Application to PS-CNT Composites

The effects of increasing the lengths of the model nanotubes from 3.6 nm to 7.3 nm can be seen in the data presented in Tables 4.1 and 4.2. These results seem to justify the intuitive notion that for a specified diameter, the energies of 

FIGURE 4.3 Smallest of the bundled nanotube models used for computing AE . 

Number of Nano tubes Length of Nano tube (nm) Surface Area of Nanotube (nm ) Number of Carbon Atoms/Area (mn ) bo (nm) AEl (kJ/mol nm ) 

The dependence of these energies on the radius of the constituent nanotubes, however, is more complicated. Consider first the AE term. If the number of atoms per unit surface area is independent of the radius of the nanotube (which is tantamount to assuming that the aromatic rings have the same strucmres), it can be shown that the energy of extraction of a CNT from a bundle (per unit surface area of the nanotube) will decrease approximately in accordance with  

A similar analysis can be applied to both AE and AE. The latter of these two terms is proportional to the surface energy of the polymer (see the discussion above), which increases linearly with the number of atoms that are brought from the interior to the surface. The area of the nanotube cavity in the polymer matrix is 2jz(R + d)l, where d = 0.25 nm is the average distance between the polymer and the surface of the nanotube. Of course, the outer surface of the polymer must also expand to accommodate the nanotube. The correction factor. 

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