Nanotube radius

Fig. 5. Band gap as a function of nanotube radius calculated using empirical tight-binding Hamiltonian. Solid line gives estimate using Taylor expansion of graphene sheet results in eqn. (7).

Second, we expect that the strain energy per carbon should increase inversely proportional to the square of the nanotube radius[23]. Based on a continuum elastic model, Tibbetts[4] derived a strain energy for a thin graphitic nanotube of the general form ... 

Fig. 7. Strain energy per carbon (total energy minus total energy extrapolated for the graphite sheet) as a function of nanotube radius calculated for unoptimized nanotube structures (open squares) and optimized nanotube structures (solid circles). Solid line depicts inverse square relationship drawn through point at smallest radius.

Figure 4. Charge transfer Aq/e from the H adatom to the zigzag BNNTs (n,0) with n = 5-10 as a function of the nanotube radius R. Solid dots and triangles refer to the adsorption on the B atom and the N atom, respectively. The numbers in parenthesis stand for the tube chirality indices. The solid and dashed lines are intended as a guide to the eye.

Figure 30 The size of the bandgap as a function of the carbon nanotube radius for non-metallic carbon nanotubes. The gap for a 10 nm tube is of the order of 0.1 eV [125].

Our model operates with four parameters 1) longitudinal effective mass 2) azimuthal effective mass m 3) thickness of a conductive layer 2A 4) effective nanotube radius r . The agreement with experiments or with existing approximations can be obtained by a variation of these parameters. 

Fig. 32. a Scanning force image of a bundle of tori (bundle of toroidal single walled nanotubes radius ca. 300 nm) generated by laser vaporisation of graphite [72]. The structure exhibits an apparent height of ca. 1.5 nm and width of 4-8 nm (Courtesy of C. Dekker). b Model of a toroidal 240-atom graphite structure (Courtesy of H. Terrones)... 

The strength of the EME coupling in nanosized ferroics is inversely proportional to the system characteristic size (e.g., nanotube radius or film thickness). Linear ME effect can be induced by the linear FME effect in nanosized ferroelectrics-... 

In this chapter we introduce a simple methodology based on molecular mechanics that can be used to estimate the free energy of mixing nanotubes with polymers and apply it to predicting the thermodynamic stability of polystyrene-CNT composites as a function of nanotube radius. We anticipate that this approach can be adapted to other systems of interest by tailoring the constituent molecular models to represent the polymers, surfactants, and functional groups under consideration as part of a rational strategy to determine the best approach to the preparation of well-dispersed and stable polymer-CNT composites. 

Consider next the A p term. From Figure 4.2, it appears that the polymer effectively encircles the nanotube. The distance between the surface of the nanotube and the polymer d) is determined by the van der Waals radii of the interacting atoms and should be relatively independent of the diameter of the nanotube. Therefore, the nature of polymer-nanombe interaction is similar to the case of two parallel sheets, for which the energy of interaction per unit surface area is constant. This is, in fact, the limiting behavior of Aii p as oo. However, because of their concentric arrangement, the number of interactions between atoms on the cylindrical surface of the polymer and atoms on the surface of the nanotube (per unit area of the nanotube) increases as the ratio of the surface areas. Thus, we infer that both AS, nanotube radius so that... 

FIGURE 4.5 Variation of the nanotube-nano tube and the sum of the nanotube-polymer and polymer-polymer energies as a function of nanotube radius. 

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