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Self-phoretic active particles interacting by diffusiophoresis: A numerical study of the collapsed state and dynamic clustering

  • Oliver PohlEmail author
  • Holger Stark
Regular Article

Abstract

Self-phoretic active colloids move and orient along self-generated chemical gradients by diffusiophoresis, a mechanism reminiscent of bacterial chemotaxis. In combination with the activity of the colloids, this creates effective repulsive and attractive interactions between particles depending on the sign of the translational and rotational diffusiophoretic parameters. A delicate balance of these interactions causes dynamic clustering and for overall strong effective attraction the particles collapse to one single cluster. Using Langevin dynamics simulations, we extend the state diagram of our earlier work (Phys. Rev. Lett. 112, 238303 (2014)) to regions with translational phoretic repulsion. With increasing repulsive strength, the collapsed cluster first starts to fluctuate strongly, then oscillates between a compact form and a colloidal cloud, and ultimately the colloidal cloud becomes static. The oscillations disappear if the phoretic interactions within compact clusters are not screened. We also study dynamic clustering at larger area fractions by exploiting cluster size distributions and mean cluster sizes. In particular, we identify the dynamic clustering 2 state as a signature of phoretic interactions. We analyze fusion and fission rate functions to quantify the kinetics of cluster formation and identify them as local signatures of phoretic interactions, since they can be measured on single clusters.

Graphical abstract

Keywords

Soft Matter: Colloids and Nanoparticles 

Supplementary material

10189_2015_178_MOESM1_ESM.avi (5 mb)
Supplementary material, approximately 4.96 MB.
10189_2015_178_MOESM2_ESM.avi (6.7 mb)
Supplementary material, approximately 6.72 MB.

References

  1. 1.
    M.C. Marchetti, J.F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, R.A. Simha, Rev. Mod. Phys. 85, 1143 (2013).CrossRefADSGoogle Scholar
  2. 2.
    I.S. Aranson, C.R. Phys. 14, 518 (2013).CrossRefADSGoogle Scholar
  3. 3.
    M.E. Cates, J. Tailleur, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).CrossRefADSGoogle Scholar
  4. 4.
    J. Bialké, T. Speck, H. Löwen, J. Non-Cryst. Solids 407, 367 (2015).CrossRefADSGoogle Scholar
  5. 5.
    J.L. Moran, J. Posner, J. Fluid Mech. 680, 31 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    R. Golestanian, Phys. Rev. Lett. 108, 038303 (2012).CrossRefADSGoogle Scholar
  7. 7.
    D. Saintillan, M.J. Shelley, C.R. Phys. 14, 497 (2013).CrossRefADSGoogle Scholar
  8. 8.
    P.H. Colberg, S.Y. Reigh, B. Robertson, R. Kapral, Acc. Chem. Res. 47, 3504 (2014).CrossRefGoogle Scholar
  9. 9.
    M.E. Cates, J. Tailleur, Phys. Rev. Lett. 100, 218103 (2008).CrossRefADSGoogle Scholar
  10. 10.
    S. Henkes, Y. Fily, M.C. Marchetti, Phys. Rev. E 84, 040301 (2011).CrossRefADSGoogle Scholar
  11. 11.
    G.S. Redner, M.F. Hagan, A. Baskaran, Phys. Rev. Lett. 110, 055701 (2013).CrossRefADSGoogle Scholar
  12. 12.
    M.E. Cates, J. Tailleur, EPL 101, 20010 (2013).CrossRefADSGoogle Scholar
  13. 13.
    J. Bialke, H. Löwen, T. Speck, EPL 103, 30008 (2013).CrossRefADSGoogle Scholar
  14. 14.
    T. Speck, J. Bialke, A.M. Menzel, H. Löwen, Phys. Rev. Lett. 112, 218304 (2014).CrossRefADSGoogle Scholar
  15. 15.
    A. Zöttl, H. Stark, Phys. Rev. Lett. 112, 118101 (2014).CrossRefADSGoogle Scholar
  16. 16.
    V. Narayan, S. Ramaswamy, N. Menon, Science 317, 105 (2007).CrossRefADSGoogle Scholar
  17. 17.
    J. Palacci, S. Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Science 339, 936 (2013).CrossRefADSGoogle Scholar
  18. 18.
    R.W. Nash, R. Adhikari, J. Tailleur, M.E. Cates, Phys. Rev. Lett. 104, 258101 (2010).CrossRefADSGoogle Scholar
  19. 19.
    M. Hennes, K. Wolff, H. Stark, Phys. Rev. Lett. 112, 238104 (2014).CrossRefADSGoogle Scholar
  20. 20.
    W.M. Durham, J.O. Kessler, R. Stocker, Science 323, 1067 (2009).CrossRefADSGoogle Scholar
  21. 21.
    A. Zöttl, H. Stark, Phys. Rev. Lett. 108, 218104 (2012).CrossRefADSGoogle Scholar
  22. 22.
    X. Garcia, S. Rafaï, P. Peyla, Phys. Rev. Lett. 110, 138106 (2013).CrossRefADSGoogle Scholar
  23. 23.
    A. Zöttl, H. Stark, Eur. Phys. J. E 36, 4 (2013).CrossRefADSGoogle Scholar
  24. 24.
    J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, Phys. Rev. Lett. 105, 088304 (2010).CrossRefADSGoogle Scholar
  25. 25.
    M. Enculescu, H. Stark, Phys. Rev. Lett. 107, 058301 (2011).CrossRefADSGoogle Scholar
  26. 26.
    K. Wolff, A.M. Hahn, H. Stark, Phys. Rev. Lett. 112, 128304 (2014).CrossRefGoogle Scholar
  27. 27.
    I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, L. Bocquet, Phys. Rev. Lett. 108, 268303 (2012).CrossRefADSGoogle Scholar
  28. 28.
    O. Pohl, H. Stark, Phys. Rev. Lett. 112, 238303 (2014).CrossRefADSGoogle Scholar
  29. 29.
    A. Attanasi, A. Cavagna, L.D. Castello, I. Giardina, T. Grigera, A. Jelić, S. Melillo, L. Parisi, O. Pohl, E. Shen et al., Nat. Phys. 10, 691 (2014).CrossRefGoogle Scholar
  30. 30.
    Q. Liu, A. Doelman, V. Rottschäfer, M. de Jager, P.M.J. Herman, M. Rietkerk, J. van de Koppel, Proc. Natl. Acad. Sci. U.S.A. 110, 11905 (2013).CrossRefADSGoogle Scholar
  31. 31.
    R.C. Gerum, B. Fabry, C. Metzner, M. Beaulieu, A. Ancel, D.P. Zitterbart, New. J. Phys. 15, 125022 (2013).CrossRefADSGoogle Scholar
  32. 32.
    A. Attanasi, A. Cavagna, L.D. Castello, I. Giardina, S. Melillo, L. Parisi, O. Pohl, B. Rossaro, E. Shen, E. Silvestri et al., Phys. Rev. Lett. 113, 238102 (2014).CrossRefADSGoogle Scholar
  33. 33.
    H.H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R.E. Goldstein, H. Löwen, J.M. Yeomans, Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012).CrossRefADSGoogle Scholar
  34. 34.
    H.C. Berg, E. coli in Motion (Springer, New York, 2004).Google Scholar
  35. 35.
    D.P. Häderi, A. Rosumi, J. Schäfer, R. Hemmersbach, J. Plant Physiol. 146, 474 (1995).CrossRefGoogle Scholar
  36. 36.
    B.T. Hagen, F. Kümmel, R. Wittkowski, D. Takagi, H. Löwen, C. Bechinger, Nat. Commun. 5, 4829 (2014).CrossRefGoogle Scholar
  37. 37.
    K. Maeda, Y. Imae, J.I. Shioi, F. Oosawa, J. Bacteriol. 127, 1039 (1976).Google Scholar
  38. 38.
    J.L. Anderson, Ann. Rev. Fluid Mech. 21, 61 (1989).CrossRefADSGoogle Scholar
  39. 39.
    J.A. Cohen, R. Golestanian, Phys. Rev. Lett. 112, 068302 (2014).CrossRefADSGoogle Scholar
  40. 40.
    M. Braun, A. Würger, F. Cichos, Phys. Chem. Chem. Phys. 16, 15207 (2014).CrossRefGoogle Scholar
  41. 41.
    T. Bickel, G. Zecua, A. Würger, Phys. Rev. E 89, 050303 (2014).CrossRefADSGoogle Scholar
  42. 42.
    S. Saha, R. Golestanian, S. Ramaswamy, Phys. Rev. E 89, 062316 (2014).CrossRefADSGoogle Scholar
  43. 43.
    F. Ginot, I. Theurkauff, D. Levis, C. Ybert, L. Bocquet, L. Berthier, C. Cottin-Bizonne, Phys. Rev. X 5, 011004 (2015).Google Scholar
  44. 44.
    J. Taktikos, V. Zaburdaev, H. Stark, Phys. Rev. E 85, 051901 (2012).CrossRefADSGoogle Scholar
  45. 45.
    I. Buttinoni, J. Bialke, F. Kümmel, H. Löwen, C. Bechinger, T. Speck, Phys. Rev. Lett. 110, 238301 (2013).CrossRefADSGoogle Scholar
  46. 46.
    L.F. Valadares, Y.G. Tao, N.S. Zacharia, V. Kitaev, F. Galembeck, R. Kapral, G.A. Ozin, Small 6, 565 (2010).CrossRefGoogle Scholar
  47. 47.
    P. de Buyl, R. Kapral, Nanoscale 5, 1337 (2013).CrossRefADSGoogle Scholar
  48. 48.
    K. Schaar, A. Zöttl, H. Stark, Phys. Rev. Lett. 115, 038101 (2015).CrossRefADSGoogle Scholar
  49. 49.
    E.F. Keller, L.A. Segel, J. Theor. Biol. 26, 399 (1970).CrossRefzbMATHGoogle Scholar
  50. 50.
    H. Masoud, M.J. Shelley, Phys. Rev. Lett. 112, 128304 (2014).CrossRefADSGoogle Scholar
  51. 51.
    O. Ciftja, I. Hysi, Appl. Math. Lett. 24, 1919 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    D. Levis, L. Berthier, Phys. Rev. E 89, 062301 (2014).CrossRefADSGoogle Scholar
  53. 53.
    S. Gueron, S.A. Levin, Math. Biosci. 128, 243 (1995).CrossRefzbMATHGoogle Scholar
  54. 54.
    F. Peruani, J. Starruß, V. Jakovljevic, L.S. Andersen, A. Deutsch, M. Bär, Phys. Rev. Lett. 108, 098102 (2012).CrossRefADSGoogle Scholar
  55. 55.
    H.S. Niwa, J. Theor. Biol. 224, 451 (2003).MathSciNetCrossRefGoogle Scholar
  56. 56.
    F. Peruani, A. Deutsch, M. Bär, Phys. Rev. E 74, 030904 (2006).CrossRefADSGoogle Scholar
  57. 57.
    F. Peruani, M. Bär, New J. Phys. 15, 065009 (2013).MathSciNetCrossRefADSGoogle Scholar
  58. 58.
    M. Ibele, T.E. Mallouk, A. Sen, ACS Nano 48, 3308 (2009).Google Scholar
  59. 59.
    M.E. Ibele, P.E. Lammert, V.H. Crespi, A. Sen, ACS Nano 4, 4845 (2010).CrossRefGoogle Scholar
  60. 60.
    S. Thakur, R. Kapral, Phys. Rev. E 85, 026121 (2012).CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

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