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A new "nanopumping" effect consisting of activation of an
axial gas flow inside a carbon nanotube by producing Rayleigh waves
on the nanotube surface is predicted. Our results show that the
atomic flux through the nanotubes can be enourmously increased by the
Actuation of a fluid flow in micro-capillaries has fundamental interest in the areas of nano-robotics, fine-printing at nano-scale, atom optics, quantum computing, hydrogen energetics, chemical process control, cell biology, medical drug delivery and molecular medicine1. Microflow control is also important for commercial applications: DNA analysis, drug screening, optical display technologies, and tunable fiber optic waveguides, thermal management of semiconductor devices and lasers, clinical and forensic analysis, environmental monitoring 2. Study of fluid flows in narrow channels has become a hot area of research since the discovery of nanotubes by Ijima in 1991. The microflow systems include liquid flows in narrow slit-pores 3, very thin liquid films on solid surfaces 4, flows in micropumps, microarrays and membranes 5, 6. Fluid-flow dynamics in carbon nanotubes has been studied in 7. Interaction of fluids with microscopic pores by filling (imbibition) of nano-tubes with gases or liquids is of great technological interests 9; various methods for atomic pumping through carbon nanotubes were proposed in 11, 12. In (11), a laser-driven pump for atomic transport through carbon nanotube (CNT) was proposed based on the generation of electric current through the tube, which in turn would move ions in it by drag forces. A nano-pipette concept for dragging metal ions through a multi-walled CNT was experimentally confirmed 12. Hydrogen storage and a feasible isotope separation method by carbon nanotube is discussed in 13, 14. Liberation of atomic form of hydrogen chemisorbed on carbon materials is discussed in 15. This process is very important for future hydrogen application in the car industry. Even if the Department of Energy target of 6.5 wt% of hydrogen storage is reachable e.g. by a chemisorption mechanism, the subsequent liberation of hydrogen by heating will need very high temperatures, which makes this application unrealistic. Contrary to the dense fluid flows in micron- and nanometer-size channels, rarefied gas flows are of interest for future gas pumping. Micro-Electro-Mechanical-Systems and microscale vacuum technology devices are yet another area of applications 17-20. Molecular Dynamics (MD) and Monte Carlo (MC) methods were applied for studying microfluids 3, 4, 7-10, 13, 14. Atomistic simulations of microfluid flows in nano-channels are rather limited.
Propagation of surface acoustic waves on metal cylinders with finite lengths and through the carbon nanotubes were discussed in 21-24. There are a few ways to activate surface traveling waves on the nanotube surface. One way is to use short laser pulses to generate thermo-acoustic waves on a tube 25. Another way is to send ultra-sound waves through the liquid or dense gaseous media to the nanotube 26. Rayleigh surface waves are activated when a longitudinal wave traveling in a liquid/gas impinges on a solid surface at an incidence angle equal to the Rayleigh angle θ (where θ = arcsin (Cp/Cs), Cp is the velocity of the incident wave and Cs is the velocity of the surface wave in the material 26.
Propagation of the specific traveling waves on the dolphin skin surface is discussed in Refs 27, 28.
The goal of this paper is to prove the nano-pumping concept by MD simulation of a carbon nanotube device that will enable pumping gases and/or liquids at a nano-scale, through the nanometer channels. A simple MD simulation model of gas-nanotube interaction was developed when the nanotube walls are moving in accordance with the Rayleigh surface traveling wave. This model is used to simulate the macroscopic flow of a few gases lighter than carbon (hydrogen, helium) inside the carbon nanotubes activated with the surface waves. The atomic flow rate and average velocity of the gas flow through the nanotube was calculated to verify the overall concept and the efficiency of the nanopumping.
As an input structure for the MD simulations, coordinates of the zigzag nanotube carbon atoms were generated. Tersoff 29 and Brenner 30 interaction potentials were employed to describe the carbon-carbon interactions. Various gases interacting via Lennard-Jones potentials with the parameters given in Table 1 were placed inside the nanotube. The system was brought into equilibrium at room temperature and the Rayleigh transverse surface waves, with phase velocity of about 22 km/s were generated by sending the traveling waves with f = 106 - 1013 Hz along the nanotube. The carbon displacements were perpendicular to the axial direction of wave propagation (so the nanotube vibrations occurred in radial directions). Radial amplitudes of the waves were chosen to be in the interval of 1-5% of the nanotube radii.
We have placed 128 or 256 gas atoms with four different masses (lighter than carbon) inside the nanotube and by applying a traveling wave along the nanotube surface. Our MD simulation explicitly incorporates the interaction between the gas atoms and the nanotube and its effect on the gas flow. The interactions between the gas atoms and the nanotube carbon atoms and the gas atomic masses have been chosen such that the gas did not penetrate through the nanotube walls, even at high velocities. The following chirality numbers of the nanotubes have been tested: (5×0), (15×0), (10×0), (15×15). The total length of the nanotubes was equal to 100Å and their diameters were of 10-20 Å. Depending on the total number of gas atoms inside the nanotube, the real simulation time was about 35 ps.
According to our simulation results shown in Fig. 1, the gas atoms inside the nanotube move almost freely, along the ballistic trajectories, and they are easily accelerated to a very high axial velocity, along the direction of the traveling wave as a result of multiple synchronous collisions with the moving (traveling) nanotube walls.
Fig.1 demonstrates the nanopumping effect for 256 He atoms (shown by red color) that were placed inside a L = 100 Ǻ long carbon nanotube (carbon atoms are shown in gray color), with the diameter of 12 Ǻ.
The nanotube has chirality of (15×0) and was built of 1410 carbon atoms. After activating the surface traveling wave, with a frequency of 10 THz and phase velocity of 22 km/s, the helium atoms started to move in the direction of the wave propagation (in Fig.1, from left to right). Various instants are shown from an initial 44 fs (Fig.1a), to final at 18 ps (Fig. 1e). (See also Movies S1, S2 for this simulation and Movies S3, S4 for simulation of 128 He atoms in a nanotube.)
Atomic fluxes generated due to the nanopumping effect for various frequencies of the surface waves for the gas initially at rest (
The frequency dependence of the flow rate though the nanopump is given in Fig. 3a) and it will depend on the total nanotube length. As the nanotube length was chosen to be 100 Ǻ, the characteristic frequency is rather high. The maximum effect is seen at approximately 38 THz. Fig. 3b shows the dependence of the nano-pumping effect on the ratio L/λ where λ the wavelength of the surface wave.
There is at least one physical effect that closely resembles the nanopumping effect. The well-known Fermi acceleration of cosmic rays occurs when an energetic ion passes through areas with periodic magnetic fields. The Fermi acceleration is zero if the initial ion velocity is zero. Contrary to the Fermi-acceleration, the nanopumping occurs in a gas at rest, with zero average velocity, for which the Fermi effect is zero.
We believe that our simulation of nano-pumping through carbon nanotubes containing gas atoms and having the walls vibrated in accordance with the Rayleigh traveling wave law confirms our concept. If this hypothesis is true, the pumping effect could be used for fueling laptop computers, which is a serious engineering problem. Another example is gas pumping. Application of the new idea to the development of new turbo molecular pumps would certainly increase the pumping efficiency.
The predicted effect has similarity in live nature, for example with the skin features of fast-swimming sea animals, such as dolphins. There are some indications that dolphins use specific (traveling) waves on their skin surface to damp the turbulence in the boundary layers near the skin surface. However, such mechanisms involving compliant surfaces are not yet well understood 27, 28.
We showed that after the Rayleigh surface wave is activated, the gas inside the carbon nanotube experiences multiple reflections from the nanotube walls. At a certain combination of the atomic masses, wave frequency, and phase velocity, the gas inside the nanotube starts flowing with a macroscopic high velocity, in the direction of the traveling surface wave, which we have called "nanopumping". The driving force for the new effect is the friction between the gas particles and the nanotube walls. A molecular dynamics model of the nano-pumping effect was developed for a nanotube filled with various gas particles and the gas flows of atomic and molecular hydrogen and helium gases in a CNT were calculated. Flow rates were calculated at various frequencies and phase velocities of the surface waves. The proposed nanopumping effect is a new physical phenomenon that reveals itself at the nano-scale. We believe that similar effects should exist for larger space/time scales.
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