Molecular Dynamics Simulations of a Linear Nanomotor Driven by Thermophoretic Forces

Harvey A Zambrano, Jens Honore Walther, Richard L. Jaffe

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Abstract

Molecular Dynamics of a Linear Nanomotor Driven by Thermophoresis Harvey A. Zambrano1, Jens H. Walther1,2 and Richard L. Jaffe3 1Department of Mechanical Engineering, Fluid Mechanics, Technical University of Denmark, DK-2800 Lyngby, Denmark; 2Computational Science and Engineering Laboratory, ETH Zurich, CH-8092, Switzerland and 3 NASA Ames Research Center, Moffett Field, CA 94035, USA ABSTRACT Thermophoresis is the motion of mass induced by thermal gradients.1,2,3,4,5 In recent investigations thermophoresis has been used for driving solid and liquids confined inside carbon nanotubes.6,7,8,9 Nanomotors are an attractive goal for nanotechnology.9-13 Such nano-scale structures capable of converting thermal energy into work will be needed in many types of nanodevices, including nanoconveyors14, memory devices15 and nano-encapsulated material delivery systems16,17. Moreover to design and manufacture future molecular machines a complete understanding of the friction forces involved on the transport process at the molecular level have to be addressed.18 In this work we perform Molecular Dynamics (MD) simulations using the MD package FASTTUBE19 to study a molecular linear motor consisting of coaxial carbon nanotubes. The system consists of an outer 42.6 nm long carbon nanotube (CNT) with a chiral vector of (22,0) corresponding to a diameter of 1.723 nm. The inner CNT is modeled as an open short 3.195 nm long carbon nanotube with a chiral vector of (12,0), and diameter 0.94 nm. We describe the valence forces within the CNT using Morse, harmonic angle and torsion potentials.19We include a nonbonded carbon-carbon Lennard-Jones potential to describe the vdW interaction between the carbon atoms within the double wall portion of the system. We equilibrate the system at 300K for 0.1 ns, by coupling the system to a Berendsen thermostat21 with a time constant of 0.1 ps. After the equilibration we impose thermal gradients in the range of 0.0–4.2 K/nm by heating two zones at the ends of the outer CNT as illustrated in Fig. 1. FIG. 1: Schematic of the computational setup. Crosssectional view of the system, the outer CNT is a (22,0) zigzag CNT and the inner one is a (12,0) zigzag CNT. A thermal gradient is imposed by heating the end sections (in gray) of the outer CNT. We measure the position of the center of mass (COM) of the inner CNT during the simulation. We observe, for gradients higher that 1.18K/nm, a directed motion of the capsule in the direction opposite to the imposed thermal gradient as shown in Fig. 2. FIG. 2: Center of mass position (COM) as a function of time for three different thermal gradients: blue (*), 3.16K/nm; green (×), 1.58K/nm, and red (+), 1.18K/nm. To confirm that the motion of the capsule is driven by thermophoresis we perform additional simulations in order to study the friction and thermophoretic forces acting on the inner CNT. In these simulations, we constrain the velocity of center of mass of the inner CNT and extract from the simulations the external forces required to drive the inner CNT for different constrained velocities and different imposed thermal gradients (Fig. 3). FIG. 3: External force acting on the constrained inner CNT as a function of the center of mass (COM) velocity for different thermal gradients: red (+), 0.0K/nm; green (×), 1.0K/nm; blue (*), 2.0K/nm; and fuchsia (squares), 3.0K/nm. To measure the isothermal friction of the system we impose a zero thermal gradient while we vary the constrained COM velocity. At nonzero thermal gradients we measure the combined friction and thermophoretic forces. A positive force indicates resistance to the motion, whereas a negative force is indicative of thermophoresis. We find a systematic increase of the thermophoretic force as higher thermal gradients are imposed on the system. Furthermore, the measured isothermal friction is small compared to the thermophoretic force cf. Fig. 3. We infer from the simulations that the magnitude of the thermophoretic force is reduced as a higher velocity is imposed to the inner CNT (Fig. 3). We conjecture that the magnitude of the driving thermophoretic force is inversely dependent on velocity. We find that, for different imposed thermal gradients, the corresponding terminal velocity is governed by the velocity dependence of the thermophoretic force velocity rather than a match between the thermophoretic force measured at zero velocity and the static friction. References 1-Duhr, S.; Braun, D. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 19678–19682. 2-Dutrieux, J. F.; Platten, J. K.; Chavepeyer, G.; Bou-Ali, M. M. J. Phys. Chem. B 2002, 106, 6104–6114. 3- Ludwig, C. S. Bayer Akad. Wiss. (Vienna) 1856, 20, 539. 4- Soret, C. Ann. Chim. (Phys.) 1881, 22 (5), 293. 5- Ibbs, T. L. Proc. R. Soc. London 1921, A99, 385. 6- Schoen, P. A. E.; Walther, J. H.; Poulikakos, D.; Koumoutsakos, P. Appl. Phys. Lett. 2007, 90 (1-3), 253116. 7- Zambrano, H.A., Walther, J. H., Koumoutsakos, P. and Sbalzarini, I. F., Nano Lett. 2009, 9, 66. 8-Shiomi, J. and Maruyama, S. Nanotechnol. 2009, 20, 055708. 9- Barreiro, A.; Rurali, R.; Hernandez, E. R.; Moser, J.; Pichler, T.; Forro, L.; Bachtold, A. Science 2008, 320, 775–778. 10-Somada, H., Hirahara, K., Akita, S. and Nakayama, Y. Nano Lett. 2009, 9, 62. 11-Delogu, F. J. Phys. Chem. C 2009,113, 15909-15913. 12-Tu, Z. C. and Ou-Yang, C. J. Phys. Condens. Matter. 2004, 16, 1287-1292. 13- Julicher F, Ajdari A, Prost J. Rev. Mod. Phys. 1997, 69 (4), 1269-1281. 14- Tokarz, M.; Akerman, B.; Olofsson, J.; Joanny, J. F.; Dommersnes, P.; Orwar, O. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 9127–9132. 15-Begtrup, G. E., Gannet, W., Yuzvinsky, T. D., Crespi, V. H. and Zettl, A. Nano Lett. 2009, 9, 1835-1838. 16- Gasparac, R.; Kohli, P.; Mota, M. O.; Trofin, L.; Martin, C. R. Nano Lett. 2004, 4, 513–516. 17-Hilder, T. A. and Hill, J. M. Drug Delivery 2009, 5, 300-308. 18-Urbakh, M.; Klafter, J.; Gourdon, D. and Israelachvili, J. Nature 2004, 430(29), 525-528. 19- Walther, J. H.; Jaffe, R.; Halicioglu, T.; Koumoutsakos, P. J. Phys.Chem. B 2001, 105, 9980–9987.
Original languageEnglish
Publication date2009
Publication statusPublished - 2009
EventNanoEurope Symposium 2009 : Moving Nanotechnology to Market - Rapperswil, Switzerland
Duration: 1 Jan 2009 → …
Conference number: 7

Conference

ConferenceNanoEurope Symposium 2009 : Moving Nanotechnology to Market
Number7
CityRapperswil, Switzerland
Period01/01/2009 → …

Keywords

  • Molecular dynamics
  • Thermophoresis
  • Molecular Nanomotors

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