A computationally-efficient method for evaluating friction in molecular rotary bearings is presented. This method estimates drag from fluctuations in molecular dynamics simulations via the fluctuation–dissipation theorem. This is effective even for simulation times short compared to a bearing's energy damping time and for rotation speeds comparable to or below typical thermal values. We apply this method to two molecular rotary bearings of similar size at 300 K: previously studied nested (9,9) (14,14) double-walled carbon nanotubes and a hypothetical rotary joint consisting of single acetylenic bonds in a rigid diamondoid housing. The acetylenic joint has a rotational frictional drag coefficient of 2 × 10−35 kg m2 s−1. The friction for the nested nanotubes is 120 times larger, comparable to values reported by previous studies. This fluctuation-based method could evaluate dissipation in a variety of molecular systems with similarly rigid and symmetric bearings.
@cite_69: 
@cite_60: Recent breakthroughs in synthesizing large amounts of C_(60), C_(70) and other fullerenes have made possible studies of the struc-tures and properties of fullerene crystals. Using a force field developed recently for sp carbon atoms, we predict here the crystal structures and cohesive energies for close-packed crystals of C_(60) and C_(70). We predict, and confirm from calculations, that for C_(60) face-centred cubic (f.c.c.) packing is more stable than hexagonal close-packing (h.c.p.), by 0.90 kcal mol−1, whereas for C70 h.c.p. is more stable than f.c.c. by 0.35 kcal mol^(−1). The cubic structure of C60 undergoes an orthorhombic distortion to space group Cmca at 0 K. At higher temperatures there is rapid reorientation (but not free rotation) of C_(60) molecules, suggesting that above about 200 K a phase transition occurs to an orientationally disordered, f.c.c. structure (with a room-temperature lattice parameter of 14.13 A). This may correspond to the first-order transition observed at 249 K. The threefold axes of the C_(60) molecules in the low-temperature structure are not aligned with the threefold crystallographic axes.
@cite_3: Atomistic simulations of double-walled carbon nanotubes (DWCNTs) as rotational bearings were performed. Molecular mechanics (MM) calculations show that the interlayer energy surface of the bearings is nearly flat. Thermal effects on the bearings were studied with molecular dynamics (MD) simulations at finite temperature. These simulations show that the interlayer corrugation against rotation, and hence the interlayer friction coefficient, is extremely small, suggesting the possible application of DWCNTs as wearless bearings. Extreme operational conditions of the bearings for which the bearings disintegrate are also reported.
@cite_56: The mechanical properties of sliding carbon nanotubes have been investigated by classical molecular dynamics simulations in the canonical ensemble. In particular we have studied damped oscillations in the separation between the centres of mass of the inner and outer tubes of double-walled carbon nanotubes (DWCN). Incommensurate DWCNs forming (7, 0)@(9, 9) structures were simulated for systems at 298.15 K with axial lengths from 12.21 to 98.24 nm. The oscillations exhibited frequencies in the range of gigahertz with the frequency decreasing as the length of the system increases. The time until oscillations become negligible exhibited a nearly linear dependence on the length of the system. Two macroscopic models were developed in order to understand the forces involved in terms of macroscopic properties like friction and shear. The first model considered constant restoring forces during the whole event, while in the second the value of these constant restoring forces depended on the initial conditions of each oscillation. Both models reproduced the oscillations quite well, while the second model allows us to predict the dynamic shear strength in terms of the axial length of the system for tubes with the same diameters. The calculated dynamic shear strength exhibited monotonic behaviour with an inverse dependence on the length of the system. For systems with unequal axial lengths, the restoring force, which drives the oscillation, is reduced compared to the system with equal lengths, regardless of whether the outer nanotube is longer or shorter. M This article contains online multimedia enhancements
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@cite_27: 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, zigzag-armchair, 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.
@cite_47: An empirical many-body potential-energy expression is developed for hydrocarbons that can model intramolecular chemical bonding in a variety of small hydrocarbon molecules as well as graphite and diamond lattices. The potential function is based on Tersoff's covalent-bonding formalism with additional terms that correct for an inherent overbinding of radicals and that include nonlocal effects. Atomization energies for a wide range of hydrocarbon molecules predicted by the potential compare well to experimental values. The potential correctly predicts that the -bonded chain reconstruction is the most stable reconstruction on the diamond 111 surface, and that hydrogen adsorption on a bulk-terminated surface is more stable than the reconstruction. Predicted energetics for the dimer reconstructed diamond 100 surface as well as hydrogen abstraction and chemisorption of small molecules on the diamond 111 surface are also given. The potential function is short ranged and quickly evaluated so it should be very useful for large-scale molecular-dynamics simulations of reacting hydrocarbon molecules.
@cite_66: Abstract Simulation of friction in carbon nanotube (CNT) bearing systems has been a popular topic, yet many questions remain open. For example, quantitative estimates of friction reported to date range by as much as eight orders of magnitude, and simulation techniques employ a variety of disparate simulation paradigms and parameters. This paper presents a new suite of consistently implemented but complementary and independent molecular simulations of rotary CNT bearing systems, which span the approaches reported to date, yet agree quantitatively within the error margin, or about one order of magnitude. A comparison between these new results, existing simulation results, and one experimental friction datum is presented. Furthermore, quantitative relationships between friction and the system operating parameters are determined. Friction is found to vary linearly with rotating speed and system temperature, while system length and mean diameter do not have a strong effect. Finally, based on phonon energy spectrum computations, we show that friction is a broadband phenomenon, which does not depend strongly on a specific vibrational mode, but rather appears to occur from the aggregate interactions of many modes at different frequencies. This work reports an in-depth analysis of the mechanics of CNT friction and shows that it can be simulated using complementary approaches, while still obtaining the same result. The analysis reveals the underlying mechanism causing friction and how the governing parameters affect its behavior.
In @cite_66 , four different MD simulation configurations using the LAMMPS code and AIREBO force field were used to obtain consistent friction estimates for a rotating nested nanotube bearing. Other dissipation estimates for rotating nested nanotube bearings have been determined using intralayer interactions based on the Brenner potential @cite_47 with interlayer interactions based on the Kolmogorov-Crespi registry-dependent potential @cite_3 , and with the COMPASS force field @cite_24 . Dissipation estimates for sliding nested nanotube bearings have been determined using a custom force field and custom numerical simulator in @cite_27 @cite_69 , and a custom force field based on @cite_60 and the r-RESPA integrator in @cite_56 .