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Simulations of single-wall carbon nanotube(SWCNT)s having a different chiral vector under axial compression were carried out based on molecular dynamics to investigate the effect of the helicity on the buckling behavior. Calculation was performed at room temperature for (8,8) armchair, (14,0) zigzag and (6,10) chiral single-wall carbon nanotubes. The Tersoff potential was used as the interatomic potential since it describes the C-C bonds in carbon nanotubes reliably. A conjugate gradient (CG) method was used to obtain the equilibrium configuration. Compressive force was applied at the top of a nanotube by moving the top-most atoms downward with the constant velocity of 10m/s. The buckling load, the critical strain, and the Young's modulus were calculated from the result of MD simulation. A zigzag carbon nanotube has the largest Young's modulus and buckling load, while a chiral carbon nonotube has the lowest values.

A metallic (semiconducting) single-wall nanotube contains an irrational (integral) number of carbon hexagons in the pitch. The room-temperature conductivity is higher by two to three orders of magnitude in metallic nanotubes than in semiconducting nanotubes. Tans et al. [Nature386 (1997) 474] measured the electrical currents in metallic single-wall carbon nanotubes under bias and gate voltages, and observed non-Ohmic behaviors. The original authors interpreted their data in terms of a ballistic transport due to the Coulomb blockage on the electron-carrier model. The mystery of why a ballistic electron is not scattered by impurities and phonons is unexplained, however. An alternate interpretation is presented based on the Cooper pair (pairon)–carrier model. Superconducting states are generated by the Bose–Einstein condensation of the ± pairons at momenta 2πℏn/L, where L is the tube length and n a small integer. As the gate voltage changes the charging state of the tube, the superconducting states jump between different n. The normal current peak shapes appearing in the transition are found to be temperature-dependent, which is caused by the electron–optical phonon scattering.

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.

Single-walled carbon nanotubes (SWNTs) synthesized by catalytic decomposition of an alcohol were purified by extraction. The purified SWNTs were characterized on the basis of visible-near infrared (vis-NIR) absorption, photoluminescence and Raman spectroscopic analyses, scanning electron microscopy (SEM) observation, and thermal analysis. Selective extraction of metallic nanotubes was also achieved by the extraction condition.