1. Preface

2. A history of Carbon Nanostructures Discovery

3. The structure of Nanocarbon Particles

3.1. Fullerenes

On an initial stage of the fullerene research the object were assigned to the class of clusters, while at a later time they became to consider as macromolecules, because as distinct of clusters the posses a strictly definite structure. The most stable and thus the most spread fullerene molecule is С₆₀. The structure of this molecule (see Figure 1) presents the truncated icosahedron consisted of 20 hexagons and 12 pentagons in which vertices carbon atoms are situated. The distance between neighboring carbon atoms accounts 0.142 нм. Therewith each carbon atom belongs to two hexagons and one pentagon so that all the carbon atoms so that the chemical state of all of them is similar. The direct confirmation of such a structure can be seen from Figure 7 presenting the image of С₆₀, obtained by means of a field ion microscope [22].

One more proof of the perfect structure of fullerene molecule С₆₀ presents the spectrum of the nuclear magnetic resonance (NMR) containing only one line (Figure 8) [23]. In distinction from this, the NMR spectrum of C₇₀ molecule, the structure of which is less perfect, contains 4 lines. This indicates that the carbon atoms in this molecule may be found in one of four chemical states.

Рис. 8. Спектры ядернoгo магнитнoгo резoнанса мoлекул фуллерена С₆₀ (сверху) и С₇₀ (снизу) [23].

Рис. 8. Спектры ядернoгo магнитнoгo резoнанса мoлекул фуллерена С₆₀ (сверху) и С₇₀ (снизу) [23].

An appropriate representation of the fullerene structure is based on the Shlegel diagram which is an image of the molecule extended onto a plane. Figure 9 shows the Shlegel diagram of С₆₀ molecule. As is seen the molecule possesses the symmetry relating to the axis passing through the centers of pentagons situated in opposition to each other. Turning the molecule around this axis by the angle aliquot to 72^o does not change its structure.

The fullerene family includes along with C₆₀ and C₇₀ molecules also a set of mote large molecules. The molecule C₇₆ the structure of which is presented on Figure 10 can serve an example of such molecules. The main structural element of higher fullerene molecules is the hexagon, as in C₆₀ molecule. The length of the site in such a hexagon is close to 0.142 nm, however the magnitude of this parameter can depend slightly (within 1%) on the molecule size and the position of the hexagon in the structure of the molecule. Along with hexagons the number of which depends on the molecule size, the structure of fullerene molecules includes 12 pentagons that are responsible for the closed structure of the molecule.

Higher fullerene molecules do not possess such a high symmetry as С₆₀ molecule, therefore they are less stable and their content in the fullerene containing soot is much lower than that of C60 molecule. Experiments indicate that in conditions of the electric arc with graphite electrodes only fullerene molecules with even number of atoms are observed. The higher fullerene family contains such molecules as С₇₆, С₇₈, С₈₀, С₈₄, С₈₆ etc. One of the peculiarities of higher fullerene molecules is in a large number of isomers distinguishing by different structural features. The most stable isomer modifications of higher fullerene molecules are subjected to the rule of isolated pentagons. In accordance with this rule each pentagon engaged into the fullerene structure should be surrounded only by hexagons. The structures subjected to the isolated pentagon rule are characterized by an enhanced stability and only such structures were observed in experiments. The values of the energy required for formation of such isomers differ from each othe only slightly differ from each other, so that various isomers form with close probabilities in gas discharge with graphite electrodes. Thus it is shown in the work [24] that the number of possible isomer modifications of fullerene molecule С₈₄ reaches 51592. Therewith the number of the most stable modifications satisfying the rule of isolated pentagons accounts 24. There has been managed to extract experimentally only 11 from those isomers [24]. Figure 11 presents the Shlegel diagrams of nine from these isomers [24].

A possibility to add various atoms and radicals to fullerene molecules expands considerably the class of fullerenes with different structures. The points of adding various adducts to the fullerene cage can be found in different positions relating to each other, which is reflected on properties of the molecule produced. The character of the distridution of adducts over the surface of fullerene volecule and interconnection between such a distribution and physical and chemical properties of molecules are the subject of many studies [25].

Endohedral Fullerenes

Fullerene molecules possess quite large cavity which is able to enclose one or several atoms or molecules. Such objects are called “endohedral structures and designated by the formula A_m@C_n, where А is the atom situated inside the fullerene cage. Relatively small size of hexagonal and pentagonal rings, making up the structure of fullerene molecules does not permit escaping atoms from the fullerene cage and provides the stability of endohedral structures. Fullerene molecule С₆₀ accomodates only one atom. Metallofullerenes M@C₆₀ where M are the metal atoms such as Ca, La, Y, Ba, Ce, Pr, Nd, Eu, Gd, Er were observed experimentally [26]. The family of metallofullerenes on the basis of higher fullerenes is considerably richer. These molecules possess more spacious cavity which can be filled with several atoms. There are a lot of publications on observation and study of endohedral fullerenes the cavity of which is filled with several metals or molecules. Thus the family of metallofullerenes on the basis of the higher fullerene molecule includes such structures as La₂@C₈₀, Sc₃N@C₈₀, Er_xSc_3-xN@C₈₀, Tm₃@C₈₀, Dy₃N@C₈₀, Tb₃N@C₈₀, Lu₃N@C₈₀, Gd₃N@C₈₀, Gd_xSc_3-xN@C₈₀, Y₃N@C₈₀, CeSc₂N@C₈₀, ScYErN@C₈₀ and many others. A special interest present metallofullerene molecules having the formula A_3-xB_xN@C_2y where x is an integer between 0 and 3, A and B are metal atoms and y takes the value 34 or 39–44. Such molecules a called as “trimetasphere”. Due to the chemical bond between nitrogen and metal atoms such molecules possess an enhanced stability and can be synthesized in a macroscopic quantity [27].

A distinctive peculiarity of metallofullerene molecules is the trend of valence electrons belonging to metal atoms to transfer onto the outer surface of fullerene molecule. Therefore inside the fullerene cage are found not atoms but metal ions. The Coulomb interaction between these positively charged ions with the negatively charged envelope results in the displacement of ions from the central position and imparts to the metallofullerene molecule an ssymmerty structure with a large dipole momentum. Figure 12 presents some of such structures.

In distinction on metallofullerene molecules the endohedral fullerene molecules containing nonmetal atoms possess the spherical symmetry. As an example can be considered the molecule N@C₆₀, in which the potential of interaction nitrogen atom and fullerene cage have the spherical symmetry and takes the minimum value in the centre of the molecule. (Figure 13). Calculations imply that the rare gas atoms occupy also the central position inside the fullerene cage.

3.2. Carbon Nanotubes

The ideal carbon nanotube (CNT) presents a hexagonal graphite layer scrolled into a single-layer or multi-layer cylindrical tube. Figure 14 presents idealized images of a single layer and multi layer CNTs. The main element of a nanotube is an elongated cylindrical surface. The ends of the cylinder present a semi-spherical structure consisted of hexagons and pentagons. Such a structure can be considered as a half of fullerene molecule. The structure of single layer nanotubes observed experimentally differs from the above-described idealized picture in many respects. First of all this relates to the ends of nanotubes the structure of which is far from the ideal semi-sphere as it follows from numerous observations. It is determined by peculiarities of formation of such structures.

3.2.1. Chirality

The result of scrolling a hexagonal graphite plane into a cylinder depends on the angle of this plane relating to the nanotube axis. The orientation angle specifies the chirality of the nanotube which governs, in particular, its electric characteristics. The property of chirality is illustrated on Figure 15 showing in what manner scrolling a rectangular fragment of a hexagonal plane at a different angle relative to the axis of cylinder results in various structures. The nanotube chirality is denoted by the pair of symbols (m; n) showing the coordinates of the hexagon on the graphite plane, which has to be superimposed on the origin hexagon as the result of scrolling. Some of these hexagons are shown in the Figure 15 along with related labeling. Another way of chirality labeling consists in indication of the angle a between the direction of a nanotube scrolling and that of the common side of two adjacent hexagons. Amongst different possible directions of nanotube scrolling are distinguished those, for which bringing of the hexagon (m; n) into coincidence with the origin requires no distortion in its structure. These directions correspond to the angles α = 0^o (armchair configuration) and α = 30^o (zigzag configuration). Such configurations are labeled by the chirality indices (m; 0) and (m; m), respectively. Scrolling the plane under an arbitrary angle results in the structure of a specific chirality.

The interconnection between the chirality indices (m, n) and diameter of the nanotube D is illustrated by Figure 16 and is expressed by the relation

D = d(2m² + 3n² + 3mn)^1/2/π,

(1)

where d = 0.142 nm is the distance between the neighboring carbon atoms in the hexagonal structure. The chirality angle α is expressed through the chirality indices through the following relationвыражается через индексы хиральнoсти следующим сooтнoшением

α = arctg{3[3m/(m + 2n)]^1/2}.

(2)

3.2.2. Structural Defects

The hexagonal surface of a nanotube is rather not perfect, it can contain numerous defects. Since hexagons making up the surface of a nanotube contains double bonds, it is possible adding various radicals to this surface during the synthesis CNT. The sort of the radicals depends on the method and regime of the synthesis. Between such radical should be mentioned firstly -О, -СО, -ОН. The existence of added radicals not only changes the chemical state of the nanotube, but also disrupts its cylindrical structure. Along to the structural defects caused by the presence of added radicals there exist also vacancy defects that show themselves in the absence od carbon atom in one of hexagons. One more type of defects in the CNT structure relates to the appearance of the pair pentagon-heptagon in the hexagonal lattice. Such defects are called as Stowne-Walls defects. Figure 17 presents the nanotube structure with the Stone-Walls defect. Stone-Walls defects disrupt cylindrical geometry of the nanotube and change its chirality. Thus the nanotube with the Stone-Walls defect presents a heterostructure consisted of elements with different chirality and therefore with different electron characteristics.

Figure 17. A nanotube with the Stone-Walls defect.

Figure 17. A nanotube with the Stone-Walls defect.

Structural defects of the CNT surface are characterized by the energy E_f, required for their formation. The value of this energy can account several eV, so that the probability of the defect formation which is proportional to exp(-E_f/T) is much less than unity. The larger nanotube the hidher the probability of defect content. The number of defects enhances with the rise of the synthesis temperature.

3.2.3. Multi Layer Nanotubes

Along with single layer nanotubes there exist also the nanotubes consisted of several concentric cylinders inserted into one other. Such nanotubes are called as multi layer CNTs. The inter-layer distance in multi layer nanotubes accounts about 0.34 nm which is close to the interlayer distance in crystalline graphene. The diameter of multi layer nanotubes can reach several tens nm, which corresponds to the number of layers of the order of a hundred. In some cases several layers inside the nanotube are absent and the nanotube contains a large cavity which can be filled with some substance.

4. Carbon Nanoparticles Production Methods

4.1. Fullerenes

4.1.1. Electric Arc Synthesis

The main method of large scale fullerene production is based on the usage of the arc discharge with graphite electrodes. The discharge burns as a rule in an Ar atmosphere at a pressure of about 100 Tor. Figure 22 presents the schema of the facility used for fullerene production. This facility designed by W. Krätchmer et al. in the Max Plank Nuclear Physics Institute (Heidelberg, Germany) includes a gas discharge chamber with graphite electrodes. The chamber has usually water-cooled double walls. Arc burning at a current of the order of 100 – 200 А results in heating and thermal sputtering graphite anode. A gas discharge setup is equipped as a rule with a device for automatic stabilization of the inter-electrode distance which is changed in result of the thermal disruption of electrodes. At a stable inter-electrode distance the arc current is also stable. A soot forming due to graphite sputtering is deposited on the walls of the gas discharge chamber. This soot contains up to 10% fullerenes at the optimal conditions.

4.1.2. The Mechanism of Fullerenes Formation

The question arises on the mechanism of fullerenes formation in the electric arc. The contemporary literature contains many models, describing the self-organization of carbon atoms into a spheroidal structure

e, there is no a clear sketch of this phenomenon until now. One of approaches to the solution of this task has been proposed in Ref. [35] where fragments С₁₀ are considered as a building element for formation of С₆₀ molecule. This fragment presents a pair of joint hexagons. Figure 23 illustrates the mechanism of formation of the semisphere which is a half of fullerene C₆₀ molecule.

Figure 23. A possible mechanism of assembling the fullerene С₆₀ molecule from graphite fragments: a)the result of assembling three graphite fragments С₁₀; (b)adding fragment C₁₀ to the result of joining three such fragments which results in a closing the plane structure into a spheroidal one. The C₆₀ molecule Мoлекула С₆₀ is resulted at adding more two С₁₀ fragments to this structure [35].

Figure 23. A possible mechanism of assembling the fullerene С₆₀ molecule from graphite fragments: a)the result of assembling three graphite fragments С₁₀; (b)adding fragment C₁₀ to the result of joining three such fragments which results in a closing the plane structure into a spheroidal one. The C₆₀ molecule Мoлекула С₆₀ is resulted at adding more two С₁₀ fragments to this structure [35].

4.1.3. Extraction of Fullerenes from Soot

The procedure of extaction of fullerenes from soot is based on the fullerenes is the only soluble modification of carbon. Such compounds as benzene, toluene, xylene, CS₂ and others can be used as solvents. Washing the soot containing fullerenes with a solvent results in the extraction of fullerenes. The fullerene solution is directed into an evaporator where in result of the thermal vaporization of the solvent the solution becomes to be oversaturated. Ths is accompanied by formation and growth of fullerite crystals which is a crystalline fullerene form. For the purpose of saving the solvent and execution of a contineous process of fullerene extraction the solvent vapor is directed to a freezer where it condences forming a liquid solvent which is used further for extracting fullerenes from the soot. Such e facility performing contineous extraction of a soluble substance with the usage of a limited quantity of a solvent is called as SOXHLET.

4.1.4. Liquid Chromatography and Separation of Fullerenes

The soot forming at thermal sputtering of graphite in the arc discharge contans fullerene molecules of different sort. The main fullerene content (about 90%) relates to fullerene С₆₀ molecules, the content of С₇₀ accounts several percent and the quarter of higher fullerenes does not exceed usually 1 %. The separation of fullerenes by sorts is performed using liquid chromatography method which is based on distinctions in the sorption ability of some sorbents in relation to fullerene molecules of various sorts. According to this method illustrated on Figure 24, a solution containing fullerene molecules of different sort is passed through a sorbent in pores of which molecules are sorbed. If a pure solvent is passed through such a sorbent, fullerene molecules of various sorts will be extracted rom the sorbent with a different rate: firstly С₆₀ is extracted, then С₇₀ afterwords higher fullerenes. Portions of the solution obtained on different stages of the extraction process are directed to various containers so that one can to get solutions containing presumably fullerene molecules of a specific sort. The degree of enrichment of the material relating to a specified fullerene molecule sort can be enhanced in result of multiple repeating the extraction procedure.

Figure 24. Illustration of the fullerene separation procedure by the liquid chromatogtaphy method. Passage a pure solvent through the sorbent containing fullerene molecules of different sort results in extraction of fullerenes from the sorbent, so that the rates of extraction of fullerenet of different sort are distinquished.

Figure 24. Illustration of the fullerene separation procedure by the liquid chromatogtaphy method. Passage a pure solvent through the sorbent containing fullerene molecules of different sort results in extraction of fullerenes from the sorbent, so that the rates of extraction of fullerenet of different sort are distinquished.

4.1.5. Synthesis of Endohedral Fullerenes

Research efforts addressed to extention of the class of molecules with fullerene structure were resulted in the discovery of endohedral compounds. An endohedral molecule can be produced by two ways. The first way is based on creation of such conditions when already in the synthesis process some part of molecules is filled with atoms or molecules of elements presenting in the synthesis region. In this case there is used usually as an initial material graphite doped with finely dispersed powder of the element to be inserted. Thermal sputtering of graphite under the action of an external energy sourse is accompanied also with the atomization of the doped material. This promotes further formation of endohedral fullerenes.

The second way of endohedral fulleenes synthesis is based on inserting atoms or molecules into the cage of already prepared fullerene molecules. If the incapsulated atoms or molecules are found in a gas state at the normal conditions such inserting can be performed simply by keeping fullerenes in an atmosphere of this gas at elevated temperatures and pressures. Heating promotes the enlargement of “windows” in fullerene molecule while the enhanced pressure facilitates the penetration of particles inside the cage. If the substance to be inserted into the fullerene cage is condensed one, this is performed in result of irradiation of fullerene crystal or film with atoms or ions of the element axelerated up to the energy sufficient for the penetration of the particle inside the cage.

At the synthesis of endohedral fullerenes by the electrical arc method the crystalline graphite with a small addition of powdered metal or metal compound (oxide, carbide) is used. The most spread approach to the realization of this idea is based on the usage of a graphite rod with a hole drilled from the end which is filled with a mixture of amorphous finely dispersed powder of metal or its oxide or carbide. The content of metal in the anode material does not exceed usually several percent. Such an approach has demonstrated its effectiveness in particularly at the synthesis of endohedral metallofullerenes M@C₈₂ (M = Sc, Y, La) [36]. Endohedral metallofullerene molecules Sc₃@C₈₂ filled with three scandium atoms were synthesized in an arc discharge with composite electrodes fabricated as a result of vacuum sintering the mineral Sc₂O₃ (2.5 g) with graphite powder (4.3 g). The arc was burned in a He atmosphere at a pressure of 50-100 Tor Не and a current of 500 А [37].

A distinctive peculiarity of the electrical arc method of production of fullerene containing soot is in an extraordinary rich content of the soot, containing fullerene molecules of various sorts. At inserting some quantity of a metal powder into the anode material this manifold expands even more due to occurrence of endohedral fullerenes. Some notion on the abundance of the spectrum of fullerenes formed in an electrical arc plasma with graphite electrodes can be formed on the basis of the results of mass-spectrometry measurements of the content of the soluble extract of the soot obtained at a thermal sputtering of a graphite rod filled with lanthanum oxide La₂O₃ [38]. The content of metal in the rod material accounted 0.5 - 5 atom %. The arc burned in a He atmosphere (180-220 Tor) at a current of 95-115 А and a voltage of 20-25 V. Enhancement of the metal content in the anode material was accompanied with a rise of quote La₂@C₇₂ between other endohedrals. Figure 25 presents the mass-spectrum of the soot extract obtained with aim of the time flight mass-spectrometer with laser desorption [38]. One should not an extraordinary richness of the spectrum containing both hollow fullerenes С_n n=74, 76, 78, 80, 84, 84, 86…, 104 and endohedral fullerenes La_m@C_n (m=1, 2; n=72, 74, 76, 78, 80, 82). Note also the absence of fullerene С₇₂ at the existence of the endohedral compound La₂@C₇₂. This indicates that the metal atom inserted into the fullerene cage acts positively on the stability of the fullerene cage.

A majority of known metal containing endohedral compounds has been produced by means of the electrical arc method. In particular one should be mentioned those containing rare earth atoms (La, Y, Sc etc). Note that the yield of endohedral metallofullerenes at the electrical arc synthesis is extraordinary low. Preparation of pure samples requires for a multiple execution of the liquid chromatography procedure. This is reflected on the selling price of the material which can reach the magnitude of the order of $1000/mg.

4.1.6. Threemetasphera

The discovery of a new structural form [27] described by the formula A_3-хB_xN@C_2y, where x is an integer between 0 and 3, A and B are the metal atoms such as Ga, Lu, Ho etc. and y is equal to 34 or 39–44, became a notable step on the road of enhancement of the metallofullerenes production scale. Such a structure called as “threemetasphere“ demonstrates an enhanced stability and can be synthesized with a relatively high yield. As an example can be considered the work [39] where it was stated that the usage as a buffer gas of nitrogen instead of the much more expensive helium decreases considerably the production cost of the process keeping the productivity on a stable level. Along to the traditional way of inserting a metal into the high temperature arc region, based on the filling a graphite rod with the metal powder the author [39] injected the finely dispersed powder Lu₂O₃ into the plasma region. This resulted in a notable enhancement of the purpose material (Lu₃N@C₈₂). Figure 26 presents the dependence of the yield of this substance from the rate of the powder supply.

4.1.7. Synthesis of Fullerenes in a Plasmatron from Dispersed Amorphous Carbon

The main initial material used at the fullerene production is crystalline graphite. Thermal sputtering of the graphite rod (anode) in the arc discharge results in formation of the soot containing some quantity of fullerenes. As is known, for production of graphite powdered amorphous carbon is sintered at elevated temperature and pressure. In this connection a question appears: Is it possible to produce fullerenes from amorphous carbon directly, bypassing the stages of powder sintering and subsequent sputtering od graphite crystal? It appears that such an approach permits one to decrease considerably the production cost of fullerenes because firstly the stage of graphite production is excluded and secondly the energy expenses for sputtering graphite material are eliminated. This approach has been realized firstly in Ref. [40]. Figure 27 presents the schema of the experimental setup. The cathode was fabricated from W, while the anode was produced from Cu. As a buffer gas was used Ar pumped with a rate of 18 - 20 l/min. The amorphous carbon powder had a specific surface 80 m²/g which corresponds to the particle size of the order of 10 nm. The plasma was generated in a gap of 1 – 3 mm in width by a power supply of 12 kW in a power. The soot formed in result of interaction of amorphous carbon with the plasma was deposited onto a collector. Figure 28 presents the dependence of the fullerene content in the soot on the rate of pumping the amorphous carbon powder. A relatively low fullerene yield is explained by that the operation regime of the plasmatron was far from the optimum.

The above-described approach to the plasma synthesis of carbon nanostructures without the usage of crystalline graphite has received a further development in works performed by a group from High Temperatures Institute RAS (see [41,42] and publications cited there). In these works was used a CW plasmatron with expanded anode channel of up to 40 kW in the power. As a carbon source were used doth amorphous carbon powder and such gases as ethanol, propane, butane, methane, and acetylene. Carbon nanostructures were synthesized at a pressure of 77-740 Tor, various geometries of the gas passage way, and different gas flows.

4.3. Graphene

4.3.1. Micromechanical Exfoliation of Graphite

Graphene samples were first separated through the micro-mechanical cleavage of graphite [20]. In accordance with this approach, graphene sheets are separated from crystalline graphite either by rubbing small graphite crystals against each other or by means of an adhesive tape whose further dissolution in acid results in separation of individual graphene sheets suitable for investigation. Measurements have shown that this approach allows separation of single-layer graphene sheets about 10 mm in width and roughly 100 mm in length having an ordered structure. Subsequently there was elaborated a lot of approaches to the graphene production, however the micromechanical graphite exfoliation heads the list of them relating to the the quality of samples obtained. However the graphene production procedure through the above-described approach seems to be rather complicated and low productive. The company found by K. Novoselov in England sells graphene samples of about 30 μm in size, prepared by this approach, for a price of $10. The mass of such a sample accounts about 10^-12 g, so that the cost of graphene produced by the micromechanical graphite exfoliation reaches about $10¹³/g. Such a cost hardly permits one to hope for a possibility of the applied usage of graphene in technologies. However this price stimulates efforts of researchers addressed to generation of new more effective and less expensive approaches to the graphene production.

4.3.2. Chemical Vapor Deposition

The graphene synthesis based on the CVD procedure has got a a wide spread. This method uses the property of carbon containing gases to decompose at elevated temperatures on the surface of some metals with subsequent self-organization of carbon atoms either to nanotubes or graphene sheets, depending on conditions. Various metals such as Ni, Cu etc were used as substrates for the graphene synthesis. The most impressive results have been obtained at the usage of a copper foil as a substrate [46,47]. The authors of those works have managed to produce large sixe graphene sheets (up to 1 m) which offers дo 1 м в пoперечнике), which offers great prospects for the applied usage of graphene. Figure 34 illustrates the procedure of grows of large scale graphene sheets on the copper substrate with subsequent transfer of the sheets onto a dielectric substrate.

One should note that while the CVD method permits production of large size graphene sheets, this method is rather complicated for incorporation into the contemporary technology of electron technique elements production. This approach is very labor consuming and requires for considerable time expenses. For these reasons this method is used for rather scientific than technology tasks.

4.3.3. Reduction of Graphene Oxide

Large scale graphene production is based on procedures of graphene oxide reduction. Relatively not expensive and high productive process of oxide graphite synthesis was elaborated by Hummers et al. as early as in 1958, well in advance of graphene discovery [48]. The process named as “Hummers method” includes the treatment of finely dispersed graphite by concentrated H₂SO₄ and KMnO₄ in the presence of NaNO₃. As is demonstrated in numerous experimental works, this procedure results in formation of multi-layer graphite oxide particles of about 1 nm thick and several tens μm size. These particles deposited onto a filter are usually experienced to pressing for formation of paper-like films of several tens μm thick. Graphene oxide can be considered as graphene sheets covered with oxygen containing hydroxyl (—ОН) and epoxy (С—О—С) functional groups. Sheet edges contain also some quantity of carbonyl (С=О) and carboxyl (СООН) groups.

Two approaches are used for reduction of graphene oxide and producing graphene samples. One of those is based on the chemical reduction procedure with the usage of chemical reagents. For this purpose were utilized successfully such reagents as hydrazine and his derivatives, hydroquinone, NaBH₄, NaOH, NaHSO₃, Na₂S∙9H₂O, Na₂SO₃, SOCl₂, Na₂H₄∙H₂O, SO₂, vitamin С etc. Extension of the set of these compounds can result in an enhancement of the graphene synthesis process productivity, lowering its production cost and enhancement of the safety level, which stimulates efforts of researchers addressed to investigations in the graphene reduction chemistry.

The main drawback of the chemical approach to the graphene reduction is in necessity of utilization of toxic or ecologically harmful chemical compounds. This limits a wide usage of chemical graphene oxide reduction methods for large scale graphene production. The thermal graphene oxide reduction method seems to be more safe and feasible. In accordance to this method, graphene oxide is reduced in result of thermal processing at a temperature up to 800 ^oС. The thermal treatment results in removal of radical added to the hexagonal graphene structure so that graphene oxide flakes transform to graphene flakes. The degree of graphene oxide reduction is controlled using the measurement of the electric conductivity of the material. Graphene oxide is a dielectric and does not conduct practically the electricity. Graphene is a semimetal and possesses the conductivity which is close to that of graphite. Therewith the conductivity of partially reduced graphene oxide increases as the reduction degree enhances at should reach the quantity 3х10⁴ S/m inherent to crystalline graphite at a total graphene oxide reduction.

Figure 35 presents a typical dependence of the electric conductivity of thermal reduced graphene oxide on the thermal processing temperature [49]. The sharp jump of the electric conductivity of a thermal processing temperature of 150 – 200 ^oС is indicative of the percolation character of the conduction in accordance to which the charge transport occurs through a limited number of channels formed by conductive reduced graphene oxide fragments contacting with each other. A rise in the thermal processing temperature results in an enhancement of the number of such fragments and therefore of the number of percolation channels.

The thermal graphene oxide reduction is accompanied with removal of oxygen and other added radicals which results in a decrease of the material density. Table 1 presents the evolution of the chemical composition on graphene oxide samples experienced to the thermal treatment at different temperatures [49]. These data have been obtained in result of processing X-ray photoelectron spectra of the material. The data presented in the table indicate that the thermal treatment at a temperature exceeding 200 ^oС results in a considerable removal of oxygen from the sample, and at the enhancement of the temperature up to 600 ^oС the concentration ratio С/О increases by almost four times.

Figure 36 presents the dependence of the density of thermally reduced graphene oxide samples on the thermal processing temperature. As is seen, the density of the material experienced to the thermal processing at a temperature of 800 ^oС is lower about by 4.5 times than that of crystalline graphite (2,2 g/cm³). This means that the average inter-layer distance in the samples experienced to the thermal treatment at the above-indicated temperature exceeds the value 0.34 nm, inherent to crystalline graphite by 4.5 times.

Figure 36. Dependence of the density of partially reduced graphene oxide samples on the thermal processing temperature [49].

Figure 36. Dependence of the density of partially reduced graphene oxide samples on the thermal processing temperature [49].

The effect of changing the inter-layer distance should be taken into account at the comparison of the electric conductivity of thermally reduced oxide graphene and crystalline graphite. Taking into consideration this effect, the electric conductivity of the reduced graphene oxide treated at a temperature of 800 ^oС (accounted by one layer) is not 7х10³ S/m as it shown on Figure 35, but 3.15х10⁴ S/m. This quantity is close to the reference value for crystalline graphite, which indicates that the thermal reduction of graphene oxide provides a material close to graphene in its characteristics. The above-described graphene production method seems to be quite appropriate as ecologically safety, comparatively not expensive and rather productive method of large scale graphene fabrication.

5. Physical and Chemical Properties of Carbon Nanostructures

5.1. Fullerenes

5.1.1. Molecular Properties and Chemistry of Fullerenes

The main peculiarity of molecular fullerene is in a high electron affinity of this compound (2.7 eV for С₆₀ molecule). At a room temperature С₆₀ can add up to six electrons. The ionization potential of fullerene molecule С₆₀ accounts 7.6 eV; the value of this parameter decreases as the molecule size increases; for very large fullerene molecules the quantity of this parameter approaches the work function for graphite (~ 5 eV). The polarizability of С₆₀ molecule accounts 80 ų. The energy necessary for splitting out carbon atom from С₆₀ accounts 7.4 eV. For higher fullerene molecules the value of this parameter is of the same order of magnitude. This determines quite high thermal stability of fullerene molecules which hold their structure (at the absence of oxygen) at temperatures exceeding 2000 К.

The structure of fullerenes contains double carbon bonds С=С due to which such molecules can add to themselves a considerable number of atoms and/or radicals. This causes a wide set of chemical derivatives of fullerenes [25,50], which differ from one another in not only sort and quantity of added atoms and radicals but also in their mutual arrangement on the surface of the molecule. The number of different fullerene derivatives accounts many thousands, and the problems relating to their synthesis, investigation and applied usage constitute the content of the fullerene chemistry, which is separated as one of the directions of the chemical science.

One of the perspective problems of the fullerene chemistry relates to the synthesis of water soluble compound of these molecules. The solution of this problem permits creation of a new class of biologically active compounds for pharmacology. The synthesis of fullerene molecule with a large number (up to 26) of added hydroxyl groups (-ОН) became an important step on this way. Figure 37 presents the structure of this molecule [51] which can be considered as fullerene alcohol (fullerol). This compound was synthesized in a water solution NaOH with the usage of tetrabutilammonium hydroxide as a catalyst.

Figure 37. Chemical structure of the water soluble fullerene compound presenting С₆₀ with added OH radicals ОН [51].

Figure 37. Chemical structure of the water soluble fullerene compound presenting С₆₀ with added OH radicals ОН [51].

One more problem of fullerene chemistry attracting considerable attention of researchers relates to the synthesis and usage of fluorinated fullerenes. In some degree this attention is supported by hopes of researchers to create new solid lubricants similar to Teflon on the basis of fullerenes. As it expected, these lubricants will conserve their high friction characteristics even at supe-low temperatures, in space conditions. A wide set of fluorinated fullerenes described by the formula C₆₀F_n (n – is an integer lower 50) has been synthesized by now. One should note that the compounds C₆₀F₃₆ and C₆₀F₄₈ possess an enhanced stability.

5.1.2. Fullerite

At a room temperature fullerenes are found in the condensed state forming a crystalline structure. Such a structure is called as “fullerite”. In such a structure the molecules are bound with each other with van der Waals interaction forces the energy of which (1.6 eV) is much less than the interaction energy of carbon atoms in the molecule (7.4 eV). For this reason fullerene molecules separate from the crystal at evaporation without destruction. Some physical parameters of fullerite С₆₀ are shown in Table 2.

Table 2. Physical parameters of fullerite С₆₀ at a room temperature [52].

Table 2. Physical parameters of fullerite С₆₀ at a room temperature [52].

Parameter	Quantity
Lattice constant (fcc), nm	1.417
Distance С60-С60, nm	1.002
Binding energy С60-С60, eV	1.6
Density, g/cm3	1.72
Molecular density, cm-3	1.44х1021
Isothermal compressibility, m2/N	6.9х10-11
Phase transition sc-fcc temperature (Тpt), К	261
dТpt/dp, К/Kbar	11
Volumetric thermal expansion coefficient, К-1	6.1х10-5
Electron work function, eV	4.7
Debye temperature, К	185
Thermal conductivity, W/m К	0.4
Electric conductivity, S/m (T= 300 K)	1.7х10-7
Melting temperature, К	1450
Sublimation enthalpy, eV (Т = 500 – 700 К)	1.74
Dielectric constant	4 – 4.5

Figure 37. Temperature dependences of the saturation vapor pressure for fullerites of different sorts [50].

Figure 37. Temperature dependences of the saturation vapor pressure for fullerites of different sorts [50].

Evaporation (sublimation) of fullerites is observed at temperatures exceeding 500 К. The temperature dependence of the saturation vapor pressure p_s(T) is described by the standard Arrhenius formula

p_s = p_s0 exp(-ΔH/T),

where ΔН is the sublimation enthalpy accounting 1.67, 1,95, 2,0 и 2,14 eV for fullerites С₆₀, С₇₀, С₇₆ and С₈₄, correspondingly, p_s0 is an empiric parameter. Figure 37 presents the measured temperature dependences of the saturation vapor pressure for fullerites of the above-listed sorts [50]. As is seen the saturation vapor pressure decreases as the molecule size enhances. This corresponds to the above-given dependence of the sublimation enthalpy on the molecule size. One should take into consideration that as it was noted above, higher fullerene molecules can be found in various isomeric states, so that the data on the temperature dependences of the saturation vapor pressure shown on Figure 37 should be treated as a result of averaging over such states.

The crystalline structure of fullerites depends on the temperature. At temperatures lower 257 К fullerite С₆₀ has a simple cubic structure (sc) in which each molecule has 12 nearest neighbors. The rotation of molecules is frozen, so that relative orientations of fullerene molecules are fixed strictly. At a temperature of 257 К the fullerite crystal is subjected to the phase transition resulting in defrosting of the rotation of molecules. The crystal takes the face-centered cube structure (fcc). Therewith fullerene molecules lose a fixed spatial orientation and behave like structureless spheres. The phase transition is accompanied with an abrupt change of many characteristics of fullerite such as forbidden gap width, conductivity etc.

Fullerites are superconductors having the forbidder gap width 1.5 eV (С₆₀), 1.91 eV (С₇₀), 0,5 -1,7 eV (С₇₈) and 1,2 – 1,7 eV (С₈₄). Therewith the data for higher fullerenes possess a considerable uncertainty which is caused by a great abundance of isomer modifications of these compounds and manifold of mutual orientations of molecules in the crystal which structure differs considerably from the spherical one inherent to С₆₀. At a room temperature fullerite crystals possess negligible electric conductivity and can be considered as insulators.

5.1.3. Superconductive Fullerites

The interest to study of fullerites increased considerably after discovery of the superconductivity of fullerites. Doping С₆₀ crystals with a some quantity of an alkali metal results in formation of a material with metal conductivity transforming into a superconductive state at low temperatures [52]. Such a material is produced in result of processing a film or polycrystalline sample with alkali metal vapor at a temperature of several hundred degrees. The most of fullerites С₆₀ containing alkali metals in stoichiometric ratio either Х₃С₆₀ or XY₂C₆₀ (X, Y – alkali metal atoms) possess superconductive properties. Table 3 contains parameters of superconductive fullerites of such a kind [53]. One can note for comparison that the critical superconductivity temperature for graphite doped with K accounts 0.55 К [54] while for fullerite К₃С₆₀ it is equal to 19 К. Values of the critical temperature for superconductive fullerenes present the record for molecular superconductors.

One should note a correlation between the lattice parameter а_o and critical superconductivity temperature Т_с. This correlation manifests itself clearly on the dependence of the critical superconductivity temperature on the lattice parameter shown on Figure 38. Such a dependence suggests a possibility of preparation of a material with enhanced superconductivity temperature on the basis of higher fullerene crystals [55]. However, practical realization of this idea meets difficulties related to non-spherical structure of higher fullerene molecules and abundance of isomer modifications. Due to these difficulties higher fullerene based crystals do not possess a perfect crystalline structure inherent to fullerite С₆₀ which prevents the occurrence of superconductivity.

Figure 38. Dependence of the critical superconductivity temperature of fullerites doped with alkali metal atoms on the crystal fcc lattice parameter а_o [53].

Figure 38. Dependence of the critical superconductivity temperature of fullerites doped with alkali metal atoms on the crystal fcc lattice parameter а_o [53].

5.1.4. Fullerenes in Solutions

As it was mentioned above, fullerenes present the only soluble carbon modification. The importance of this fullerenes feature relates to the possibility to extract fullerenes from soot and separate fullerenes of different sort from each other. Table 4 shows the values of solubility of fullerenes in various solvents. One should stress that fullerenes are dissolved presumably in non-polar solvents and practically not soluble in such standard solvents as alcohol and water. This implies an insignificant role of the solvation mechanism of solution which is based on formation of long living complexes (solvates) presenting the molecule of the dissolved substance surrounded with an envelope consisted of solvent molecules oriented in a specific manner.

As it can be seen from the data presented in the Table, the most high fullerene solubility is inherent to aromatic hydrocarbons and their derivatives the first place between them belongs to derivatives of naphthalene. Aromatic compounds are based on one or several benzene rings the structure of which is very close to regular hexagons forming the surface of a fullerene molecule. For this reason a high solubility of fullerenes in aromatic compounds appears to be explicable. One can suppose that a high solubility of fullerenes in compounds containing hexagonal rings in their structure is caused by a magnetic interaction of a ring current in the sonvent molecule with that in fullerene molecule. The specific surface energy of this interaction is of the same order as the inter-molecular interaction energy in a fullerite crystal, therefore the solubility thermal effect is relatively low. The magnetic field caused by an intra-molecular current in the hexagonal fullerene ring arranges the aromatic compound molecule in such a manner that the current inside this molecule is directed opposite to the current of the fullerene ring. The thermal effect of fullerene molecule solubility is determined by the energy of the magnetic interaction.

Figure 38. Temperature dependence of the solubility of fullerene C₆₀ + in hexane (times 55); □ in toluene (times 1.4); ◊ in CS₂; ● in xylene [57]. The solid line shows the results of calculations using the droplet model [56,58].

Figure 38. Temperature dependence of the solubility of fullerene C₆₀ + in hexane (times 55); □ in toluene (times 1.4); ◊ in CS₂; ● in xylene [57]. The solid line shows the results of calculations using the droplet model [56,58].

A remarkable peculiarity of the behavior of fullerenes in solutions relates to the temperature dependence of the solubility of fullerene С₆₀. This dependence measured in Ref. [57] is presented on Figure 39. As is seen the temperature dependence of fullerene solubility has a non-monotone character, which is rather rare manifestation of the solubility nature. The solubility of the most substances increases as the temperature enhances which is caused by a decrease of the influence of the interaction of dissolved molecules with solvent molecules on the solution behavior. One should note that other fullerene modifications do not possess non-monotone temperature dependence of the conductivity. In particular, the solubility of fullerene С₇₀ is characterized by a standard rising dependence.

Non-monotone character of the temperature dependence of fullerene solubility is explained within the frame of the cluster model of the fullerene solubility [56,58]. According to this model, fullerene molecules С₆₀ in solutions form clusters consisted of some number of fullerene molecules. At relatively low temperatures (lower 280 – 300 К) these clusters keep their stability, so the rise of the temperature is accompanied with an enhancement of the solubility, which corresponds to the traditional behavior of solutions. Further enhancement of the temperature causes the thermal decomposition of clusters which results in an increase of the solute and therefore with a rise of the interaction energy between solute and solvent molecules. This is reflected on the temperature dependence of the fullerene solubility which has a decreasing shape in the temperature range (above 280 – 300 К) under consideration.

The above-described mechanism has permitted the explanation of the observed experimentally temperature dependence of the fullerene С₆₀ solubility [57] (solid line on Figure 38) and evaluation on the basis on this experiment the cluster size distribution function in dependence on the temperature and solution concentration. The calculation was based on the droplet model of cluster, in accordance to which fullerene clusters present droplets of spherical form. Some results of such calculations are presented on Figure 39 [56] showing the cluster size distribution function at various temperatures and solution concentrations.

The cluster origin of fullerene solubility is reflected on many features of the behavior of fullerenes in solutions. Thus the diffusion coefficient of fullerene clusters is much less of that for single fullerene molecules (for example С₇₀, which do not form clusters) therefore it is possible to realize the procedure of the diffusion separation of different sorts fullerenes in solutions [56].

5.2. Carbon Nanotubes

Carbon nanotubes possess exclusively wide diversity of physical and chemical properties. A high chemical and thermal stability in association with a record mechanical rigidity, high emission characteristics, unique sorption characteristics and high thermal and electric conductivity make this material unique and attract to its investigation and usage a large set of researchers and engineers.

5.2.1. Mechanical Properties

A single walled nanotube can be considered as a thin cylindrical shell. Mechanical properties of such structures are well studied in connection with the development of aviation. While in distinction on macroscopic shells, CNT do not possess a solid wall and have a thickness of the order of an atomic size, the classical notions on the mechanics and elastic properties of cylindrical shells are applicable practically in full to this exotic object.

Elastic mechanical properties of an elongated cylindrical shell are characterized by a set of parameters (elasticity modules) which present the proportianelity coefficient between the stress and caused by that deformation of the shell in a specified direction. The elasticity modules are defined at a condition of low loadings when the deformation has a reversible character. Figure 40 prsents the most important deformation types of a single walled CNT. Along with the above-listed deformation types one should note also the torsion of a shall relating to its axis.

The man parameter characterizing the tensile strength of CNTs (Figure 40а) is the longitudinal Young modilus defined by the expression

Е = σ/ε = N/2πRhε,

(5.1)

Here, σ is the longitudinal stress representing the ratio of the longitudinal tensile force N applied to a nanotube to its cross section area, ε is the relative tension (change in the length) of the nanotube due to the action of the force, R is the radius of the nanotube, and h is the thickness of its shell. Expression (5.1) constitutes one of the specific formulations of the Hook law.

For defectless CNTs the Young modulus is expressed through the interaction potential for two neighboring carbon atoms constituting the structure of the nanotube. A simple estimation [59], based on the usage of known parameters of the interaction potential results in the value Е ~ 10¹² Pa. This is a record value for all the known materials. However the accuracy of ths estimation is limited because the thickness of the nanotube’s wall h is of the order of the atom soze and is not known exactly. Nevertheless there are known experiments confirming such a high tensile strength of CNTs. Thus Ref. [60] shows the value of the Young modulus of a single walled CNT E = 1.3 ± 0.45 TPa, obtained in result of averaging the data for 27 nanotubes of different length and diameter. The Young modulus for nanotubes was determined on the basis of measuring the free-running frequency of the nanotube with a fixed end. Numerious calculations performed with the usage of the molecular dynamics and other modern approaches result in about similar values. One should note for comparison that the characteristic value of the Young modulus for many substances known as very rigid materials (steel, molibden, copper etc) ranges in the interval 10 – 30 GPa. Therewith the tensile strength of CNTs exceeds th corresponding value for the most rigid materials by several tens times. This difference is explained by relatively small size of CNTs for which occurrence of structural defects has a low probability. Such defects exist allways in the structure of macroscopic materials and their existence limits their mechanical properties. The equilibrium concentration of structural defects is proportional to the factor exp(-D/T), where D ~ 2 - 4 eV is the defect formation energy so that only quite elongated nanotubes (more that 1 μm) possess defects.

The axial compression of a nanotube considering as a thin cylindrical shell is accompanied by an increase of its diameter (buckling, Figure 40b). At low loadings the axial compession has a reversible, elastic character so that the corresponding Youns modulus coincides with that determined for the case of tension. Exceeding some crytical force results in so called Euler instability, which is accompanied with an abrupt decrease of the elasticity modulus and non-reversible distortion of the nanotube’s structure the surface of which is compressed into a “harmonica” (Figure 40f).

The Euler instability at an axial compression of CNTs has been studied in detail by the aithors of Ref. [61]. A highly ordered array of vertically oriented nanotubes of 50 or 100 μm in height and 40 nm in the inner diameter was synthesized in result of pyrolysis of acetilene in the presence of the cobalt catalyst. This array was placed on an anodized aluminium substrate at an average inter-tube distance of 100 nm. Figure 41 presents the schema of the experiment on investigation of the axial compression. The axial compression of CNTs was performed by means of an indentor having a conical tip of 100 nm in radius. There has beer registered both loading and the indentor displayment.

Carbon nanotubes present thinnest filaments which can be utilized for fabrication of a textile in analogy with the textile production on the basis of silk, cotton, linen and other kinds of filaments. Fabrication of textile from filaments is a multi-stage procedure the first stage of which is in preparation of a yarn from individual nanotubes or bundles consisted of hundreds such nanotubes. The process of yarn fabrication from nanotubes is identical with the standard procedure used in the textile production. A CNT array is experienced to spinning which results in the occurrence of a macroscopic length fiber. This procedure is illustrated on Figure 42 where types of ropes fabricated from such fibers are also shown. Figure 43 shows successive stages of fabrication of a transparent textile from the fibers.

5.2.2. Electrical Properties

Electrical properties of a carbon nanotube depend on its chiral structure (see chapter 3.2). Investigations have shown that the nanotubes with the chirality indices (m, n) possess a metal conductivity if m - n = 3к, where к is an integer. Such nanotubes have the chair structure. Other CNTs are semiconductors in which the forbidden gap width decreases in a monotone manner as the diameter increases (Figure 44) [63]. Taking into consideration that a nanotube presents a graphene layer scrolled into a cylinder, such a character of the dependence appears to be natural. The larger the nanotube’s diameter the closer it to graphene in its electric characteristics. Remind that graphene possesses metallic conductivity and zero forbidden gap width.

The measurement of electric characteristics of CNTs presents a complicated technical problem which is caused by a miniature size of a CNT and the resistance of nanotubes is usually lower that the contact resistance. A interesting approach to the solution of this problem has been proposed and realized in Ref. [64] where the resistance of a single walled nanotube was measured using contacts with multi layer CNTs. The role of the contact resistance was eliminated through the usage of four contact method permitting the measurement of the resistance of a nanotube fragment in dependence on its length. The schema of the measurement is shown on Figure 45.

In the absence of defects an electron propagates along a conductor without scattering. Such a type of conductivity has a quantum character and is called as ballistic. The relevant value of the ballistic resistance is expressed as

R_o = 1/(2G_o) = h/4e² = 6.45 KΩ.

(5.1)

In the case of ballistic conduction both resistivity ρ = R_oS/l of quantum objects and their specific conductivity σ = G_ol/S depend on the sample length l and cross section area S. Thus the dimension effect manifests itself that is inherent to objects of a nanometer size which are CNTs.

The conduction properties of a single walled CNT were studied experimentally in dependence of the inter-contact distance in Ref. [65]. Results of these measurements are presented on Figure 46 which illustrates the transition of the ballistic conduction into the Ohmic one. At low distance (less ~ 8.5 μm) the ballistic conduction occurs, so that the conductance does no almost depend on the inter-contact distance. Obviously a CNT fragment of such a length does not contain almost defects, so that the ballistic conduction occurs. At further enhancement of the inter-contact distance the probability of defect occurrence increases and the conductance lowers abruptly. The ballistic conduction mechanism is substituted by the Ohmic one for which the nanotube resistivity is proportional to its length. The similar behavior relates to the thermal conduction of a CNT, which has ballistic character for short inter-contact distances and transforms to the diffusion thermal conductivity for elongate CNT.

The dependence of the resistance R of a nanotube on its length L is convenient to describe by the interpolation formula

R = (h/4e²)(L + λ)/λ,

(5.2)

where λ is the mean free path of an electron relating to the scattering on defects. This formula describes the transition from the ballistic (L << λ) to Ohmic (L >> λ) charge transport. As it follows from numerous measurements, the value of parameter λ ranges between 0.5 and 10 μm, in dependence of the method and conditions of nanotubes fabrication.

5.2.3. Thermal Conduction of CNTs

The thermal conduction of CNTs is determined by phonons so that the role of electrons is not sufficient. If the characteristic mean free path of phonons in relation to the scattering on structural defects and phonons exceeds its length, the ballistic heat transport occurs, when phonons transfer the thermal energy without scattering. The simplest description of the ballistic phonon thermal conduction corresponds to the high temperature limiting case which occurs at the condition ħω << T (ω is the characteristic phonon frequency, Т is the temperature). In this case the thermal conductance of each channel is described by the quantum value G_th, having the following form:

G_th = π²k²T/3h = 9.46x10^-13 (W/К²)Т.

(5.3)

Therewith the ballistic thermal conductance of a defectless nanotube is expressed as the product of the quantum thermal conductance G_th by the total number of phonon channels N_p in the nanotube. The latter is a tripled number of atoms in a single cell N, where N is expressed through the chirality indices (m, n) as follows [52]:

N = 2(n² + m²+nm)/d_R.

(5.4)

Here, d_R is the greatest common divisor of (2n + m) and (2m + n). For a single walled CNT having the armchair structure and chirality indices (n, n) d_R = n and N = 6n. For example, a single-walled CNT which the chirality indices (10, 10) (diameter 1.4 nm) has Np = 120 phonon channels. Therefore, the ballistic thermal conductance of (10, 10) and (200, 200) CNTs amounts to 120 G_th and 2400 G_th, respectively.

The scattering of phonons on defects and impurity centers can be taken into account by analogy with the above-considered description of the ballistic electric conduction of CNTs at the presence of defects by the usage of the correcting factor k_d = (L + λ_p)/λ_p, where λ_p is the mean free path of phonons in relation to the elastic scattering and L is the nanotube’s length. In accordance with this approach the thermal conduction coefficient of a nanotube is expressed through the following relation:

G = G_thNλ_p/(L + λ_p),

(5.5)

where the quantum thermal conductivity G_th and the number of phonon channels N are determined by the relations (5.3) and (5.4). The above-described approach to the description of the CNT thermal conduction is quite convenient for analysis of experimental data, because it permits determination of the heat transport mechanism on the basis of experimental dependence of the thermal conductance on the nanotube’s length. As it follows from Eq.(5.5), the thermal conductance of a long nanotube (L >> λ_p) is inversely proportional to its length. It is one more manifestation of the dimension effect which is inherent to nanosize objects.

Dependence of the thermal conductance of a long single walled nanotube of the inter-contact distance has been presented on Figure 46 (curve 1). In analogy to the electric conductance, the thermal conductance does not practically change for the inter-contact distances less 8.5 μm after which it decreases abruptly. Such a behavior indicates the ballistic character of the thermal conduction for the nanotube fragment shorter than 8.5 μm and the occurrence of defects and other scattering centers on longer distances.

5.2.4. Emission Properties

As is known, elongated conducting object are able to amplify the electric field. If such an object having the length L and diameter d to place vertically on a grounded substrate inserted into an inter-electrode gap of d in width apply an electrical field with the voltage of U, then the electric field in a vicinity of the tip of such an object will exceed the averaged over the gap value F = U/d by about L/D times. Hear the ratio L/D is called as “aspect ratio”. Carbon nanotubes possess record value of aspect ratio reaching 10⁴. This permits one to obtain high electric field at a relatively low applied voltage. At such fields the nanotube if a source of an electron beam due to the electron field emission phenomenon. This phenomenon is based on the effect of quantum tunneling of electrons residing inside a grounded conductor through the barrier formed by the conductor lattice and external electric field (Figure 47). A simple quantum mechanical approach has resulted on the following dependence of the electron forld emission current density j on the electric field strength F, called as Fowler-Nordheim equation:

j = C₁F²exp(-C₂/F),

(5.6)

where the parameters С₁ and С₂ are expressed through the electron work function φ for the conductor under consideration and basis constants (electron charge and mass e and m and Plank constant h):

C₁ = e³/8πhφ; C₂ = [8π(2m)^1/2φ^3/2]/3he.

(5.7)

The emission current I is determined in result of integration of the current density J over the surface of the emitter.

The Fowler-Norheim equation (5.6) has rather approximate character, because it was derived supposing a plane geometry of the emission source. However this equation describes quite well evission properties of CNTs the geometry of which is distinguishes from the plane one. This follows in particular from the results of measuring the current-voltage characteristics of CNTs presented on Figure 48. As is seen, the dependences of ln(I/V²) versus 1/V, presented in the Fowler-Nordheim coordinates keep the straight shape for the emission current alternating within the range of more than four orders of magnitude. This permits the usage of this equation for analysis and processing of numerous experimental data.

The ability of an emitter to enhance the electric field is characterized by the field amplification factor β, which is defined as the ratio of the real magnitude of the electric field strength E to the average value E_o:

β = E/E_o =ED/U

(5.8)

where D is the inter-electrode distance, U is the applied voltage. Since the value of the aspect ratio for CNTs can reach 10³ and even higher, the electron field emission of nanotubes occurs at much lower values of the applied voltage than in the case of conventional electron field emitters. This offers an opportunity for the development of a new generation of electro-vacuum devices distinguished by a lower level of the applied voltage and power consumption. The dependence of the electric field amplification factor on the geometry of the nanotube and interelectrode gap is determined through the solution of the Laplace equation for a ground CNT with the boundary conditions corresponding to zero potential on the cathode surface and a fixed value of the potential on the anode surface. The numerical calculations allow the determination of the electric field strength within the gap space and, therefore, the evaluation of the field amplification factor according to Eqn (5.8). An example of such a calculation has been performed in Ref. [67,68]. As is seen, the aspect ratio dependence of the field amplification factor is close to the linear one:

β ≈ h/d.

(5.9)

The calculations were done for an individual nanotube 10 nm in diameter and of various heights. The inter-electrode gap was set to 200 mm, and the applied voltages to 1000 V. performed for a nanotube 10 nm in diameter and of variable length. The interelectrode gap is 200 mm, and the applied voltage is 1000 V. The degree of sensitivity of the field amplification factor of a nanotube, β, to the structure of its end tip is determined through the calculations of the aspect ratio dependences of this factor performed for nanotubes with various tip structures [67,68]. Figure 49 a - e demonstrate five types of tips for which the calculations were performed: (a) hemisphere; (b) cone with a vertex angle of 90; (c) open hollow cylinder with a wall 1 nm in thickness; (d) flat cap, and (e) cone with a vertex angle of 30 . The calculated results obtained for various nanotube’s tip are given in Figure 49f. As is seen, a change in the tip structure results in a corresponding variation in the field amplification factor within the range of 5±7%. A notably higher value of the field amplification factor is observed for a conical cap with a cone angle of 30^o_. In this case, the tip's structure produces an additional field amplification effect.

Figure 49. (a) – (e) Various types of the nanotube’s tip used in the calculation of the dependence of the field amplification factor on the aspect ratio: (a) hemisphere; (b) cone with a vertex angle of 90^o; (c) open hollow cylinder with a wall 1 nm in thickness; (d) flat cap, and (e) cone with a vertex angle of 30^o_; (f) results of such calculations performed for the inter-electrode gap of 200 mm, the applied voltages to 1000 V, the nanotube diameter of 10 nm and of variable length.

Figure 49. (a) – (e) Various types of the nanotube’s tip used in the calculation of the dependence of the field amplification factor on the aspect ratio: (a) hemisphere; (b) cone with a vertex angle of 90^o; (c) open hollow cylinder with a wall 1 nm in thickness; (d) flat cap, and (e) cone with a vertex angle of 30^o_; (f) results of such calculations performed for the inter-electrode gap of 200 mm, the applied voltages to 1000 V, the nanotube diameter of 10 nm and of variable length.

The above-cited calculations were performed for a large interelectrode distance D comparing to the nanotube's height h. In the case of an interelectrode distance comparable to the nanotube’s height the factor β should depend not only on the aspect ratio of the nanotube but also on the ratio h/D. Thus, if a nanotube with a flat cap is spaced from the anode surface by a distance D which is much shorter than the nanotube's diameter d, the nanotube and the anode surface can be considered as a flat capacitor. For this configuration the electric field strength E₁ in the space under consideration is expressed as E₁ = U/D. Since the average magnitude of the electric field strength in the gap is E_o = U/(h + D), the approximate relation for the field amplification factor β in these conditions is has the following form:

β = E₁/E_o ≈ U(h +D)/DU ≈ (h+D)/D.

(5.10)

Usually as an electron emitter is used rather not a single CNT but an array containing a large quantity of vertically oriented nanotubes. These emitters differ from each other in their geometry, orientation, electronic properties etc. Therewith the electrical field amplification factor for nanotubes is characterized by a statistical spread. Due to a sharp character of the dependence of the current of an individual CNT on the electrical field strength in a vicinity of its tip and hence on the amplification factor, the main contribution into the emission is caused usually by a minor quantity of nanotubes for which the amplification factor has a maximum value. As a rule these are the highest nanotubes growing out from the array. As the applied voltage increases, the relative contribution into the emission of remainder nanotubes enhances. Therefore the emission characteristics of a cathode combine the current-voltage characteristics of individual CNT, however they can differ essentially from the dependence determined by the Fowler-Nordheim equation (5.6). Figure 49 presents the results of the analysis of the influence of the statistical spread of CNTs parameters on the current-voltage characteristic and emission properties of an array. As is seen (Figure 49a), the largest difference between the current-voltage characteristic of an array and the Fowler-Nordheim function (5.6) occurs at low emission currents. In this range the difference can be multifold. The effect of the statistical spread of CNT parameters in an array is manifested also in the images of the distribution of the glow generated by the electron beam over the anode surface covered with a phosphor (Figure 49 (b) – (d)). At low voltages and emission currents (Figure 49b) this distribution has a strongly non-homogeneous character and contains a set of disordered bright spots. As the applied voltage increases the nanotubes with lesseer value of the field amplification factor are engaged, and the glow became more homogeneous (Figure 49 (c) and (d)).

Figure 49. Illustration of the influence of the statistical spread of CNT parameters on operation characteristics of the electron field emitter cathode; (а)comparison of the Fowler-Nordheim dependence (5.7) (dash-dotted line) with the calculation result obtained with taking into account the statistical spread of CNT parameters [67] and with the results of measurements [68] (dots). (b) – (d) images of the distribution of the glow intensity over the phosphor surface obtained at various values of the electrical field strength and emission current [68].

Figure 49. Illustration of the influence of the statistical spread of CNT parameters on operation characteristics of the electron field emitter cathode; (а)comparison of the Fowler-Nordheim dependence (5.7) (dash-dotted line) with the calculation result obtained with taking into account the statistical spread of CNT parameters [67] and with the results of measurements [68] (dots). (b) – (d) images of the distribution of the glow intensity over the phosphor surface obtained at various values of the electrical field strength and emission current [68].

One more reason of distinction of the current-voltage characteristic of a CNT array from the Fowler-Nordheim dependence (5.7) relates to a distortion of the electrical field in a vicinity of an individual nanotube engaged into the array under the screening action of neighboring CNTs. This action causes the dependence of the electrical field amplification factor β on not only the aspect ratio of individual nanotubes but also on the geometry of the array and the density of the CNTs arrangement in it. The screening effect manifests itself in a non-monotone dependence of the emission current density on the density of the CNT arrangement in the array. If nanotubes adjacent to each other, the array should be considered as a single emitter whose diameter corresponds to that of the array. In this case the amplification factor is rather minor corresponding to the ration of the height of the array to its diameter. The maximum emission current density is reached at an inter-tube distance of the order of the height of nanotubes comprising the array. If nanotubes are placed far from each other the effect of the electrical field amplification is maximum corresponding to the aspect ratio of an individual nanotube however the emission current density will be rather minor due to a low arrangement density of nanotubes on a substrate. Therefore, the electrical field amplification factor increases in a monotone manner as the average inter-tube distance in the array enhances, while the emission current density depends on this parameter in a non-monotone manner. Figure 50 presents these dependences calculated on the basis of the solution of Laplace equation for a CNT array [69], представлены на рис. 48. As s seen the maximum emission current density is reached at an inter-tube distance of an order of the array’s height.

Enhancement of the nanotube’s temperature due to Joule heating during the emission can change the emission characteristics of the nanotube. These changes can be reflected on both transport characteristics of a CNT( electric conductivity, thermal conductivity) and its emission ability. Indeed a conductor heated up to a high temperature is able to emit electrons even at rather low values of the applied voltage (thermo-electron emission). This occurs due to the existence in a heated conductor of high energy electrons which are able to overcome the potential barrier formed by the crystal lattice. Therefore one can expect for the transition from electron field emission to the thermo-electron emission. Such a transition has an avalanche-like character and can be treated as an instability occurring at exceeding some value of the applied voltage [70]. The physical mechanism of this instability relates to the distortion of the emitter’s thermal balance, when the heat released in result of the Joule heating can’t keep up to remove in result of yjr thermal conductivity. This results in an avalanche-like enhancement of the temperature and the transition from the electron field emission to the thermo-electron emission. This transition is reflected on the current-voltage characteristic of the emitter which is deviated from the Fowler-Nordheim dependence in these conditions. As an example can be considered the current-voltage characteristics of an individual CNT measured in Ref. [71] and calculated in Ref. [70] at various assumptions on the temperature dependence of the thermal conductivity and electric conductivity coefficients (Figure 51). As is seen at high emission currents the current-voltage characteristics differ considerably on the Fowler-Nordheim dependence which is caused by the transition of the emission mechanism from the field one to the thermo-electronic.

5.2.5. Sorption Properties

Sorption properties of CNTs are related to the occurrence of a cavity inside a nanotube which can be filled with not only atoms and molecules but also various liquid or solid substances. One should not that a liquid can penetrate into a nanotube with the open end due to the capillary drawing in effect. Thus filling a nanotube with liquid lead resulted in formation of a thinnest wire of 1.5 nm in diameter [72]. Results of investigations indicate an interconnection between the magnitude of the surface tension of a substance and its capacity to be capillary drawn inside a carbon nanotube. Some of these results are summarized in Table 5 where the experimentally established possibility of capillary drawing various liquid substances is corresponded with the value of the surface tension of these liquids. As is seen capillary properties manifest themselves only in relation to the substances having rather low (less 200 mN/m) surface tension value.

An interest to the problem of filling CNTs with metals and other substances is caused to a large extent by a possibility of a directional impact on electronic characteristics of CNTs. Thus a metal atom inserted into an inner cavity of a nanotube demonstrates a trend to the transition of a valence electron to the external surface of the nanotube нанoтрубки, containing non-filled electron states. The movement of electrons through these states provides an additions mechanism of the conductivity. Thus filling CNTs with potassium or Br₂ results in enhancement of the room temperature conductivity of a CNT sample by 20 – 30 times [74]. Besides of that, filling nanotubes with various substances provides changing the band structure of electronic states and the Fermi level position. Therewith filling nanotubes is an effective tool for control their electronic characteristics.

In some cases the substance filling a nanotube forms a regular crystalline structure inside its inner cavity. Investigation in such structures promotes better understanding the principles of self-organization of a substance. As an example of such investigation can serve Ref. [75] the authors of which have observed a regular crystal KI of 2х2 in size grown inside a single walled nanotube of 1.4 nm in diameter. The electron microscope image of such a crystal is shown on Figure 52. Observations have indicated that the structure of KI crystal situated inside a CNT differ from that of a macroscopic crystal. Thus the lattice constant of the nanocrystal (0.4 nm) exceeds the corresponding value (0.35 nm) for a macroscopic crystal.

There are possible chemical transformations resulting in a change of the chemical content of the substance filling a nanotube. Thus electron beam irradiation with the energy of 300 KeV of single walled nanotubes filled with ZnCl₄ crystal results in decomposition of the molecules which is accompanied with the avulsion of Cl₂ molecule and the partial reduction of Zn after which the clusterization of the remained structure ZnCl_x (x < 4) followed by the spatial cluster separation is observed [76]. Figure 53 presents idealized high resolution electron microscope images of the structures observed at various points in time. The final result of the described procedure is the formation of Xn nanocrystals that possess the properties of quantum dots and can be considered as super-miniature elements of nanoelectron devices.

5.2.6. Peapods

The characteristic value of diameter of single walled nanotube accounts 1 – 1.5 nm. This is quite sufficient for filling CNT with not only atoms or molecules of various substances but more complicated molecular structures. One of the most interesting objects formed at filling CNTs with a condensed substance is obtained as a result of filling a nanotube with fullerene molecules. Such a structure is caked as peapod. The fullerene molecule С₆₀ has a diameter of about 0.7 nm. Besides of that the equilibrium distance between hexagonal layers is about 0.34 nm. Therefore a nanotube can be filled with fullerene molecules С₆₀ under the condition that its diameter exceeds 1.38 nm. One should not that such a diameter is inherent to nanotubes with the chirality indices (10, 10) having the armchair structure. Such nanotubes are formed in a large quantity at the usage of plasma methods of synthesis. In analogy to endohedral fullerenes that are labeled as М_k@С_n (fullerene molecule С_n containing k atoms of the element М) peapods are labeled sometimes as C_n@SWNT (SWNT is a single walled carbon nanotube). Peapods С₆₀@SWNT were synthesized firstly by the authors of Ref. [77] who used for filling CNTs a suspension containing nanotubes and С₆₀ fullerenes in a mixture of nitric acid and sulfuric acid. The obtained material contained single walled CNTs of about 1.4 nm in diameter partially filled with С₆₀ molecule chains. The distance between the centers of molecules accounted about 1 nm which is close to that in fullerite crystal. The degree of filling the nanotubes with fullerene molecules reached of 5.4%.

The most spread method of filling peapods is based on the usage of fullerene vapor at elevated temperatures (500 – 800 К). In this case nanotubes with open end are kept in fullerene vapor which results in their partial or full filling.

An important distinctive peculiarity of peapods relates to an enhanced chemical stability of fullerene molecules enclosed into the CNT envelope. Therewith the nanotube wall serves as a protecting film avoiding the decomposition of the encapsulated substance under the influence of an external chemical action.

Single walled nanotubes can be filled with not only С₆₀ fullerene molecules but also С₇₀ molecules the structure of which reminds the rugby ball. С₇₀ molecule is characterized by two sizes, longitudinal and transverse, which suggests a possibility of occurrence of two types of C₇₀ peapods having structures with differed from each other character of the orientation ordering of C₇₀ molecules inside the nanotube. Such a difference was observed by the authors of Ref. [78] who filled CNTs of 1.37 nm in diameter with С₇₀ molecules and found two types of peapods differed from each other in the average distance between the centers of molecules (1.0 ± 0.01 and 1.1 ± 0.01 нм). These two types of peapod correspond to the longitudinal and transverse orientation of С₇₀ molecules. Measurements imply that the ratio of the number of peapods with the longitudinal orientation to that with transverse ordering accounts 7:3.

Interesting peculiarity in the character of filling nanotubes with fullerene molecules have been established by the authors of Ref. [79] who used not single walled but two walled CNTs for this purpose, The distance between the inner and outer layer in such a structure is equal always to 0.335 nm, while the diameter of the inner tube ranges between 1.0 and 2.6 nm. A sample CNTs was kept in concentrated nitric acid for two hours in order to open the ends, after which it was dried and was experienced to the action of fullerene С₆₀ vapor for 24 hours at a temperature of 500 – 800 К. This resulted in formation of peapods with the filling degree depending on the temperature and reaching 100% at a temperature of 800 К. Transmission electron microscope observations indicate a variety of endohedral structures formed at filling CNTs with fullerenes.

The structure of peapods formed by fullerene molecules and presented on Figure 54 depends on the diameter of the inner CNT. In nanotubes of less than 1.45 nm in diameter С₆₀ molecules form a practically homogeneous linear chain. For nanotubes with the inner diameter exceeding 1.45 nm the arrangement of type “zigzag” is observed (Figure 54a). Therewith the positions of C₆₀ molecule centers are placed in one plane and form a sawtooth line. Further enhancement of the nanotube’s inner diameter is accompanied by a complication of the inner structure of the fullerite crystal.. The centers of fullerene molecules display relating to the nanotube axis and form a spiral structure inside the nanotube. The helix pitch of this structure depends on the inner diameter of the nanotube (Figure 54 b). The nanotubes with the inner diameter exceeding 2.6 nm are able to accommodate in the cross-sectional plane up to four fullerene molecules (Figure 54c).

The further development of investigations addressed to the fabricating and studying peapods has resulted in the creation of nanotubes filled with endohedral fullerene molecules i. e. fullerene molecules containing one or several encapsulated atoms in their inner cavity. The structures formed therewith are labeled as M_k@C_n@SWNT. Thus there were produced and studied the peapods formed in result of filling single walled CNTs of 1.4 nm in diameter with endohedral fullerene molecules La₂@C₈₀ [80]. Investigations have shown the equilibrium distance between La atoms in the molecule La₂@C₈₀ enclosed into the nanotube (0.47 nm) exceeds notably the corresponding value for an isolated La₂@C₈₀ molecule. Such a distinction is caused by the action of the nanotube whose diameter is slightly lesser than the diameter of La₂@C₈₀ molecule plus the optimal value of a gap between the fullerene molecule surface and nanotube wall (2 х 0.34 nm). Therefore the metal-fullerene molecule is exposed to the action of compression forces from the nanotube wall which results in a change of the equilibrium distance between La atoms.

Parameters of the 1D crystal formed in result of filling a single walled nanotube with endihedral fullerene molecules can differ notably from those of the 3D crystal. The reason of such a difference is in the partial or total transition of valence electron found on the external metal shell onto the surface of the fullerene molecule. Therefore the atomic rest situated inside the fullerene cavity possesses a positive charge the interaction of which with the charged fullerene surface or another rest (if it exists) results in a definite localization of the metal atom inside the fullerene cage. The position of the atomic rest is usually displaced notably relating to the center of the fullerene molecule, and if the fullerene cavity contains more than one atomic rest they are found at a considerable distance from each other.

The displacement of the charge atomic rest relating to the center of an endohedral fullerene molecule determines the occurrence of a considerable dipole moment at such a molecule. This promotes the formation of an ordered crystalline structure inside the nanotube filled with endohedral fullerene molecules. Dipole moments of endoheddral fullerene molecules are arranged in a similar manner. Such a structure has been observed in particular in Ref. [81], devoted to the production and investigation of peapods Gd@C₈₂@SWNT.

5.2.7. The Problem of Hydrogen Storage

The interest to sorption characteristics of CNTs relates largely to the problem of hydrogen storage, the solution of which can result in the creation of an ecologically clean auto-transport. Usage of gaseous hydrogen as a fuel in the auto engine permits one to avoid practically fully the environmental pollution with harmful emissions, because the only product of the hydrogen oxidation is water vapor. Therewith it is assumed that the hydrogen production from water can be performed with the usage of the energy of nuclear or wind energy plants during a decreased loading. However on this way arise the problems of gaseous hydrogen safe storage the effective solution of which determines the possibility of thr development of ecologically save transport.

The possibility of usage of carbon nanomaterials for hydrogen storage is determined by two circumstances. Firstly, these materials possess a purely surface structure which permits one to consider them as the most proper object for filling with a gaseous substance through the physical sorption. In this case the quantity of the adsorbed substance is proportional to rather the surface are of the structure but not its volume so that the systems with maximum specific surface are characterized by the highest sorption ability. Secondly, carbon nanostructures possess as a rule with a good electric conductivity which in combination with a high specific surface area permits their usage as a basis of electrochemical devices. Therewith filling a carbon nanomaterial with a gaseous substance occurs in result of a surface electrochemical reaction. Finally one should note that such carbon nanostructures as nanotubes, nanospheres and nanofibers possess an inner cavity which under favorable conditions can be filled in a reversible manner with a gaseous substance. In such a situation not only surface gas sorption but also volumetric filling the cavity occurs, so that the degree of filling the material with a gaseous substance can exceed notable that reached at the surface physical sorption.

The first experiments addressed to filling CNTs with hydrogen have shown encouraging results. These experiments have been reviewed in detail in Ref. [82]. According to results of these experiments, the quantity of hydrogen which is managed to insert into a material containing CNTs in a reversible manner reaches 67% from the material mass. Such a quantity is more than enough for the solution of the hydrogen storage problem and creation of the ecologically safe auto transport. However the mentioned results have not been confirmed in subsequent works, where the quantity of adsorbed hydrogen does not exceeds 1 – 2 % (by weigth).

Contradictive results of experiments on filling CNTs with hydrogen encourage one to estimate the maximum quantity of hydrogen that can be absorbed by the material in result of physical sorption. The maximum sorption ability of a graphene layer in respect to molecular hydrogen can be estimated supposing that this layer is covered with a monomolecular hydrogen film. It is naturally to suppose that the maximum surface density of hydrogen in the monomolecular layer σ_Н = 2.56 х 10^-9 g/cm² corresponds to the density of liquid hydrogen ρ_Н ≈ 0.07 g/cm³. At such a suggestion the maximum sorption ability of a graphene surface is estimated by the expression

η_Н = σ_Н/(σ_С + σ_Н) ≈ 3.2 % (weight),

(5.11)

where σ_С = 7.7 х 10^-8 g/cm² is the surface density of the graphene layer. In the case of two-side coverage of the graphene surface with monomolecular hydrogen layers the result of the performed estimation doubles: η_Н ≈ 6.4 % (by weight). However one should take into consideration that multi-layer crystalline structures (crystalline graphite, multi-walled nanotubes, single-walled nanotube bundles etc) are characterized by the inter-layer distance about 0.34 nm, which is comparable to the gas kinetic size of the hydrogen molecule (about 0.3 nm. Therefore it is hard to expect the two-side coverage of all the surfaces with hydrogen monolayers which just don't fit in between graphene layers. Thus the estimations performed have shown that at the surface coverage of a multi-layer graphene structure the degree of molecular hydrogen filling hardly can exceed 3% (by weight).

In the case of volumetric filling the inner caavity of CNT with hydrogen but not the surface surption the quantity of stored hydrogen depends on the nanotube’s diameter. Thus if a nanotube is filled with liquid hydrogen thrr maximum, filling degree is expressed as follows

η_Н = ρ_Н/(ρ_Н + ρ_t)

(5.12)

where ρ_t = 4σ_C/D = 30.4/D g/cm³ is the density of the nanotube material, D is the nanotube’s diameter, 10^-8 cm. This results in the following dependence of the sorption ability of a CNT η on its diameter D:

η_Н = ρ_Н/(ρ_Н + ρ_t) ≈ 0.07/(0.07 + 30.4/D).

(5.13)

As is seen, the hydrogen filling degree of a nanotube enhances as its diameter increases. The typical value of the diameter of nanotubes synthesized by thee above-described methods ranges usually between 1.2 and1.5 nm, so that the maximum hydrogen filling degree for such CNTs accounts 2.7 – 3.4 % (by weight). The filling degree η_Н = 6.5 % sufficient for the usage of CNTs as the basis of hydrogen storage technology is reached if the nanotube’s diameter exceeds 3 nm. Therefore the analysis performed shows that the usage of CNTs is hardly effective tool for solution the hydrogen storage problem and development of ecologically safe car engines. Graphene.

5.2.8. Phonons

Thermophysical characteristics of graphene (heat capacity, thermal conductivity, thermal expansion coefficient) are determined by phonons which are the vibrations of the crystalline lattice. Peculiarities of the phonon spectrum of graphene and graphene=based materials relate to the 2D structure of the graphene sheet. Graphene possesses the hexagonal structure with two carbon atoms in each cell which results in six phonon branches in the dispersion spectrum: three optical (LO, TO, ZO) and three acoustic (LA, TA, ZA). Yje phonon modes LA and TA correspond to longitudinal vibrations of carbon atoms within the graphene plane. The mode ZA corresponds to vibration of carbon atoms in the direction perpendicular to that of vibrations LA and TA modes with escaping atoms from the graphene plane.

Exploration of phonon characteristics and the lattice vibration dynamics is usually performed using the Raman spectroscopy. [5]. Interaction of the incident optical radiation with vibrations of the crystal lattice atoms results in its inelastic scattering on crystal atoms. In result of this interaction the spectrum of the scattered radiation contains along with the incident radiation line also satellite lines the frequencies of which differ from the incident radiation one by the lattice vibration natural frequencies. Both the frequency and the intensity of the scattered light depend on the temperature and incident radiation frequency so that the Raman spectrum of a material contains the information on its temperature. In the case of non-homogeneous distribution of the temperature the coordinate dependence of the Raman spectrum permits the determination of the character of such a distribution. In graphene similarly to graphite the most intense Raman lines are the peaks G and D (1580 и 1350 cm^-1), the first of which corresponds to the mode related to symmetric vibration of sp² bonds while the second one is determined by defects in graphene structure. Figure 55 presents a typical Raman spectrum of graphene [5].

5.2.9. Thermal Conductivity

As it follows from the results of numerous measurements, graphene possesses the highest room temperature thermal conductivity between all the known materials. Its thermal conductivity coefficient accounts 4800 – 5300 W/m K, which exceeds the corresponding value for diamond (3320 W/m K) and single walled CNTs (3500 W/m K). The thermal conduction of graphene is determined by phonons, and extraordinary high value of this parameter relates to a miniature size of the sample for which the existence of defects has rather low probability. The thermal conductivity of a defectless graphene at a room and higher temperatures is limited by the phonon-phonon scattering.

The most effective approach to the measurement of the thermal conductivity of graphene is based on the temperature dependence of the Raman spectrum of this material [83]. In accordance to this approach a laser beam of about 0.5 – 1.0 μm in diameter is focused onto the center of a graphene sheet suspended between supports like bridge. This causes a heating of the central region of the graphene sample by several yens degrees. The temperature of the heated graphene region is determined on the basis of results of measuring the shift of the peak G position in the Raman spectrum. At a relatively low heating the dependence of the local temperature enhancement on the laser radiation intensity has a linear character so that the factor in this dependence is proportional to the thermal conductivity coefficient of graphene.

Figure 56 presents the schema of the experiment on measuring the longitudinal thermal conductivity of graphene [83]. As a substrate was used a Si/SiO₂ plate having a set of longitudinal surface tranches of about 300 nm in depth an up to 5 μm in width. The substrate was covered with a large quantity of graphene sheets produced by micromechanical exfoliation of pyrolytic graphite. Then longitudinal graphene samples having close to rectangular form and covering a trench like a bridge were selected by means of a Raman spectrometer. Argon ion laser with the wavelength of 0.48 μm was used as a source of radiation. The focal spot size was about 0.5 μm, however the size of the heated region increased up to 1 μm due to the electron diffusion. The value of the thermal conductivity coefficient measured by the above-described method turned out to be in the range of 4840 – 5300 W/m К. Treatment of the measurement results permitted also the determination of the diffusion mechanism of the heat transport. According to the analysis the phonon mean free path relating to the scattering is equal to λ_р ≈ 775 nm. This value is much lesser than the characteristic size of the graphene samples (5 – 10 μm) which indicates a prevailing role of the diffusion heat transfer mechanism over the ballistic one.

The measurement results imply that the thermal conductivity of graphene exceeds more than twice the relevant value for graphite (κ ≈ 2000 W/m К), which presents the structure consisted of a set of graphene layers. One can conclude from this that the occurrence of neighboring layers situated on the distance of 0.34 nm lowers the thermal conductivity coefficient of graphene. This is caused by inter-layer interaction determining an additional mechanism of phonon scattering. The dependence of the thermal conductivity coefficient of graphene on the number of layers in the sample was measured by the authors of Ref. [84] who used the above-described method based on the Raman spectroscopy. The few layer graphene samples were obtained by the micromechanical exfoliation of pyrolitic graphite. The number of layers in the samples under investigation was determined on the basis of processing the Raman spectra. The quantities of the thermal conductivity coefficient of the samples were evaluated using the temperature shift of G-line (ω ≈ 1579 см^-1) of the Raman spectrum under the action of the laser radiation which was agreed with the solution of the heat conductivity equation by the finite difference method. The measurements results are shown on Figure 57.

One should note that the main physical reason of the recordable thermal conductivity of graphene relates to a miniature size of samples that does not practically content defects. Enhancement of the sample size provides an increase of probability of defect occurrence, which results in lowering the thermal conductivity coefficient. Figure 58 presents the dependences of the thermal conductivity coefficient on the concentration of vacancy defect (a) and defects related to OH adducts (b) calculated within the frame of various models [85]. As is seen the thermal conductivity of graphene at a defect content on the level of 1% is an order of magnitude lowers that that for defectless graphene.

5.2.10. Mechanical Properties

Mechanical characteristics of graphene are similar to those for carbon nanotubes for which the Young modulus has a recordable value (on the level of TPa). Such a high magnitude of the mechanical rigidity is caused by a miniature size of nanocarbon samples (CNT, graphene) for which the probability of defect existence lowering the graphene rigidity is rather low. Figure 59 presents the dependence of the Young modulus of a graphene ribbon on its area calculated by the quantum chemistry method [86]. These data are in a qualitative agreement with results of a direct experiment [87] where the interconnection between the tensile load and stretch value was measured. The Young modulus determined in such a manner turned out to be equal to (1 ± 0.1) TPa. This value is close to that for defectless carbon nanotubes. For the comparison one should not that the Young modulus of a steel cable is of about 5 GPa i. e. about 200 times lower than that for nanocarbon.

The tensile strength of graphene was determined on the basis of direct measurements of the load providing the destroy of the sample. The result of evaluation of this parameter depends on the assumed value of the thickness of a graphene layer. Supposing that the thickness of a graphene layer is equal to 0.335 nm one obtains the tensile strength of graphene accounts 130 ± 10 GPa at a maximum value of the relative tension of 0.25.

5.2.11. Electrical Properties

Each carbon atom included into graphene possesses a free electron which is able to move along the lattice under the action of the electric field. This determines the conductivity of graphene. Important parameter determining electrical properties of a conductor is the mobility of charged particle μ that is defined as the ratio of the drift velocity of charge curriers w to the magnitude of the electrical field F. The electron mobility is graphene is determined by the measurement conditions and defect content which in its turn depends on the synthesis conditions. Thus if the graphene sheet is placed on a SiO₂ substrate, the electron mobility accounts 10000 – 15000 cm²/V s, as it follows from the measurements [88]. The electron mobility in graphene suspended between two electrodes at a temperature 5 K reaches the value 200000 cm²/V s [88,89].

The electric resistance of defectless graphene samples has a ballistic character and is expressed by Eq. (5.1), similarly to defectless CNTs. Structural defects present the scattering centers for electrons of conductivity so that the occurrence of such centers lowers the conductivity of the material. An enhancement of the sample size is accompanied with a transition from ballistic to Ohmic conduction mechanism. The resistance of samples having the size lesser than the electron mean free path relating to the scattering on defects λ_е corresponds to Eq. (5.1) and does not depend on the sample size, in distinction on the known dependence for macroscopic objects. As the sample size increases the role of the electron scattering on defects enhances, which results in a rising size dependence of the sample resistance. The transition from the ballistic to Ohmic conduction mechanism was observed, in particular, by the authors of Ref. [90], who determined the temperature dependence of the electron mean free path λ_е in relation to scattering on defects on the basis of measurements of the size dependence of the conductance of graphene samples. The measurements have stated that λ_е = 4.5 μm at a temperature of 2 К and 2.3 μm at a temperature of 250 К. The corresponding values of the mobility accounted 3х10⁷ and 1.4х10⁷ cm²/V s.

5.2.12. Optical Properties

The character of propagation of electromagnetic radiation through graphene relates to the interaction of photons with electrons. Due to a difference in the mass of electron and photon this interaction is determined by the fine structure constant α = е²/ħс = 1/137 so that the absorption coefficient of the optical radiation in graphene is equal to πα = 2.3%. Here е is the electron charge, с is light velocity and ħ is the Plank constant. In the case of a few layer graphene the absorption coefficient is equal to the above-given quantity multiplied by the number of layers. Therewith the effect on non-linear absorption is observed [91] in accordance with which at exceeding some value of the radiation intensity the absorption is saturated and the material becomes to be transparent.

6. Applications of Nanocarbon

7. Conclusions

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