Carbons graphene sheets

High-resol utlon TEM images of SiC nanoparticles top - evidence of crystallization fringes bottom -presence of carbon graphene sheets on the nanoparticle surfaces in nanopowders synthesized with an excess of carbon (Charpentier et al. 1999) (O Figure la has been reproduced with permission from Boucle et al. (2006). O Figure 1b has been reproduced with permission from Kassiba et al. 

The circumference of any carbon nanotube is expressed in terms of the chiral vector = nai ma2 which connects two crystallographically equivalent sites on a 2D graphene sheet [see Fig. 16(a)] [162]. The construction in... 

Closely related to the ID dispersion relations for the carbon nanotubes is the ID density of states shown in Fig. 20 for (a) a semiconducting (10,0) zigzag carbon nanotube, and (b) a metallic (9,0) zigzag carbon nanotube. The results show that the metallic nanotubes have a small, but non-vanishing 1D density of states, whereas for a 2D graphene sheet (dashed curve) the density of states... 

Fig. 24. Adsorption of lithium on the internal surfaces of micropores formed by single, bi, and trilayers of graphene sheets in hard carbon.

Powder X-ray diffraction and SAXS were employed here to explore the microstructure of hard carbon samples with high capacities. Powder X-ray diffraction measurements were made on all the samples listed in Table 4. We concentrate here on sample BrlOOO, shown in Fig. 27. A weak and broad (002) Bragg peak (near 22°) is observed. Well formed (100) (at about 43.3°) and (110) (near 80°) peaks are also seen. The sample is predominantly made up of graphene sheets with a lateral extension of about 20-30A (referring to Table 2, applying the Scherrer equation to the (100) peaks). These layers are not stacked in a parallel fashion, and therefore, there must be small pores or voids between them. We used SAXS to probe these pores. 

Fig. 32. Reversible capacity of microporous carbon prepared from phenolic resins heated between 940 to 1 I00°C plotted as a function of the X-ray ratio R. R is a parameter which is empirically correlated to the fraction of single-layer graphene sheets in the samples.

Carbon nanotube research was greatly stimulated by the initial report of observation of carbon tubules of nanometer dimensions[l] and the subsequent report on the observation of conditions for the synthesis of large quantities of nanotubes[2,3]. Since these early reports, much work has been done, and the results show basically that carbon nanotubes behave like rolled-up cylinders of graphene sheets of bonded carbon atoms, except that the tubule diameters in some cases are small enough to exhibit the effects of one-dimensional (ID) periodicity. In this article, we review simple aspects of the symmetry of carbon nanotubules (both monolayer and multilayer) and comment on the significance of symmetry for the unique properties predicted for carbon nanotubes because of their ID periodicity. 

In the theoretical carbon nanotube literature, the focus is on single-wall tubules, cylindrical in shape with caps at each end, such that the two caps can be joined together to form a fullerene. The cylindrical portions of the tubules consist of a single graphene sheet that is shaped to form the cylinder. With the recent discovery of methods to prepare single-w alled nanotubes[4,5), it is now possible to test the predictions of the theoretical calculations. 

Fig. 3. The 2D graphene sheet is shown along with the vector which specifies the chiral nanotube. The pairs of integers ( , ) in the figure specify chiral vectors Cy, (see Table I) for carbon nanotubes, including zigzag, armchair, and chiral tubules. Below each pair of integers (n,m) is listed the number of distinct caps that can be joined continuously to the cylindrical carbon tubule denoted by (n,wi)[6]. The circled dots denote metallic tubules and the small dots are for semiconducting tubules.

Fig. 2. By rolling up a graphene sheet (a single layer of ear-bon atoms from a 3D graphite erystal) as a cylinder and capping each end of the eyiinder with half of a fullerene molecule, a fullerene-derived tubule, one layer in thickness, is formed. Shown here is a schematic theoretical model for a single-wall carbon tubule with the tubule axis OB (see Fig. 1) normal to (a) the 6 = 30° direction (an armchair tubule), (b) the 6 = 0° direction (a zigzag tubule), and (c) a general direction B with 0 < 6 < 30° (a chiral tubule). The actual tubules shown in the figure correspond to (n,m) values of (a) (5,5), (b) (9,0), and (c) (10,5).

Carbon nanotubes were first thought of as perfeet seamless eylindrieal graphene sheets —a defeet-free strueture. However, with time and as more studies have been undertaken, it is elear that nanotubes are not neeessarily that perfeet this issue is not simple bc-eause of a variety of seemingly eontradictory observations. The issue is further eomplicated by the faet that the quality of a nanotube sample depends very mueh on the type of maehine used to prepare it[l]. Although nanotubes have been available in large quantities sinee 1992[2], it is only recently that a purification method was found[3]. So, it is now possible to undertake various accurate property measurements of nanotubes. However, for those measurements to be meaningful, the presence and role of defeets must be elearly understood. 

Abstract—Experimental and theoretical studies of the vibrational modes of carbon nanotubes are reviewed. The closing of a 2D graphene sheet into a tubule is found to lead to several new infrared (IR)- and Raman-active modes. The number of these modes is found to depend on the tubule symmetry and not on the diameter. Their diameter-dependent frequencies are calculated using a zone-folding model. Results of Raman scattering studies on arc-derived carbons containing nested or single-wall nanotubes are discussed. They are compared to theory and to that observed for other sp carbons also present in the sample. 

A single-w all carbon nanotube can be visualized by referring to Fig. 3, which shows a 2D graphene sheet with lattice vectors a and U2, and a vector C given by... 

The yield strengths of defect-free SWNTs may be higher than that measured for Bacon s scroll structures, and measurements on defect-free carbon nanotubes may allow the prediction of the yield strength of a single, defect-free graphene sheet. Also, the yield strengths of MWNTs are subject to the same limitations discussed above with respect to tube slippage. All the discussion here relates to ideal nanotubes real carbon nanotubes may contain faults of various types that will influence their properties and require experimental measurements of their mechanical constants. 

MWCNT synthesized by catalytic decomposition of hydrocarbon does not contain nanoparticle nor amorphous carbon and hence this method is suitable for mass production. The shape of MWCNT thus produced, however, is not straight more often than that synthesized by arc-discharge method. This differenee could be aseribed to the strueture without pentagons nor heptagons in graphene sheet of the MWCNT synthesized by the catalytic decomposition of hydrocarbon, which would affect its electric conductivity and electron emission. 

FIGURE 4.4 Graphene sheet and single-walled carbon nanotube. 

Carbon nanotubes (CNTs) were discovered in 1991 by Iijima [182] and since then they have attracted much attention in many research fields. CNTs can be described as tubular structures rolled up from a graphene sheet. Depending on the number of tubular walls CNTs can be classified as single-walled carbon nanotubes (S WCNTs)... 

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