Randomly oriented carbon molecules

Calculate the entropy of a tiny solid made up of four diatomic molecules of a compound such as carbon monoxide, CO, at T = 0 when (a) the four molecules have formed a perfectly ordered crystal in which all molecules are aligned with their C atoms on the left (top-left image in Fig. 7.7) and (b) the four molecules lie in random orientations (but parallel, any of the images in Fig. 7.7). 

Solution Carbon monoxide has a small electric dipole moment (approx 0.1 Debye), which gives the molecules an energetically preferred orientation as T — 0. However, this dipole moment is so small that the preference is not appreciable until very low temperatures, and the random orientation of the molecules (the dipole has equal probability of pointing in one direction or its opposite) remains as the temperature is lowered. For a mole of CO, each molecule can point in either of two directions and there are 2Na configurations that are about equally probable. This model predicts a residual entropy of... 

Figure 9. Organization of carbon sheets in nanocrystalhne carbons. Case (A) represent bent sheets which are stacked concentrically and randomly. In the high-resolution TEM of fullerene black filamentous structures from carbon macrocycles which did not react to fullerene molecules can also be seen (weak contrasts). Case (B) shows the arrangement of stacks of planar graphene units. Only few of these stacks are oriented with the o-axis parallel to the electron beam and can be imaged as illustrated in the sketch, the majority are randomly orientated and give hence an amorphous contrast. Case (C) is the same as (B) with the addition of covalent bonding interactions between the stacks. These bonds are invisible by electron microscopy but influence the graph-iti/ability of the carbon.

As an example, consider a crystal of carbon monoxide (CO). The dipole moment of CO is quite small (0.12 D) and carbon and oxygen are very similar in size, so the CO molecule is very nearly symmetrical. In a perfect crystal of CO [Figure 8.8(a)], the CO molecules are all aligned in an ordered fashion. However, because the two ends of the molecule are so similar, the molecules in a real crystal may be randomly oriented [Figure 8.8(b)]. 

On the basis of the study of the solvent, temperature, and pressure effects, we show how the NMR rotational correlation times T2k for a heavy water molecule in neat liquid and organic solvents are cotrelated with the strength of solute-solvent interactions, in particular, H bonds. At room temperature (30 C), the correlation time is 2.1 ps in the random H-bond network in heavy water, whereas it is as small as 0.1 ps in such an apolar, hydrophobic solvent as carbon tetrachlmi because of the absence of the H bonds between water molecules. Pressure distorts H bonds and accelerates the orientational motion of water molecules in neat liquid. I%m evidence is collected for the limitations of the Stdces-Einstein-Debye (SED) law in solution. 

Although Kekule and Couper were correct in describing the tetravalent nature of carbon, chemistry was still viewed in a two-dimensional way until 1874. In that year, Jacobus van t Hoff and Joseph Le Bel added a third dimension to our ideas about molecules. They proposed that the four bonds of carbon are not oriented randomly but have specific spatial directions. Van t Hoff went even further and suggested that the four atoms to which carbon is bonded sit at the corners of a regular tetrahedron, with carbon in the center. 

Much less ordered than PAN-based high-strength CFs are the isotropic CFs. They are produced by the carbonization of isotropic pitch fibers (or other fibrous precursors such as phenolic resins or cellulose, including rayon), without any attempt to obtain a preferred orientation of the polyaromatic molecules in the fiber direction. Consequently, they have a random nanotexture and belong to the low modulus class of CFs [16]. Rather than being used for high-performance reinforcement purposes, they find their application as thermal insulators for furnaces or as reinforcements for cement [1]. Another important use of isotropic CFs is as a feedstock for the production of activated carbon fibers, a material dealt with in Section 2.4.4. 

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