Double-wall nanotubes: classification and barriers to walls relative rotation, sliding and screwlike motion A.V. Belikov, Yu.E. Lozovik a, * , A.G. Nikolaev, A.M. Popov a Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 142092, Moscow Region, Russia Received 6 September 2003 Published online: 14 January 2004 Abstract Classification scheme for double-wall carbon nanotubes (DWCNT) based on their symmetry is proposed. According to the scheme each DWCNT ascribes to a family of DWCNTs with the same geometrical parameters: interwall distance, nanotube unit cell length and difference of wall chirality angles. This geometrical parameters, the barriers for the relative rotation of the wall, sliding along the nanotube axis and helical line of ÔthreadÕ and threshold forces causing the relative motion of the walls are calculated for a set of DWCNTs. The results of calculations allow to select DWCNTs that can be used in mechanical nanodevices such as nano- bearings and of bolt-and-nut pairs. Possibility of orientational melting of DWCNTs with commensurate walls is discussed. Ó 2003 Published by Elsevier B.V. 1. Introduction Since the discovery of carbon nanotubes [1] their unique electronic and mechanical properties are finding promising applications in nanoelectronics and na- nomechanics. The weak van der Waals interaction be- tween walls of a nanotube allows them easily to slide and rotate with respect to one another. The arbitrary [2,3] and controlled by a manipulator [4] telescopic ex- tension of walls in many-wall carbon nanotubes has been recently experimentally studied. This property provides a possibility to construct a new set of me- chanical and electromechanical nanodevices where the nanometer size motion is the relative sliding, rotation or screwlike motion of nanotube walls. This set in- cludes now several possible devices: nanobearings [5] and nanogears [6] driven by a laser electric field; con- stant-force nanosprings [4], mechanical nanoswitch [7], electrical nanoswitch [8], gigahertz oscillator [9] and nanodrill [8] were proposed. Therefore, the studies of geometrical [10] and energetic [8,11–15] parameters that characterize relative position and motion of neighbour walls of a nanotube are actual for nanomechanics development. At the present time the classification scheme for nonchiral DWCNTs is developed [10], energetic barri- ers to the relative sliding and rotation of walls for several DWCNTs [8,11–15] and to the rotation of shells for some double-shell nanoparticles [16–18] are calcu- lated, theory for dynamics of the relative rotation, sliding and screwlike motion of nanotube walls is de- veloped [8]. Since a carbon nanotube wall is a one- dimensional crystal [19,20], neighbour walls can be both commensurate and incommensurate [14]. It was dis- cussed, that nanotubes with commensurate and incom- mensurate walls can be used in principally different mechanical nanodevices [21]. In this connection we de- veloped the classification scheme for DWCNTs with commensurate walls. This classification scheme is used in the present work as a base for search of DWCNTs that can serve as movable elements (nanobearings, bolt- and-nut pairs) of mechanical nanodevices. For this purpose the barriers to the relative rotation and sliding of walls along nanotube axis and helical line of ÔthreadÕ and threshold forces cause this kinds of wall relative motion are calculated here for tens of DWCNTs with commensurate walls. It is found also that the barriers to relative rotation of walls for majority of DWCNTs with * Corresponding author. E-mail address: lozovik@isan.troitsk.ru (Y.E. Lozovik). 0009-2614/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/j.cplett.2003.12.049 Chemical Physics Letters 385 (2004) 72–78 www.elsevier.com/locate/cplett