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.
In addition to the relatively simple cases of nested nanotubes and graphene-graphene sliding, MD studies have evaluated more complex nanomachines. One example is a study of meshing gears made from functionalized carbon nanotubes @cite_5 using the Brenner potential @cite_47 . In @cite_13 a complex molecular planetary gear mechanism is analyzed using the UFF forecefield and Gasteiger partial charges. In @cite_9 a custom integrator is used with a custom force field based on CHARMM and AMBER force fields, with partial charges determined by calculations, to model the behavior of the experimentally realized nanocars" @cite_36 rolling on a gold surface.
@cite_36 @cite_9 @cite_5 @cite_47 @cite_13
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We use a molecular dynamics simulation to investigate the properties and design space of molecular gears fashioned from carbon nanotubes with teeth added via a benzyne reaction known to occur with C60. Brenner's reactive hydrocarbon potential is used to model interatomic forces within each molecular gear. A Lennard-Jones 6-12 potential or the Buckingham (exp +6) potential plus electrostatic interaction terms are used for intermolecular interactions between gears. A number of gear and gear shaft configurations are simulated on parallel computers. One gear is powered by forcing the atoms near the end of the nanotube to rotate, and a second gear is allowed to rotate by keeping the atoms near the end of its nanotube constrained to a cylinder. The meshing aromatic gear teeth transfer angular momentum from the powered gear to the driven gear. Results suggest that these gears can operate at up to 50-100 GHz in a vacuum at room temperature. The failure mode involves tooth slip, not bond breaking, so failed gears can be returned to operation by lowering the temperature and or rotation rate. M This article features multimedia enhancements available from the abstract page in the online journal; see http: www.iop.org. 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. 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 Over the past two years at the Materials and Process Simulation Center, we have been developing simulation approaches for studying the molecular nanomachine designs pioneered by Drexler and Merkle. These nanomachine designs, such as planetary gears and neon pump, are described with atomistic details and involve up to 10 000 atoms. With the Dreiding and universal force fields, we have optimized the structures of the two planetary gear designs and the neon pump. At the Fourth Foresight conference, we reported rotational impulse dynamics studies of the first and second generation designs of planetary gears undergoing very high-frequency rotational motions. We will explore stability of these designs in the lower frequency regimes which require long time simulations. We will report the molecular mechanics and molecular dynamics simulations performed on these model systems. We explore the following modes in these studies: (1) impulse mode; (2) constant angular velocity—perpetual rotation; (3) constant torque—acceleration from rest. M This article features multimedia enhancements available from the abstract page in the online journal; see http: www.iop.org.