The effect of boundary conditions on the vibrations of armchair, zigzag, and chiral single-walled carbon nanotubes

Abstract

Low-field mobility in ultrathin silicon nanowire junctionless transistors Appl. Phys. Lett. 99, 233509 (2011) Influence of cross-section geometry and wire orientation on the phonon shifts in ultra-scaled Si nanowires J. Appl. Phys. 110, 094308 (2011) Thermal transport in double-wall carbon nanotubes using heat pulse J. Appl. Phys. 110, 074305 (2011) Phonon coherent resonance and its effect on thermal transport in core-shell nanowires J. Chem. Phys. 135, 104508 (2011) Single mode phonon energy transmission in functionalized carbon nanotubes Single-walled carbon nanotubes (SWCNTs) have three distinct structures: armchair, zigzag, and chiral. It is known that they have different electronic properties, but the situation regarding their vibrational behavior is less clear. Doubly clamped nanotubes of all three types exhibit the same vibrational modes, and their vibrations in the directions perpendicular to the nanotube axis are degenerate. In nanotube applications, such as sensors based on nano-electro-mechanical systems, their ends are not fully clamped, thus their vibrational behavior could differ. Careful molecular dynamics simulations of SWCNTs with boundary conditions, which imitate the partly clamped experimental conditions, show that armchair, zigzag, and chiral nanotubes indeed vibrate differently. The symmetry between the two perpendicular directions is broken, and SWCNT type does influence the vibrational modes.

Visualization of electronic density

“…Our motivation for the study of nanotube vibrations was to study the way that the adsorption of DNA onto a nanotube would change the vibrational frequencies, hence enabling evaluation of the DNA mass. Part of this project also relates [26] to the nature of the nanotube boundary conditions, and in order to mimic the experimental case, where it sits on two side supports we need to know how the nanotube settles on these.…”

“…For a nanotube of radius r, length L, and volume V the frequency of the nth mode, f n , of its vibrations depend on the nanotube's width, w and radius r via two quantities used in its calculation: the moment of inertia, I = π rw(4r 2 + w 2 ) and mass linear density ρ L = 2π rwρ V (ρ L is the density per unit length and ρ V the density per unit volume) which are related to the tubes' Young's modulus, E. The exact relation depends on the boundary conditions and model; and the main point of [24][25][26][27][28] was to deduce these frequencies without explicit use of any of the competing analytic models. Literature estimates of E range between 1-6 Tpa, and this is known as Yakobson's paradox [30].…”

“…The nanotube simulations at the atomistic scale that form the basis for the present study are described in [24][25][26][27][28] with codes given in [29]. In brief the tube is equilibrated with periodic boundary conditions, then ''cut open'' and clamped with the appropriate boundary conditions.…”

“…The essential parameter for model analysis is the width of the nanotube wall, and it is the electronic cloud around the atomic nuclei that determines this. In a series of papers and a thesis, Pine and coworkers [23][24][25][26][27][28][29] reviewed the literature and carried out extensive classical molecular dynamics simulations at the atomistic scale to carefully determine the limits of applicability of the analytic theory. While values for the wall width were deduced indirectly by us and many others, direct estimation is of course more desirable.…”

Ultrafast spectroscopy of super high frequency mechanical modes of doubly clamped beams

“…27 Experimentally, it has also been shown that the support compliance plays a role in the performance of micromechanical devices. 28 Here, by laying the beam on the substrate, a condition of full bottom support is obtained and investigated, numerically and experimentally, and compared with the free standing condition.…”