Carbon dangling bonds

Apparently, the cohesive energy of these clusters shows a very slow convergence with the size of the molecule. This should not be surprising, since the number of unsaturated valences "dangling bonds" per carbon atom is one in 1,1/2 in 2 and 1/3 in 3. 

Assuming an approximately constant cohesive energy per C-C bond, that trend is understandable. With clusters on the above general type, the number of carbon atoms is 6N, the number of dangling bonds is 6N, and the number of C-C bonds is 9N -3N. The energy per bond shows a smoother trend, the numbers being 71.0, 77.6 and 79.9 kcal/mol, respectively. Alternatively, the energies can be fitted to a two-parameter expression of the form... 

If the focus of interest is on the carbon clusters themselves, then of course no substitute system can be used. However, for studying the convergence of properties towards bulk values one can minimize the termination effects by saturating the dangling bonds in the simplest possible way, i.e. with hydrogen. By that approach one can both avoid the problem of handling an excessive number of open shells, and obtain a series of molecules that converge towards bulk properties more smoothly than the bare carbon clusters. 

Breaking one bond in an ethylenediamine complex leaves the en ligand dangling but tethered to the metal by the second nitrogen atom. (Each carbon atom bonds to two hydrogen atoms that are not shown.)... 

Figure 6 Polyhedral view (to scale) of structure types ai(a), a2(b) and two orientations of 03(0 and d) for CtqMu. The muon is at the end of the dangling bond and in views (a) and (b) lies in the plane of the paper. For views (a), (b) and (c) four edge carbon atoms are also in the plane of the paper. The other visible atoms are above the paper. Each atom above the paper hides a corresponding atom below the paper except for type 03 where in the region of the muon the undistorted structure below the plane is shown with dashed lines. This is useful since it clearly shows the nature of the distortion. View (d) is an orientation of type 03 to illustrate that the distortion is similar to the other type a structures...

In this paper, we presented new information, which should help in optimising disordered carbon materials for anodes of lithium-ion batteries. We clearly proved that the irreversible capacity is essentially due to the presence of active sites at the surface of carbon, which cause the electrolyte decomposition. A perfect linear relationship was shown between the irreversible capacity and the active surface area, i.e. the area corresponding to the sites located at the edge planes. It definitely proves that the BET specific surface area, which represents the surface area of the basal planes, is not a relevant parameter to explain the irreversible capacity, even if some papers showed some correlation with this parameter for rather low BET surface area carbons. The electrolyte may be decomposed by surface functional groups or by dangling bonds. Coating by a thin layer of pyrolytic carbon allows these sites to be efficiently blocked, without reducing the value of reversible capacity. 

In addition to diamond and amorphous films, nanostructural forms of carbon may also be formed from the vapour phase. Here, stabilisation is achieved by the formation of closed shell structures that obviate the need for surface heteroatoms to stabilise dangling bonds, as is the case for bulk crystals of diamond and graphite. The now-classical example of closed-shell stabilisation of carbon nanostructures is the formation of molecules and other Fullerenes by electric arc evaporation of graphite [38] (Section 2.4). 

The structure of CNTs can be understood as sheets of graphene (i.e. monolayers of sp2 hybridized carbon, see Chapter 2) rolled-up into concentric cylinders. This results in the saturation of part of the dangling bonds of graphene and thus in a decrease of potential energy, which counterbalances strain energy induced by curvature and thus stabilizes the CNTs. Further stabilization can be achieved by saturating the dangling bonds at the tips of the tubes so that in most cases CNTs are terminated by fullerene caps. Consequently, the smallest stable fullerene, i.e. C60, which is - 0.7 nm in diameter, thus determines the diameter of the smallest CNT. The fullerene caps can be opened by chemical and heat treatment, as described in Section 1.5. 

One can observe that carbon nanoshells, as consisting of small domains of graphitic sp sheets, must exhibit multitude of dangling bonds at their peripheries. These domains of stacked graphene sheets can also be seen as layered graphitic nanocrystals. The dimensions of these nanocrystals (few tenths nanometers thick by few hundred nanometers length) provide efficient constrains for mobility of n... 

Fig. 4.17 Model of a carbon nanoshell pointing to the stacks of 5-10 aligned layers within the shell. Hydrogen can possibly bond to the dangling bonds on the periphery of layered graphitic...

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