paper, they were content with a photograph of a soccer ball on Texas grass and named the molecule “buckminsterfullerene” by analogy with the geodesic domes designed by the architect Buckminster Fuller. How could a metaphor ventured on the basis of a unique experiment convince Nature’s editors and demanding referees? “It was such a beautiful and perfect structure, how could it have been wrong?” Kroto said later (Seeman & Cantrill, 2016).

40Right after the release of their Nature report, the group was told that the structure had already been postulated and calculated several times, although they were the first to have claimed (since there was no experimental confirmation of the structure) its synthesis. The discovery of Daedalus’ speculations attracted Kroto’s attention to the consequences of the Euler-Poincaré characteristic for fullerenes, namely that all fullerenes of any size have 12 pentagons – a magic number for all the family of fullerenes!

41Fullerenes, however, were not so much hyped at the moment. They remained “a puff in a helium wind” (Harris, 1999), not a material but a trace detected in a gas obtained in a unique home-made instrument whose result could barely be replicated. Fullerenes could well have experienced a fate similar to the series of other putative “third carbon forms” like carbyne or hexagonal diamond (Bundy & Kaspers, 1967; Hoffmann et al., 2016) – namely, oblivion. But they really took shape and became a hot topic five years later when Wolfgang Krästschmer managed to produce solid C₆₀ (Krätschmer et al., 1990). Now the new form of carbon was materialized as a very pure (90% C₆₀ and 10% C₇₀) and beautiful plate-like crystal called “fullerite”. Since it was able to form a solid, a new carbon allotrope was added to graphite and diamond: fullerene, “the third man” (Kroto, 1993). Of course this “new” carbon was probably here long ago, widely distributed in the universe from stars to soot. But it did not exist as a technoscientific object until a method was established for producing macroscopic amounts of it with a simple technique accessible to any laboratory: a graphite electric arc.

42From then on, it multiplied and contributed to engendering a new world of low dimensions: the world of nanocarbons. Fullerene, being zero-dimensional, can be considered its starting point. The genesis of nanotubes – 1D – will now be examined, before turning to graphene – 2D. All these materials existed before: the turbulent carbon filaments, the academic graphene, the speculative carbon balloon. But by the 1990s their mode of existence shifted to technoscientific objects. As they came to interweave their life stories and mutually refer to each other, these objects have helped to unfurl a space of indefinite technological possibilities saturated by promises of radical novelty also known as the “nanoworld”.

5. Nanotubes: From Brand to Bench

43Hidden in the bulk of the carbon fibers, the filaments came out of them transformed. But only with the help of fullerenes could they stabilize their new mode of existence.

45Simultaneously, the attention of researchers was shifted from the set of causes leading to the formation of the filament (the catalytic decomposition of hydrocarbon) to the effect itself. For instance, Baker et al. (1975) identified “a new mode of filament growth (…) in which the complete detachment of a catalyst particle from the surface of the metal was not a necessary prerequisite”. They established two modes of filament growth: “tip growth” (known since the 1950s) and “root growth” (newly characterized). The catalyst activated the filament’s growth but in the case of “root growth” it possessed its own dynamics. In other words, the catalyst acted as an occasional cause of the filament’s growth, a trigger. Then the growing filament starts a life of its own with different possible arrangements occurring during the rolling of graphene: circular, spiral, or helical arrangements controlled by chirality (Nesterenko et al. 1982). As a result, the tubular carbon structures came to be considered for themselves, partly independently from their generating causes. Effects overtake defects. Effects matter.

46If catalytic triggering and thermal growth are two different processes, then it would also become possible to decouple them in order to better control the filament’s growth and produce well separated aligned tubules. This feat is claimed in the widely cited US patent claiming “cylindrical discrete carbon fibrils”, filed in 1984 and issued in 1987 to Howard Tennent of Hyperion Catalysis (Tennent, 1984). The patent covers a very large area, including multiple kinds of fibrils, compounds, and processes. In addition to applications in reinforcement of composites by embedding of the fibrils in a polymer matrix (a common, mainstream application of carbon fibers), other embodiments were claimed in which the fibrils could enhance the electrical or thermal conductivity of a material, increase the surface area of an electrode or a capacitor, provide a support for a catalyst, or shield an object from electromagnetic radiation. With such a large spectrum of applications (more or less reminiscent of the uses of nanotubes today), it is a root patent, referenced by more than 300 subsequent patents up to today – including by one of the many patents filed by Endo (2002) since his seminal 1986 vapor-grown carbon fiber patent (Endo, 1986). Since the mid 1990s, it has been referenced by many nano-related patents: “nanowhiskers”, “nanofiber”, “nanofibrils”, “nano-composites”, and then, by the turn of 2000, mostly “nanotubes”. In contrast with carbon fibers, the main industrial target is no longer structural applications but electrical ones: conductive materials for microelectrodes, batteries, coatings and inks, and electrochemical cells.

50The divorce with Bacon’s growth model for carbon fibers did not just cut the hierarchical link between the two objects (deterritorialization); it also provided a new reinterpretation of their relationship (reterritorialization). Since Bacon’s scroll model is false, then Bacon’s “graphite whiskers” should have been multi-wall nanotubes, not scrolls.

51Thus, Iijima deterritorialized the tubes from carbon fibers as well as from any field of application, and reterritorialized them onto fullerenes. His tubules were indeed finite structures closed by two hemispheres, and so fullerenes were both materially and symbolically capping the tubes. Thank to them their genesis was completed, looping back on itself. They could exist fully as individual objects in their own right (deterritorialization), while establishing structural and generative relationships with the other nanocarbons with which they appear in forming a family (reterritorialization). Fullerenes contributed to making the tubes more real and more attractive while, in turn, the tubes helped bring fullerenes the Nobel prize in 1996.

52The tubes also helped make graphene more prominent. The existence of graphene was already implicated, enveloped in that of fullerenes and nanotubes as the virtual plane necessary for their mental reconstruction, the surface required for their design, their generative matrix. This is visible in the diagram displayed in Iijima’s 1991 report (figure 5), as well as in two papers co-authored by Mildred and Gene Dresselhaus et al. one year later (Dresselhaus et al. 1992a, 1992b). The first explains the formation of fullerenes “by their projection on a honeycomb lattice” (i.e. graphene), and the second accounts for the structure (both topologic and electronic) of “graphene tubules” based on fullerenes.

53It was in these 1992 papers that Dresselhaus transposed the topological “zig-zag/armchair” language from organic chemistry into carbon materials science. For nanotubes, zigzag and armchair are two specific non-chiral topologies located at the endpoints of an indefinite range of chiral topologies having various helical pitches. But this armchair-or-zigzag character also gathers together the three main nanocarbons within a generative topology by which they all shape each other. The way C₆₀ fullerenes are cut affords armchair or zigzag tubes, and enucleating the end hemispheres of chiral nanotubes affords fullerenes of different specific geometries (figure 6). Similarly, rolling graphene in a zigzag or armchair way affords different specific tubes.

54In the period following the publication of Iijima’s observations a growing number of materials physicists and carbon scientists jumped on the electronic properties of nanotubes and embarked on the task of determining their band structure. But how to do so since the number of possible nanotube structures is theoretically infinite? Such was the role played by the nomenclature invented in 1992 by one of Iijma’s colleagues at NEC Semiconductors labs, physicist Noriaki Hamada (Hamada et al. 1992). Hamada’s notation (figure 7) was a crucial contribution, used right away in most of the nanotube papers that would follow.

55A combination of two numbers, m n, defines a vector on graphene lattice. This “roll-up vector” uniquely identifies all specific types of nanotubes. Zigzag nanotubes are those in which one of the two indices = 0, armchair nanotubes those where m = n, all other types are chiral. This vector determines the orientation of the tube circumference and its “helical pitch” α. Thus, each type of nanotube of any circumference, length, and wrapping angle can be specified by a simple index of only two numbers.

58Allowing the specifation of an infinite number of nano-objects having well defined properties, Hamada’s notation opened a field of possibilities that is beyond imagination. This partly explains the blossoming of promises about a new revolution in nanoelectronics that arose during the 1990s.

6. Graphene: Extreme Carbon Reborn

59We have seen that graphene was not discovered in Manchester University by Geim and Novoselov. The Nobel Prize in Physics awarded in 2010 honors their “ground-breaking experiments regarding the two-dimensional material graphene”. What were the experiments that marked its entrance into a new existence, the rebirth of graphene?

60The “Random walk to graphene” is nicely recounted in Geim’s Nobel lecture: two Russian physicists, tired about the monotony of solid-state physics and looking for fancier science in “Madchester”; an inexperienced Chinese PhD student; a Ukrainian scanning tunneling microscopist; and British scotch tape (Geim, 2010). Three initially unarticulated “thought clouds”: Geim’s own youthful dream of “metallic electronics”, his daze from all the fuss about carbon nanotubes, his reading of a thorough review of Dresselhaus on graphite intercalation compounds (1981), and his observation that despite the maturity of the field little was known about thin films of graphite. So Geim proposed a not-too-hard project for his PhD student: try to make graphite as thin as possible and see what would come from this idea. The suggestion to use scotch tape came from Oleg Shklyarevskii, an STM colleague from Ukraine working nearby on a fellowship. STM researchers customarily used highly-oriented pyrolytic graphite (HOPG) to prepare a standard reference test for STM imaging. In doing so, they would prepare a fresh surface of HPOG by removing a top layer with sticky tape, but they never paid attention to the stuff thrown away with the tape!

61However, they did not get the Nobel Price only for this “MacGyver exploit”. Whereas all previous incarnations of graphene were observational, they moved straightaway beyond observation and crafted a device showcasing the extreme tunability of its electric resistivity from a conducting to an almost semiconducting behavior. It was the end of the dual mode of existence of graphene: pure theory, impure incarnations. The two merged into a single new mode of existence. The “academic material” was turned into a technical device.

62The Manchester team also claimed to have isolated freestanding graphene (Novoselov et al. 2005), although Peierls and Landau stated that 2D crystals cannot exist in their free state. According to them, instead of getting graphene in a particular and context-dependent incarnation, they showed and valued graphene “for what it really is”:

After all, we now know that isolated monolayers can be found in every pencil trace, if one searches carefully enough in an optical microscope. Graphene has literally been before our eyes and under our noses for many centuries but was never recognised for what it really is. (Geim, 2010, p. 88)

63But what is it that graphene “really is”? First and foremost, graphene is a pure surface. Prior incarnations never involved freestanding graphene as a self-sustained surface. Now the surface was deterritorialized, freed from the volume, freed even from the “of ” (it is no more the surface of something… other than itself): a “surface in-itself” and no more an “overlayer” on the top of something or standing on something. As a scientific blogger nicknamed “Carboffiliac” put it:

It is clear that the graphene films that Boehm et al made are not freestanding graphene, since they are in a dilute alkaline solution – hence at best they are free-floating, not freestanding, and if you don’t know the difference, try standing on water, only few have accomplished that! (Carboffiliac, 2009)

64What does “freestanding” mean for those who, like Geim, Novoselov, and many Carboffiliacs, sing this “ode to one” (Geim, 2010, p. 90)? Strictly speaking, it is not about standing in empty space like the Holy Ghost. In Carbofilliac’s joke, Jesus, unlike the Holy Ghost, can stand on something (walking on water) while still being “freestanding” (maintaining His walking behavior instead of swimming). Similarly, “freestanding graphene” refers to the ability of graphene to be reterritorialized in various contexts, transferred from one kind of substrate or environment to another while still maintaining its distinctive high “quality”.

65Indeed graphene beats records in electron mobility, with conducting electrons behaving as massless particles much like photons, even in ambient conditions. For optics it absorbs light over a wide spectrum from infrared to ultraviolet. It is both nano and macro and can be engineered at both scales. It can potentially make membranes, flexible screens, conductive ink, transparent electrodes, magnetic shielding… In short, graphene fully meets the objectives of nanotechnologies as it is par excellence an “enabling material”. But even more is expected from it: a technological breakthrough not yet thinkable, for what distinguishes graphene from all known materials is less its performances taken one by one than the unique combination of “qualities” it affords.

66Remarkably, graphene scientists often speak about its electronic, mechanical, magnetic, optical, or chemical “qualities” instead of using the more neutral “properties”. No doubt the use of this term shows a concern for valuating graphene and often goes with superlatives: astonishing, mystifying, counter-intuitive (Geim, 2010, p. 89)^. But beyond the hyperbolic effects this term emphasizes that graphene is qualitatively different. For instance, the extremely high amplitude of the electric field effect reported in Novoselov et al. (2004) – “thousands of times more than the few per cent changes observed previously for any metallic system” – is said to amount to a “qualitative difference” (Geim, 2010, p. 88). Or else, the properties of the individual monolayer are so different from those of the multiple stacked layers composing graphite – starting with the fact that it is a surface with two sides, pushing to its extreme the “surface matters” motto characteristic of nanotechnology – that the variation is not a matter of more or less, but one of sameness and otherness.

67“Quality” is also an old technical term of metaphysics. Unlike essence or the nature of being (what something is), qualities designate the modes of being, the ways by which something is (how something is). Etymologically, qualities (qualia) refer to the state of something that is qua, “that which is like that”. It differs thereby from essential properties, that which define something. 17th century mechanistic philosophers distinguished between “primary” (solidity, extension, figure, movement…) and “secondary” qualities (colors, odors, heat, textures, but also emotions, feelings and values). Primary qualities are caused by the essential properties of the substance; they are inseparable from its existence but separable from the existence of the perceiving subjects. “Secondary qualities” are deemed merely subjective, inseparable from the existence of their perceiving subject but separable from the substance. What about graphene’s qualities?

68For a pure surface there is no more ontological difference between the material substance and its surface properties, between primary and secondary qualities, superficiality and depth. There is only a superficial ontology – an ontology of surface qua surface – wherein the stuff identifies itself with its qualities. Graphene has an intrinsic technical value as a pure surface, a “technicity” in the sense of Gilbert Simondon (1958), which is close to aesthetic beauty. When graphene champions speak of “recognizing graphene for what it really is”, they do not refer to an objective substrate that “stands under” (sub-stare) the surface and its properties. What graphene “really is” is not its essence but its high “quality”, a category that, in this context includes both being and value. The existence of a 2D structure in its free state is both an ontological reality and a technical opportunity, a mode of existence characterizing a “technoscientific object” (Nordmann, 2017). The objective and the subjective, the physical and the social meet on the same plane of existence – on the same surface, one might say.

7. Conclusion

69This chapter suggests that carbon has repeatedly attempted to attract the attention of researchers by deploying a variety of figures: filaments, whiskers, hollow tubes, soccer balls… but their dispositions and affordances remained buried in the black soot of furnaces and their small dimensions drowned in the mass of heavy industry. The nanotubes acceded to existence only in association with fullerenes as heads of a large family of nano-objects captivating thousands of researchers. In this process, everything happened as if the three main nano-allotropes had mutually been “giving assistance” to each other – which is generally not the case with materials, which are often positioned in fierce competition to conquer markets. Each of them has become more real and more attractive by referring to each other in a space of emotional and material transformations comparable to the system of basic figures that makes the world of painting according to Kandinsky (1929): the point (fullerene), the line (nanotubes) and the plane (graphene).

70The analogy conveys several meanings associated with this new mode of existence: that of artistic quality, the view of carbon as an artistic material instead of a dumb piece of matter. That also, of a system of generative geometry: just as for Kandinsky the line is the result of a living force applied to displace the point in a given direction and the plane is obtained by displacing the line, graphene can wrap into fullerenes or tubes, fullerenes can cap graphene cylinders into tubes, and tubes can be cut into graphene ribbons. Interobjectivity matters: just as the figures of painting can be described by their mutual relationships, the analogy allows one to pay – and to attract – attention to the relationships between objects, and not only between subjects and objects (Latour 1991, Harman 2011). Moreover, for Kandinsky, the point is not a mathematical abstraction; it has a certain shape, extension, and affective resonance with regard to its position relative to other objects. The line is a result of a living force with a certain direction and inflexion. As to the surface or “basic plane”, to Kandinsky it is not a mere substrate but a living matrix that requires the artist in order to be “fertilized” and to be felt “breathing”. Just as Kandinsky’s figures take on different affective tonalities shaping the sensibility of the beholder or the artist according to their mutual relationships, the configurations and dimensions of nanocarbons instantiate a subjective geometry. This emotional load may explain why fullerenes and nanotubes have (and surely will) remain molecules that matter even if they never deliver the tremendous applications promised over about twenty years of nanoscale research programs (Mody, 2008).

71Despite all the proofs of concept for nanoelectronics and the indefinite field of possibilities opened for their design during the 1990s, nanotubes face great difficulty in finding their way to real-world applications while still maintaining their identity as individual nano-objects. Graphene supplants carbon nanotubes in this respect because it offers a homogeneous material, whereas sorting a batch of carbon nanotubes with specified wall numbers and helicity is barely feasible at an industrial scale. However, due to its lack of band gap graphene is not destined to replace silicon. Basic technoscientific research has made considerable progress in recent years thanks to interdisciplinary mobilization but also because graphene has benefited from all the available nanoscale instrumentation as well as the know-how acquired in the chemical manipulation of carbon nanotubes. But graphene no longer has the right to exist as an academic material; it cannot remain a material on the shelf. Yet the number of cleanrooms, ultra-high vacuum instruments, postdocs, and European funding filling the “Home of Graphene” at Manchester University indicates the amount of means required to maintain graphene “freestanding”! Even if industrial production of large surfaces is possible, graphene cannot be introduced into macroscopic objects without a substrate and then it loses the affordances of the pure surface.

72This is to say that the announced revolution may be delayed… However, graphene is also impelling a new movement back from brand to bench. Indeed it is perhaps unique but it is generic. Its mode of existence as a pure surface reveals to the possibility in other elements as well. Although it displays a unique combination of qualities graphene is neither perfect nor even optimal for the applications for which it is intended. Depending on the specifications of each sector, research begins to lurch towards other 2-D materials. Performances of the same order can be expected of any material displaying strong bonding within the plane and weak connections between planes. Thus graphene now appears as the head of a new family of 2-D “gigamolecules” including boron nitride, tungsten disulphide, and metal carbides, sulphides or selenides. Two-dimensional ceramic oxides are being made. After deploying a wide range of possibilities and opening the way to a new class of materials, carbon can fade into the background and give way to new competitors.