# Carbon, a unique modele material for condensed matter physics and engineering science

A. Celzard, Vanessa Fierro

► To cite this version:

A. Celzard, Vanessa Fierro. Carbon, a unique modele material for condensed matter physics and engineering science. Fundamental and Applied Nano-Electromagnetics, Springer, pp.1-26, 2016, NATO Science for Peace and Security Series B: Physics and Biophysics, 978-94-017-7476-5. 10.1007/978-94-017-7478-9_1. hal-04962794

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CARBON, A UNIQUE MODEL MATERIAL FOR CONDENSED
MATTER PHYSICS AND ENGINEERING SCIENCE

SHORT TITLE: CARBON, A UNIQUE MODEL MATERIAL

ALAIN CELZARD*, VANESSA FIERRO

Institut Jean Lamour, UMR CNRS – Université de Lorraine

n°7198, ENSTIB, 27 rue Philippe Séguin, 88000 Epinal, France

**Abstract.** Although poorly known by the general public, carbon materials are everywhere in our life, and are present in multiple applications. But many more devices and systems might be based on carbon, considering the number of forms this element may take. In the present work, focus is given to black forms of carbon, and many structures are presented. Such different architectures, associated with different anisotropies and transport properties, may lead to materials presenting an outstanding number of distinct features. So broad range of characteristics is possible through the number of textures carbon may take. As far as the authors know, no other element can generate so many different materials.

Keywords: carbon materials, nanotexture, graphitization, anisotropy, physical properties.

**1. Introduction.**

Carbon is a unique element that allows preparing objects having extremely versatile and controllable properties. Carbonaceous materials can thus present chemical and thermal resistance, electrical conductivity, conductive or insulating thermal character, airtightness or permeability, porosity or not, surface areas sometimes exceptionally high, weightlessness, high mechanical resistance or ductility. This non-restrictive list of sometimes very antagonistic properties is the result of the outstanding variety of textures that the carbon

<footnote>* To whom correspondence should be addressed. Institut Jean Lamour, UMR CNRS – Université de Lorraine n°7198, ENSTIB, 27 rue Philippe Séguin, 88000 Epinal, France, alain.celzard@univ-lorraine.fr</footnote>
element may generate. To each particular texture, related to relative proportions of atom layers either parallel or corrugated, mainly with possible sp2 or sp3 hybridizing, corresponds one given functionality, and the modification of the texture induces that of the related properties [1].

For instance, the most suitable nanotexture for one given application can be achieved through the use of relevant precursors associated with convenient thermal history, as well as with appropriate post-treatments if required. Nanotexture has a direct impact on microporosity (pore size below 2 nm), whereas meso- (2 – 50 nm) and macroporosity (> 50 nm) can be controlled through the way the carbon precursors are processed. Both the process and the heat-treatment of well-chosen precursors therefore allow controlling size distribution, total volume, connectivity and morphology of pores. Besides, the surface of carbon can be functionalized, either for grafting various chemical species or for making it more or less acidic or basic, or more or less hydrophobic or hydrophilic. In addition to these key advantages that most other materials don't have, carbon is generally cheap, especially if biosourced precursors are used.

Whereas a huge number of published works now deal with the most recent and “fashionable” carbon nanomaterials, such as nanotubes, graphene and their relatives, most people ignore that many other carbon forms are available and worthy of interest, such as glasslike carbon and the innumerable carbon forms presenting intermediate disorder between graphite and amorphous carbon. To cite the late P.L. Walker, one of the “giants” of carbon science, carbon is indeed “an old but new material” [2].

In the present paper, many – but not all – carbon materials are presented, having quite different properties and, therefore, many potential applications. Fig. 1 thus shows a few examples recently obtained using natural polyphenols as carbon precursors [3]. From such broad range of materials, plenty of engineering applications and condensed-matter physics studies are possible but not allowed by any other single element.

<figure><img src="image_2.png" /><figcaption>Figure 1. Examples of carbon materials derived from tannins (natural polyphenols extracted from wood barks). From left to right: cellular vitreous carbon foam; porous carbon microbeads; emulsion-templated carbon monolith; N-doped carbon microspheres; ordered mesoporous carbon.</figcaption></figure>
## 2. General points about carbon materials.

Carbon materials are widespread in the industry, as a variety of common applications and devices are based on various carbon forms. To name only a few, industrial sectors consuming carbonaceous solids on a daily basis are:

- Electrometallurgy, using electrodes based on black ceramics, themselves made of graphite, carbon black and a more disordered carbon binder;

- Chemical engineering, using heat exchangers, seals and gaskets, catalysts and filters made of black ceramics again, flexible graphite, porous and activated carbons, respectively;

- Electrical and electronics industries, using conductive additives, inductors, resistors and other conductive parts for engines, made of carbon black, graphite, glassy carbon, anthracite, etc.

- Transports and sports, using very different kinds of composites based on carbon fiber, carbon black and various carbonaceous binders;

- Energy, using batteries based on carbon black and graphite, but also (super)capacitors and tanks for gas storage, all based on activated carbons.

Beyond these quite common uses consuming huge amounts of carbon everyday worldwide, new applications are emerging and are developing rapidly such as nanotechnologies, based on carbon nanotubes, fullerenes and graphene for sensors and transducers, transistors, fine chemistry, etc., and medical applications, based on glassy carbon, pyrocarbon, and carbon nanotubes for prostheses, drug delivery, imaging, theranostics, etc.

It might be useful to recall at this point of the paper, as various carbon forms have been named already, what these carbonaceous materials are. For a better understanding, it is advantageous to separate ordered carbons and disordered carbons, the latter family being by far the largest ones.

Ordered carbon structures may be classified as 3D (diamond and lonsdaleite), 2D (graphite and graphene), 1D (single-walled carbon nanotubes) and 0D (fullerenes), as shown in Fig. 2(a). But multilayered structures are also possible for 1D and 0D structures, such as multi-walled carbon nanotubes and multi-layer fullerenes (also known as nano-onions), respectively. It should be also noticed that even other polymorphs likely to appear under extreme pressure conditions have been observed or conjectured, but as they are either extremely rare, unstable or still controversial, no further mention will be given here to these materials [4]. A short comment should be made, however, about the many hypothetical, or poorly known, carbon allotropes assumed to be stable, according to some molecular dynamics studies. The list is too long for presenting them all, but the interested reader may refer to [5,6]. A few of them are pictured in Fig. 2(b). One of the most promising is the linear acetylenic carbon, whose outstanding predicted properties (it is assumed to be the world's strongest material [7]) will for sure make it the new carbon king. It'll also be
most probably the object of a future Nobel Prize, given the former series: Curl, Smalley and Kroto (1996) for fullerenes, Geim and Novoselov (2010) for graphene, whereas Iijima still is considered as a prime candidate for the Prize for his discovery of carbon nanotubes.

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>Figure 2. (a) Most common ordered carbon forms; (b) Examples of conjectured or poorly known carbon allotropes (adapted from [8] and [9]).</figcaption></figure>
3D ordered structures are based on purely sp3-hybridized carbon (cubic and hexagonal diamond), whereas ordered structures of lower dimensionality are all based on sp2-hybridized carbon. The combination of sp2 and sp3 carbons allows producing many defects as well as corrugated carbon sheets of limited extent, loosely packed on each other and disoriented with each other, and the incorporation of heteroelements. Among the latter, N, O and H are by far the most common. Such deviations from the previous ideal, ordered, (nano)structures give rise to a broad family of disordered carbons, and explain why most of the latter are porous. Depending on how the perfect stacking of aromatic carbon sheets is prevented within the structure, microporosity is indeed produced, and the presence of cracks occurring during the thermal treatment of the corresponding carbons may produce meso and macroporosity. However, meso and macroporosity can also be created by a lack of continuity in the carbon architecture, or be deliberately created through suitable preparation methods (see section 4). Similarly, microporosity can be advantageously open and developed through the process called activation, by which huge surface areas can be reached, leading to the well-known activated carbons widely used for their excellent adsorption properties. Fig. 3 presents a few examples of disordered carbons.

<figure><img src="image_5.png" /><figcaption>Figure 3. (a) Most common disordered carbon forms (not to scale) (adapted from [1]).</figcaption></figure>

Anthracite is almost graphite, but the carbon layers are distorted and defective, hence the presence of heteroelements (as well as ashes) and of slit-shaped micropores. Vitreous carbon is based on folded carbon layers so that closed porosity is trapped inside the structure. As its name suggests, vitreous carbon is a brittle, hard and shiny form of carbon, leaving a conchoidal feature once broken, very similar to glass indeed. Soot has an onion-like structure, but
based on facets made of graphite-like structural units. The latter, when packed
in a loose way, also give rise to what is known as coke or hard carbons in
general, being non-graphitizable, porous, materials. Sucrose char is one
example of such hard carbon. Carbon fibers are roughly graphitic, at least
locally at the nanoscale, but remain very disordered, although the carbon sheets
are oriented parallel to the fiber direction, therefore explaining their excellent
mechanical properties. Finally, amorphous carbon is a random combination of
sp4, sp3 and sp2 carbons.

Order in carbon structure therefore appears to be the key for controlling the
properties of carbonaceous materials, and hence their applications. A trivial
example consists in comparing diamond and graphite. Whereas both are made
of pure carbon, the former is isotropic, colorless, transparent, hard (for long the
hardest material) and brittle, highly thermally conducting but electrically
insulating, and the latter is highly anisotropic, black, shiny, soft and weak,
much less thermally conducting but electrically conducting. Different carbon
structures can be obtained, depending on the precursors, (i.e., the organic matter
that will be submitted to pyrolysis to yield the final material), on the preparation
method (i.e., on the presence of other chemicals, of pressure, on the value of the
heating rate ...), and on the highest treatment temperature (also called “HTT”).
Fig. 4 illustrates what typically happens when an organic precursor is heated in
an inert atmosphere.

<figure><img src="image_6.png" /><figcaption>*Figure 4.* Progressive organization of a carbonaceous material submitted to increasingly high temperatures (adapted from [10]).</figcaption></figure>
At moderate HTT, heteroelements and especially oxygen (pictured by
circles at the edges of carbon rings in Fig. 4) are first released as volatile
matters ($H_2O$, CO, $CO_2$, $H_2$, tars, etc.). This produces an increasing
aromatization of the remaining carbon network, with less and less non-
hexagonal carbon rings. As a consequence, the aromatic (flat) domains grow
and merge, and the corresponding sheets become closer and more parallel, i.e.,
more graphitic, as order appears in the 3rd direction. At the highest HTT,
graphitic crystallites can be obtained, provided that the organic precursor was
graphitizable. In some cases indeed, and even after heating at temperatures as
high as 3000°C, the disorder remains so high that the resultant material can
never be called graphite, which is characterized by an hexagonal structure based
on infinite carbon sheets with interlayer spacing of 0.335 nm.

However, the corresponding production of small crystallites based on
parallel aromatic carbon sheets induces a dramatic increase of thermal and
electrical conductivity. These very important physical properties can therefore
be significantly improved by such graphitization process, which can even be
achieved at moderate temperature in the presence of a suitable catalyst. Fig. 5
shows, for example, the nanotexture of a same char obtained by pyrolysis of
sucrose at 900°C under nitrogen flow, in the presence or not of nickel.

<figure><img src="image_7.png" /><figcaption>Figure 5. Catalytic graphitization induced by nickel catalyst. Left: totally disordered carbon. Right: graphitized capsules at different magnifications, showing the layered carbon structure.</figcaption></figure>

Before closing this introductory part, it is worth stressing that virtually all
organic materials can be carbon precursors, provided that the yield upon
pyrolysis is high enough. But the result, and hence the properties, dramatically
depend on the nature of the precursor and on the conditions of its thermal
treatment, leading to a very broad range of structures and of physical properties.
In the following, such huge variety of materials is presented through a selection
of examples, with the aim of showing that, depending on what the engineer or
the physicist wants to do or investigate, carbon materials can probably provide
solutions and answers.
### 3. Carbon particles.

As far as the authors are aware, no other material but carbon is able to provide a choice of electrically conducting particles being isotropic and isometric, isotropic but anisometric, anisotropic but isotrometric, or anisotropic and anisometric, as suggested in Fig. 6. As explained in the previous section, depending on the precursor and on how the carbon was prepared, obtaining different shapes, different conductivities and different anisotropies is possible.

<figure><img src="image_8.png" /><figcaption>Figure 6. Different valuable features that carbon particles may exhibit.</figcaption></figure>

A far from being exhaustive list of examples is now given. Dense, highly porous or even hollow carbon spheres, see Fig. 7, can be obtained by different methods so that different features in terms of average diameter, porosity, connectivity between the spheres and electrical anisotropy are accessible.

<figure><img src="image_9.png" /><figcaption>Figure 7. Various kinds of carbon spheres: (a) derived from tannins treated in hydrothermal conditions (see [11,12] for details); Spheron carbon black from Cabot (USA); (c) molecular sieves derived from tannin through suspension polymerization; (d) spherical graphite from Qingdao Sungraf Materials Co., Ltd (China); hollow spheres prepared: (e) from tannins by inverse polymerization; (f) from tannin solution by spray drying; (g) from biological templates.</figcaption></figure>
A very illustrative example of how different a “same” carbon can be obtained with very different particle sizes and different aggregation states is given by carbon black, see Fig. 8. In the context of carbon black, “structure” means “size of the particle chains”, as many carbon blacks are based on small spherical particles associated into necklace-like / grape-like agglomerates.

<figure><img src="image_10.png" /><figcaption>Figure 8. Various kinds of carbon blacks from Cabot (USA).</figcaption></figure>

Fig. 9 presents flattened (oblate) spheroids. Being made of highly disordered carbon, they are electrically isotropic. But when the particles become very thin, they are flakes. Such a shape is favored by the intrinsically bi-dimensional character of the layered (graphitic) structure they are made of, see Fig. 10. As a consequence, all materials presented in Fig. 10 are highly anisotropic. Similarly, elongated (prolate) particles are considered in Fig. 11, all having isotropic electrical properties. But, again, the extreme situation corresponds to fibers, short or long, straight or curled, macro or nano, as shown in Fig. 12. As soon as an anisotropic texture is involved, these carbon fibers are highly electrically anisotropic.

<figure><img src="image_11.png" /><figcaption>Figure 9. Oblate carbon particles: activated anthracite grains (see [13] for details).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 10. Carbon flakes: (a) Synthetic graphite from Timcal (Switzerland) (see [13] for details); (b) Natural graphite from Madagascar mine (see [13] for details); (c) flat micronic graphite (see [14] for details); (d) carbon nanodiscs prepared by pyrolysis of heavy oil.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 11. Prolate carbon particles (see [13] for details): (a) needle coke; (b) activated carbon from pine wood; (c) activated carbon from coconut shells.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 12. Carbon fibrous materials: (a) Carbon fibers with “Pan Am” (in reference to the famous logo of the former US airlines), radial or concentric structures; (b) *Pyrograf III* carbon nanofibers from Applied Sciences, Inc. (USA); (c) carbon nanotubes (adapted from [15]).</figcaption></figure>
Many other particles have also been reported, not really belonging to the former classes. Fig. 13 shows some examples, to which fluorescent carbon dots and graphene and their derivatives were intentionally not included for limiting the length of the list. Exfoliated graphite deserves a special mention as its porosity may be as high as 99%, and therefore its constitutive particles occupy a huge volume even if the corresponding mass of material is very low. Producing electrically conductive composites from such filler therefore requires low amounts of materials as the percolation threshold is also quite low [16].

<figure><img src="image_15.png" /><figcaption>Figure 13. Other carbon particles: (a) carbon micro- and nanocoils (from Microphase Co., Ltd., Japan, and adapted from [17]); (b) carbon nanohorns – also called nanocones – (from [18]); (c) carbon peapods (adapted from [19, 20]); (d) exfoliated graphite at different magnifications (more details in [21]).</figcaption></figure>

Composites prepared by dispersing carbon particles in polymer matrices may have many different electrical, dielectric and electromagnetic behaviors, depending on the many possibilities offered by such fillers. Not only particles of different shapes and different aspect ratios will lead to very different
percolation thresholds at constant filler amount, but the threshold can be changed through the aggregation state of the particles, their mutual orientation (which can be induced by extrusion or by application of a strong external magnetic field, for example), their distribution of sizes, their ability to curl or to maintain their initial morphology. And obviously, the composite behavior can be tuned through the amount of carbon filler inside the matrix and by blending various kinds of particles together. Fig. 14 schematically recalls the meaning of the percolation threshold, and how it is influenced by the filler aspect ratio.

<figure><img src="image_16.png" /><figcaption>Figure 14. (a) Formation of a conductive path by contact between filler particles by exceeding the percolation threshold (From TDA Research, USA); (b) Influence of filler aspect ratio: the higher the aspect ratio, the lower the percolation threshold, all other things being equal (adapted from [22]), unless high-aspect ratio particles are curled like in (c) (adapted from [23]); (d) Example of effect of aspect ratio on the percolation threshold: comparison of non-structured carbon black (CB) with carbon nanotubes (CNT) (adapted from [24]).</figcaption></figure>

Regardless the value of the percolation threshold, composites made from carbon filler may be either anisotropic or fully isotropic, depending on whether fillers are globally oriented along some direction or not, respectively, as shown in Fig. 15.

<figure><img src="image_17.png" /><figcaption>Figure 15. Composites based on the same filler having an aspect ratio different from 1. Whatever the intrinsic isotropic or anisotropic properties of the filler, orientation leads to overall anisotropy (left) whereas random orientation leads to overall isotropy (right).</figcaption></figure>
Finally, if the composites not only need to have special electrical / dielectric properties, but also have to present some given magnetic properties, using carbon filler doped with ferromagnetic nanoparticles is also possible. When the considered nanoparticles are small enough, and given their encapsulation inside carbon nanostructures, see Fig. 16, they can even be superparamagnetic, giving new physical properties to the corresponding composites.

<figure><img src="image_18.png" /><figcaption>Figure 16. (a) Magnetic nanoparticles embedded within a carbon nanotube (adapted from [25]); (b) Cobalt-based nanoparticles encapsulated in the hollow core of carbon nanotubes at different magnifications (adapted from [26]).</figcaption></figure>

4. Porous carbon monoliths.

Porous materials are massively used by industry in the form of thermal or acoustic insulators, adsorbents and absorbents, filters and catalysts, impact and vibration absorbers, etc. The most relevant applications of each porous material depend on both its physical and chemical properties, these properties being themselves function of its composition and on the nature of its porosity: more or less open and interconnected, more or less narrow. Such applications are most of the time related to the major actual challenges that are energy and environment. Various kinds of porous materials are indeed involved in devices allowing to store energy (thermally, electrochemically or in the form of combustible gases), or to save energy (heat flow management, thermal insulation, burners, supported catalysts ...). As for environmental conservation, porous materials are used for filtering or trapping liquid or gaseous pollutants, depending on their porosity.

In such context, porous carbons play a major role. Again, their unique ability of presenting highly diverse textures at both macro- and microscopic levels, as well as a tunable surface chemistry, make them particularly suitable in many energy and environmental applications, but also for special studies in physics. The control which can be exerted on their porosity, surface chemistry, surface roughness, etc., allows the preparation of ideal solids for comparing
measurements to theoretical predictions, in order to model porous media and optimize properties of applicative interest.

The most well-known carbon materials having pores at the macroscopic level are carbons foams. Depending on how the porosity is structured, i.e., whether it is based on struts or on roughly spherical cells, the corresponding foams are referred to as reticulated or cellular, respectively. In other words, cellular foams have pore walls, whereas reticulated foams don't. Fig. 17 shows some examples.

<figure><img src="image_19.png" /><figcaption>Figure 17. Carbon foams: (a) *Duocel* reticulated vitreous carbon foams (from ERG Corp., USA); (b) *POCOfoam* graphite cellular foam (from ORNL, USA).</figcaption></figure>

Most of the time, reticulated carbon foams are derived from reticulated polymer (thermoset) foams (e.g. polyurethane), hence the glasslike character of the corresponding carbon. These materials are called reticulated vitreous carbon (RVC) foams. On the other hand, cellular foams are frequently derived from thermoplastic, highly aromatic, precursors (e.g. pitch), hence their graphitic nature. Such materials are therefore cellular graphitic carbon (CGC) foams. Consequently, not only RVC and CGC foams have different electrical conductivities and permeabilities to fluids, but their thermal conductivities are also very different. Whereas RVC are quite good thermal insulators, CGC foams are excellent conductors [27]. But getting reticulated graphite foams or cellular vitreous carbon foams is also possible, provided that the precursors and the preparation methods are suitably chosen, as exemplified in Fig. 18.

<figure><img src="image_20.png" /><figcaption>Figure 18. (a) Reticulated graphite foam, prepared by hard-templating method using polyimide (adapted from [28]); (b) cellular vitreous carbon foam, prepared by foaming a resin based on natural polyphenols (adapted from [29]).</figcaption></figure>
The porosity of carbon foams can be tuned, for one given composition and carbon texture (vitreous carbon, in the examples of Fig. 19 and 20), so that highly accurate studies can be carried out. Mechanical, acoustic, thermal, and electromagnetic properties can therefore be investigated with an unprecedented accuracy in order to, for example, separate the contributions of different parameters characterizing the materials: overall porosity, cell size and morphology, inter-connectivity of cells, pore wall opening, structure and thickness.

<figure><img src="image_21.png" /><figcaption>Figure 19. Cellular vitreous carbon foams having different cell sizes (adapted from [30]).</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Figure 20. Tuning the interconnectivity of cellular carbons: (a) totally open porosity in tannin-based carbon monoliths prepared by emulsion-templating (adapted from [31]); closed-cells polybenzoxazine-based carbon foams (seen by scanning electron microscopy using secondary electron detector and backscattered electron detector: left and right, respectively).</figcaption></figure>

Porous carbon monoliths can also be made with much more calibrated structures, such as those presented in Fig. 21, or have hierarchical porous structures, whether macro/macro (i.e., with two very different cell sizes), macro/meso or macro/microporous, see Fig. 22. This kind of hierarchical structures is very important as soon as transport properties are required in combination with other phenomena such as filtration, catalysis, adsorption, etc. Additionally, the same carbon structures can be made more hydrophobic (by chemical reduction of grafting of relevant moieties) or more hydrophilic (by oxidation, for example) to be more suitable to one solvent or target molecules, or be functionalized for being more specific for adsorbing or converting some gaseous or liquid compounds.
<figure><img src="image_23.png" /><figcaption>Figure 21. Examples of “calibrated” cellular carbon structures: (a) vitreous carbon monolith with squared channels prepared by extrusion of phenolic resin (adapted from [32]); (b) vitreous carbon foams prepared by templating using sacrificial spheres of various sizes (same magnification).</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Figure 22. Hierarchical carbon foams: (a) macroporous / macroporous vitreous carbon, prepared from aerated tannin-based emulsions (see [33] for details); (b) macroporous / mesoporous vitreous carbon, prepared from both hard and soft templating (adapted from [34]); (c) macroporous / microporous vitreous carbon, prepared by physical activation of tannin-based carbon foams (see [35] for details).</figcaption></figure>

In most foams, the typical cell size is typically a few hundreds of microns large. When the cell size is below 100 µm and 1 µm, the corresponding materials are frequently referred to as micro and nanofoams, respectively. Fig. 23 and 24 are examples of such porous carbons, prepared by very different methods and from various precursors.
<figure><img src="image_25.png" /><figcaption>Figure 23. Carbon microfoams: (a) vitreous carbon prepared by ice-templating (adapted from [36]); (b) carbon gel activated in liquid phase (adapted from [37]); graphene foam produced by hydrothermal reduction of graphene oxide (adapted from [38]); few-layers graphene foam from glucose blowing (adapted from [39]).</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>Figure 24. Carbon nanofoams: (a) vitreous opal-like carbon prepared by PMMA microbeads-templating (adapted from [40]); (b) graphite nanofoam prepared by pulsed laser ablation of graphite in liquid nitrogen (adapted from [41]).</figcaption></figure>

Carbon gels are other highly porous monoliths, but having even smaller pores, mainly in the mesoporosity range. Their names refer to the main way they are prepared, i.e., by gelation of a polymer diluted in a solvent and subsequently dried and converted into carbon through pyrolysis. The drying process has a critical influence on the resultant porosity, which is best retained when capillary forces are minimized. For this reason, supercritical drying is generally preferred as it leads to what is known as aerogels, which are among the lightest materials ever. Most carbon gels are produced from phenolic precursors, and present a typical nodular structure, whose nodule size can be easily controlled by adjustment of the preparation pH, as shown in Fig. 25. Therefore, the porosity itself is also controlled by the initial pH.

<figure><img src="image_27.png" /><figcaption>Figure 25. Carbon aerogels at different magnifications: (a) phenolic carbon aerogel; (b) tannin-based carbon aerogels prepared at two different pHs (adapted from [42]).</figcaption></figure>
In some cases, carbon gels can also be directly prepared by hydrothermal treatment of condensable monomers, in the absence of crosslinker. Hydrothermal treatment is a powerful method for preparing many carbonaceous materials, depending on the experimental conditions (time, temperature, pressure, concentration, pH, additives, ...), and gels are only part of them, as shown in Fig. 26(a). Gels prepared this way may have a fractal structure, as the same image is obtained after a 10 times magnification, see Fig. 26(b).

<figure><img src="image_28.png" /><figcaption>Figure 26. (a) Carbonaceous materials prepared by hydrothermal treatment of tannins in different conditions, among them carbon gels (see [43] for details); (b) self-similar structure of such carbon gels.</figcaption></figure>

But aerogels have also been prepared by auto-assembly and mutual interlocking of carbon nanoparticles such as carbon nanotubes and graphene nanosheets, see Fig. 27. Unlike the previous phenolic carbon gels, such materials are flexible and can be reversibly compressed. Graphene aerogels are presently the world's lightest materials, with a density as low as 160 g m⁻³ [44].

<figure><img src="image_29.png" /><figcaption>Figure 27. Aerogels from: (a) carbon nanotubes (adapted from [45]); (b) graphene (from Graphene Supermarket®, USA).</figcaption></figure>
Whereas aerogels are mainly mesoporous but are highly disordered, getting ordered mesoporous carbons is possible through the suitable use of soft- templating. In such process, amphiphilic surfactants and especially triblock copolymers, able to auto-assemble into micelles of various geometrical configurations, play a major role. Depending on the conditions, the pores can constitute a periodic structure, e.g., lamellar, cubic, hexagonal, ..., having a well-defined lattice parameter, or behave as wormlike holes inside the material. But in both cases, these pores are characterized by an extremely accurate and perfectly calibrated size, see Fig. 28, characteristic of the original micelle dimensions and of the material shrinkage occurring during pyrolysis.

<figure><img src="image_30.png" /><figcaption>Figure 28. Ordered mesoporous carbons prepared by soft-templating from phenolic resins: strictly ordered (a) hexagonal; (b) cubic; and (c) cubic bicontinuous structures, prepared by evaporation-induced self-assembly (adapted from [46]); (e) wormlike calibrated pores prepared using tannins in hydrothermal conditions.</figcaption></figure>

To close the part related to highly porous carbon monoliths, a special mention should be given to activated carbons. These are carbonaceous materials that are highly disordered, and that comprise most of the time macro-, meso- and microporosity simultaneously, organized according to the hierarchical structure schematized in Fig. 29. However, depending on the process by which their porosity has been open and developed, called “activation process”, some activated carbons are mainly microporous, whereas others are mainly mesoporous. Microporosity and mesoporosity are most useful for adsorption in gaseous and in liquid phases, respectively. Whereas activated carbons are generally poorly selective adsorbents, functionalization of such materials can be useful for making the adsorption process more specific towards some given molecules of interest. This might be especially advantageous for trapping more or less acidic molecules, or for recovering heavy metals.
<figure><img src="image_31.png" /><figcaption>**Figure 29.** Simplified view of the hierarchical porous structure of activated carbons: micropores mainly account for the value of the surface area and are the most efficient for adsorbing gaseous molecules diffusing throughout meso- and macroporosity.</figcaption></figure>

The slit-shaped geometry of micropores in activated carbons, as pictured in Fig. 30, allows the overlap of adsorption potentials in the narrowest pores, thereby enabling the retention of supercritical gases such as methane and hydrogen. If all the carbon sheets were separated, making their surface available to adsorbates, the theoretical surface area would be as high as 2630 m² g⁻¹ [47]. Such value is indeed frequently reported and even widely exceeded by BET surface area measurements (based on not-so-realistic assumptions, therefore overestimating the reality), so that values up to 3500 m² g⁻¹ are not so rare in the literature. For this reason, activated carbons remained for long the materials presenting the highest surface area ever, until some metal-organic frameworks (MOFs) presented even higher values.

<figure><img src="image_32.png" /><figcaption>**Figure 30.** (a) Simplified view of the structure of activated carbons, based on a loose, disordered, packing of aromatic carbon sheets; (b) adsorption of a supercritical gas (e.g. methane at room temperature and pressure, represented by blue spheres) on the material: the density of the adsorbate is much higher in the narrower pores.</figcaption></figure>
Activation not only produces porosity but surface roughness. Such roughness can be characterized by a fractal dimension estimated from adsorption measurements. Innovative studies of fluid flow in porous structures such as those presented in Fig. 23 and 24(a) can therefore be carried out, and especially considering that such more or less rough surfaces can be made independently more or less hydrophilic / hydrophobic for interacting more or less with the fluids passing throughout the structures. Roughness may also impact the way acoustic waves dissipate inside the pores, and therefore change the acoustic properties of the porous structures. Finally, the very narrow pores created by activation lead to Knudsen effects for gaseous molecules trapped inside them, and therefore have a significant impact on the gaseous conductivity of porous structures, which is a major contribution to their thermal conductivity. Only carbon is able to generate porous structures whose surface area can be easily tuned from less than $1 \text{ m}^2 \text{ g}^{-1}$ to at least $1000 \text{ m}^2 \text{ g}^{-1}$ at constant cellular structure, thereby allowing unprecedented investigations in physics and engineering science.

**5. Engineered carbon forms.**

Even more rigorous studies can be carried out when porous structures are not only fully ordered but have the desired geometry with the desired lattice parameter. This might allow, for example, the strict comparison of properties of foam models, like those presented in Fig. 31, with those of true foams of similar cell size. Preparing such structures can be achieved through 3D-printing following a non-straightforward process as carbon cannot be 3D-printed directly. Either templates have to be used, or carbon needs to be processed with other compounds that have to be removed or pyrolysed afterwards (see [48] for details). Fig. 32 shows some examples of carbon structures prepared by use of 3D-printers. Even carbon aerogel could recently be processed by such additive manufacturing technology.

Other techniques were also successfully used for producing ordered periodic carbon architectures, such as those shown in Fig. 33. At the nanometer level, nanolithography or catalytic carbon growth on micropatterned surfaces proved to be efficient, whereas oriented photopolymerization led to 3D structures as well, although with very limited possible geometries.
<figure><img src="image_33.png" /><figcaption>**Figure 31.** Building blocks of the main foam models and their corresponding 3D packing: (a) truncated octahedron (with 8 regular hexagonal and 6 squared faces), known as Kelvin cell; (b) assembly of tetradecahedra (with 2 hexagonal and 12 pentagonal faces) and dodecahedra (with 12 pentagonal faces), leading to the Weaire-Phelan structure; (c) Gibson-Ashby cell.</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>**Figure 32.** Examples of 3D-printed carbon architectures: (a) using rapid prototyping extrusion, with a paste based on graphite dispersed in phenolic resin, PVB and solvent (adapted from [49]); (b) using direct ink writing of a suspension based on silica powder and graphene (adapted from [50]); (c) using rapid prototyping of photocurable resins, followed by hydrothermal impregnation of phenolic resin (adapted from [48]).</figcaption></figure>
<figure><img src="image_35.png" /></figure>

*Figure 33. Ordered periodic carbon architectures prepared by other methods: (a) micropatterned pillared graphene nanostructures based on highly aligned carbon nanotubes pillars on graphene film, synthesized using surface catalysis and vapor-liquid-solid mechanisms (adapted from [51]); (b) ordered porous carbon nanopillars synthesized using a negative SU8 (epoxy-A resin) photoresist employing interference lithography and additional crosslinking (adapted from [52]); (c) microlattice carbon structure synthesized based on micro-scale truss structures formed from self-propagating photopolymer waveguides (adapted from [53]).*

3D-printing applied to carbon materials, despite being an indirect process, therefore combines many advantages such as extreme flexibility in the geometry of as-produced architectures, reproducibility and accuracy. However, such architectures are always monolithic and can neither be recycled after use or repaired when broken. A significant advance from this point of view has recently been achieved through the production of 3D structures made of building blocks which can be assembled and dismantled like “Lego bricks” or replaced when damaged. Such bricks are vertex-connected octahedral based on carbon fibers impregnated with epoxy resin, formed into the shape of a flat X. Each X has a hole in the middle, which the leg of another X slots into. The resultant structure, shown in Fig. 34, is typically 10 times stiffer than other materials of the same density.
<figure><img src="image_36.png" /><figcaption>*Figure 34. Reversible carbon-based architectures: (a) building blocks based on interlocking carbon fibers; (b) views of structures built from such bricks (adapted from [54]).*</figcaption></figure>

**6. Conclusion.**

Although known from prehistoric times, carbon still remains associated with the highest present technologies. It has even been predicted by Kroto that, whereas the 20th century has been the age of silicon, the 21st century will be the age of carbon [55].

Carbon is indeed definitely not only an amazing element because of the infinite number of organic molecules it can generate, including the most complex ones based on which life exists. It is also outstanding because of the number of materials with irreplaceable properties based on it. But the carbon world is not only the world of diversity; it is also the world of superlatives. Hardest, strongest, lightest, highest, unique, etc., are terms that have been used all along this manuscript. Besides, although these aspects have not been too much detailed here, carbon was, remains and will be for long a key material at the basis of many nanotechnologies. Last but not least, we are presently in the era of carbon allotropes, and many exciting discoveries are to be expected.

Before such new allotropes are confirmed and mass-produced, more classical carbon forms can be used for building infinity of shapes with extremely diverse sizes. Besides, for such materials, surface chemistry, bulk nanotexture and overall structure can be tuned independently. Therefore, do physicists or engineers need a conducting material with special shape, special size, special structure, special properties (anisotropy, electrical conductivity ...)? Alone, or doped with different elements, plated with metals or with a semi-conducting or insulating coating ...? For sure chemists, based on the carbon element, will be able to prepare such materials.
## ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support of the CPER 2007–2013 “Structuration du Pôle de Compétitivité Fibres Grand’Est” (Competitiveness Fiber Cluster), through local (Conseil Général des Vosges), regional (Région Lorraine), national (DRRT and FNADT) and European (FEDER) funds. This research was also partially supported by FP7-PEOPLE-2013-IRSES-610875 NAmiceMC and Belarus-CNRS project BRFFI F13F-004.

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