Translational dynamics and friction in double-walled carbon nanotubes

Abstract

We report on a study of the translational sliding motion and dynamic friction in systems of double-walled carbon nanotubes using molecular dynamics simulations combined with theoretical analysis. The sliding motion is described by a one-dimensional analytical model which includes the van der Waals force between the nanotubes, a dynamic friction force, and a small Langevin-type fluctuating force. The dynamic friction force is shown to be linear in the velocity over a large domain of initial conditions in armchair-armchair, zigzagarmchair, and zigzag-zigzag double-walled nanotubes. Beyond this domain, evidence is obtained for nonlinear effects which increase friction. In armchair-armchair systems, the dynamic friction is observed to be nonlinearly enhanced by the excitation of internal modes. In the linear domain, the coefficient of proportionality between the dynamic friction force and the velocity is shown to be given by Kirkwood's formula in terms of the force autocorrelation function.

Oscillating carbon nanotori along carbon nanotubes

“…The ultralow friction observed by Cumings and Zettl 3 was further investigated by Guo et al, 4 Servantie and Gaspard, 5 and Rivera et al 6 The interlayer resistance force against sliding, although small when compared to the van der Waals force, can prevent sustained oscillation as a result of the friction induced energy dissipation. 4 Servantie and Gaspard 5 also concluded that friction is small relative to the van der Waals force, by two orders of magnitude.…”

“…It has been shown by a number of researchers [3][4][5][6] that frictional forces are small in comparison to the van der Waals force, and in some cases by several orders of magnitude. 6 As a first approximation to this potential device we therefore ignore the effects of friction so that F r ͑Z͒ = 0.…”

“…Although there may exist corrugation effects, these are neglected here due to the resulting high oscillation frequency. 5 Minimizing the nanotorus ring radius has a greater effect on increasing the frequency of oscillation, since it also reduces the mass requiring movement along the nanotube. Figure 6 illustrates how reducing the ring radius increases the frequency.…”

“…In any real physical system inevitably frictional forces will occur, however, as detailed above, the existing evidence [3][4][5][6] suggests that frictional forces are much less than the van der Waals interaction force, sometimes by several orders of magnitude. 6 In addition, in order to further simplify the problem, we choose the geometric parameters of the nanotube and nanotorus such that the nanotorus always remains symmetrically located around the nanotube, by ensuring that the stability condition is satisfied so that the minimum energy position of the nanotorus occurs on the nanotube axis.…”

Carbon Nanotube Electron Windmills: A Novel Design for Nanomotors

“…2a Before describing the theory leading to Fig. 2, it is also of interest to ask if F motor can overcome the dynamical friction between the two CNTs [15], [16], [17]. For a spinning CNT with carbon atoms of mass m c moving with a tangential velocity v c , the dynamical friction force per carbon atom is [17] ∞ (E) of equation (12), which is proportional to the total tangential velocity carried by all right-moving channels of energy E in an infinite (6,4) This demonstration that an "electron wind" can cause a chiral "CNT windmill" to rotate, could lead to range of applications [18].…”