The oscillatory damped behaviour of incommensurate double-walled carbon nanotubes

Abstract

The mechanical properties of sliding carbon nanotubes have been investigated by classicalmolecular dynamics simulations in the canonical ensemble. In particular we have studieddamped oscillations in the separation between the centres of mass of the inner and outertubes of double-walled carbon nanotubes (DWCN). Incommensurate DWCNs forming (7,0)@(9, 9) structures were simulated for systems at 298.15 K with axial lengthsfrom 12.21 to 98.24 nm. The oscillations exhibited frequencies in the range ofgigahertz with the frequency decreasing as the length of the system increases. Thetime until oscillations become negligible exhibited a nearly linear dependence onthe length of the system. Two macroscopic models were developed in order tounderstand the forces involved in terms of macroscopic properties like friction andshear. The first model considered constant restoring forces during the whole event,while in the second the value of these constant restoring forces depended on theinitial conditions of each oscillation. Both models reproduced the oscillations quitewell, while the second model allows us to predict the dynamic shear strength interms of the axial length of the system for tubes with the same diameters. Thecalculated dynamic shear strength exhibited monotonic behaviour with an inversedependence on the length of the system. For systems with unequal axial lengths, therestoring force, which drives the oscillation, is reduced compared to the systemwith equal lengths, regardless of whether the outer nanotube is longer or shorter.