End-cap effects on vibrational structures of finite-length carbon nanotubes

Vibrational structures of C60-related finite-length nanotubes, C(40+20n) and C(42+18n) (1 < or = n < or = 4), in which n is, respectively, the number of cyclic cis- and trans-polyene chains inserted between fullerene hemispheres, are analyzed from density functional theory (DFT) calculations. To illuminate the end-cap effects on their vibrational structures, the corresponding tubes terminated by H atoms C(20n)H20 and C(18n)H18 (1 < or = n < or = 5) are also investigated. DFT calculations show a broad range of vibrational frequencies for the finite-size nanotubes: high-frequency modes (1100-1600 cm(-1)) containing oscillations along tangential directions (tangential modes), medium-frequency modes (700-850 cm(-1)) whose oscillations are located on the edges or end caps, and low-frequency modes (300-600 cm(-1)) involving oscillations along the radial directions (radial modes). Broadening of the calculated frequencies is due to the number of nodes in the standing waves of normal modes in the finite-size tubes. In the capped tubes, calculated vibrational frequencies are insensitive to the number of chains (n), whereas in the uncapped tubes, most vibrational frequencies change significantly with an increase in tube length. The discrepancy in the size dependency is reasonably understood by their C-C bonding networks; the capped tubes have similar bond-length alternation patterns within the polyene chains irrespective of n, whereas the uncapped tubes have various bond-deformation patterns. Thus, DFT calculations illuminate that the edge effects have strong impacts on the vibrational frequencies in the finite-size nanotubes.