Skip to main content
SpringerLink
Log in

Growth of two-dimensional dodecagonal colloidal quasicrystals: Particles with isotropic pair interactions with two length scales vs. patchy colloids with preferred binding angles

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

We explore the growth of colloidal quasicrystals with dodecagonal symmetry in two dimensions by employing Brownian dynamics simulations. On the one hand, we study the growth behavior of structures obtained in a system of particles that interact according to an isotropic pair potential with two typical length scales. On the other hand, we consider patchy colloids that possess only one typical interaction length scale but prefer given binding angles. In case of the isotropic particles, we show that an imbalance in the competition between the two distances might lead to defects with wrong nearest-neighbor distances in the resulting structure. In contrast, during the growth of quasicrystals with patchy colloids such defects do not occur due to the lack of a second interaction length scale. However, as a downside, the diffusion of patchy particles along a surface typically is slower such that domains occur where the particles possess different phononic and phasonic offsets. Our results are important to understand how soft matter quasicrystals can be grown as perfectly as possible and to obtain a deeper insight into the mechanisms of the growth of quasicrystals in general.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984)

    Article  ADS  Google Scholar 

  2. D. Levine, P.J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984)

    Article  ADS  Google Scholar 

  3. R. Lifshitz, Isr. J. Chem. 51, 1156 (2011)

    Article  Google Scholar 

  4. N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)

    Article  ADS  Google Scholar 

  5. E. Maciá, Rep. Prog. Phys. 69, 397 (2006)

    Article  ADS  Google Scholar 

  6. W. Steurer, Chem. Soc. Rev. 41, 6719 (2012)

    Article  Google Scholar 

  7. X.B. Zeng, G. Ungar, Y. Liu, A.E. Dulcey, J.K. Hobbs, Nature 428, 157 (2004)

    Article  ADS  Google Scholar 

  8. X.B. Zeng, Curr. Opin. Colloid Interface Sci. 9, 384 (2005)

    Article  Google Scholar 

  9. A. Takano, W. Kawashima, A. Noro, Y. Isono, N. Tanaka, T. Dotera, Y. Matsushita, J. Polym. Sci. Polym. Phys. 43, 2427 (2005)

    Article  ADS  Google Scholar 

  10. K. Hayashida, T. Dotera, A. Takano, Y. Matsushita, Phys. Rev. Lett. 98, 195502 (2007)

    Article  ADS  Google Scholar 

  11. S. Fischer, A. Exner, K. Zielske, J. Perlich, S. Deloudi, W. Steurer, P. Lindner, S. Förster, Proc. Natl. Acad. Sci. U.S.A. 108, 1810 (2011)

    Article  ADS  Google Scholar 

  12. T. Dotera, Isr. J. Chem. 51, 1197 (2011)

    Article  Google Scholar 

  13. A.R. Denton, H. Löwen, Phys. Rev. Lett. 81, 469 (1998)

    Article  ADS  Google Scholar 

  14. M. Engel, H.-R. Trebin, Phys. Rev. Lett. 98, 225505 (2007)

    Article  ADS  Google Scholar 

  15. M. Engel, PhD Thesis (Universität Stuttgart, 2008)

  16. M. Engel, M. Umezaki, H.-R. Trebin, T. Odagaki, Phys. Rev. B 82, 134206 (2010)

    Article  ADS  Google Scholar 

  17. K. Barkan, H. Diamant, R. Lifshitz, Phys. Rev. B 83, 172201 (2011)

    Article  ADS  Google Scholar 

  18. K. Barkan, M. Engel, R. Lifshitz, Phys. Rev. Lett. 113, 098304 (2014)

    Article  ADS  Google Scholar 

  19. T. Dotera, T. Oshiro, P. Ziherl, Nature 506, 208 (2014)

    Article  ADS  Google Scholar 

  20. G. Doppelbauer, E. Bianchi, G. Kahl, J. Phys.: Condens. Matter 22, 104105 (2010)

    ADS  Google Scholar 

  21. M.N. van der Linden, J.P.K. Doye, A.A. Louis, J. Chem. Phys. 136, 054904 (2012)

    Article  ADS  Google Scholar 

  22. A. Reinhardt, F. Romano, J.P.K. Doye, Phys. Rev. Lett. 110, 255503 (2013)

    Article  ADS  Google Scholar 

  23. C.L. Phillips, E. Jankowski, M. Marval, S.C. Glotzer, Phys. Rev. E 86, 041124 (2012)

    Article  ADS  Google Scholar 

  24. C.L. Phillips, E. Jankowski, B.J. Krishnatreya, K.V. Edmond, S. Sacanna, D.G. Grier, D.J. Pine, S.C. Glotzer, Soft Matter 10, 7468 (2014)

    Article  ADS  Google Scholar 

  25. É. Duguet, C. Hubert, C. Chomette, A. Perro, S. Ravaine, C. R. Chim. 19, 173 (2016)

    Article  Google Scholar 

  26. D. Morphew, J. Shaw, C. Avins, D. Chakrabarti, ACS Nano 12, 2355 (2018)

    Article  Google Scholar 

  27. D. Levine, T.C. Lubensky, S. Ostlund, S. Ramaswamy, P.J. Steinhardt, J. Toner, Phys. Rev. Lett. 54, 1520 (1985)

    Article  ADS  Google Scholar 

  28. J.E.S. Socolar, T.C. Lubensky, P.J. Steinhardt, Phys. Rev. B 34, 3345 (1986)

    Article  ADS  Google Scholar 

  29. J.A. Kromer, M. Schmiedeberg, J. Roth, H. Stark, Phys. Rev. Lett. 108, 218301 (2012)

    Article  ADS  Google Scholar 

  30. J.A. Kromer, M. Schmiedeberg, J. Roth, H. Stark, Eur. Phys. J. E 36, 25 (2013)

    Article  Google Scholar 

  31. M. Sandbrink, M. Schmiedeberg, in Aperiodic Crystals (Springer, Berlin, 2013) p. 261

    Google Scholar 

  32. M. Martinsons, M. Sandbrink, M. Schmiedeberg, Acta Phys. Pol. 126, 568 (2014)

    Article  Google Scholar 

  33. J. Hielscher, M. Martinsons, M. Schmiedeberg, S.C. Kapfer, J. Phys.: Condens. Matter 29, 094002 (2017)

    ADS  Google Scholar 

  34. K. Nagao, T. Inuzuka, K. Nishimoto, K. Edagawa, Phys. Rev. Lett. 115, 075501 (2015)

    Article  ADS  Google Scholar 

  35. S. Förster, K. Meinel, R. Hammer, M. Trautmann, W. Widdra, Nature 502, 215 (2013)

    Article  ADS  Google Scholar 

  36. S. Förster, J.I. Flege, E.M. Zollner, F.O. Schumann, R. Hammer, A. Bayat, K.-M. Schindler, J. Falta, W. Widdra, Ann. Phys. 529, 1600250 (2017)

    Article  Google Scholar 

  37. G.Y. Onoda, P.J. Steinhardt, D.P. DiVincenzo, J.E.S. Socolar, Phys. Rev. Lett. 60, 2653 (1988)

    Article  ADS  Google Scholar 

  38. C.T. Hann, J.E. Socolar, P.J. Steinhardt, Phys. Rev. B 94, 014113 (2016)

    Article  ADS  Google Scholar 

  39. C.V. Achim, M. Schmiedeberg, H. Löwen, Phys. Rev. Lett. 112, 255501 (2014)

    Article  ADS  Google Scholar 

  40. M. Schmiedeberg, C.V. Achim, J. Hielscher, S.C. Kapfer, H. Löwen, Phys. Rev. E 96, 012602 (2017)

    Article  ADS  Google Scholar 

  41. R. Lifshitz, D.M. Petrich, Phys. Rev. Lett. 79, 1261 (1997)

    Article  ADS  Google Scholar 

  42. M. Schmiedeberg, J. Roth, H. Stark, Phys. Rev. Lett. 97, 158304 (2006)

    Article  ADS  Google Scholar 

  43. J. Rottler, M. Greenwood, B. Ziebarth, J. Phys.: Condens. Matter 24, 135002 (2012)

    ADS  Google Scholar 

  44. M. Schmiedeberg, H. Stark, Phys. Rev. Lett. 101, 218302 (2008)

    Article  ADS  Google Scholar 

  45. J. Mikhael, J. Roth, L. Helden, C. Bechinger, Nature 454, 501 (2008)

    Article  ADS  Google Scholar 

  46. J. Mikhael, M. Schmiedeberg, S. Rausch, J. Roth, H. Stark, C. Bechinger, Proc. Natl. Acad. Sci. U.S.A. 107, 7214 (2010)

    Article  ADS  Google Scholar 

  47. M. Schmiedeberg, H. Stark, J. Phys.: Condens. Matter 24, 284101 (2012)

    Google Scholar 

  48. A.J. Archer, A.M. Rucklidge, E. Knobloch, Phys. Rev. Lett. 111, 165501 (2013)

    Article  ADS  Google Scholar 

  49. S. Savitz, M. Babadi, R. Lifshitz, IUCrJ 5, 247 (2018)

    Article  Google Scholar 

  50. T. Neuhaus, M. Marechal, M. Schmiedeberg, H. Löwen, Phys. Rev. Lett. 110, 118301 (2013)

    Article  ADS  Google Scholar 

  51. T. Neuhaus, M. Schmiedeberg, H. Löwen, New J. Phys. 15, 073013 (2013)

    Article  ADS  Google Scholar 

  52. T. Neuhaus, A. Härtel, M. Marechal, M. Schmiedeberg, H. Löwen, Eur. Phys. J. ST 223, 373 (2014)

    Article  Google Scholar 

  53. A.S. Keys, S.C. Glotzer, Phys. Rev. Lett. 99, 235503 (2007)

    Article  ADS  Google Scholar 

  54. H. Pattabhiraman, A.P. Gantapara, M. Dijkstra, J. Chem. Phys. 143, 164905 (2015)

    Article  ADS  Google Scholar 

  55. M. Engel, P.F. Damasceno, C.L. Phillips, S.C. Glotzer, Nat. Mater. 14, 109 (2015)

    Article  ADS  Google Scholar 

  56. R. Ryltsev, N. Chtchelkatchev, Soft Matter 13, 5076 (2017)

    Article  ADS  Google Scholar 

  57. M. Zu, P. Tan, N. Xu, Nat. Commun. 8, 2089 (2017)

    Article  ADS  Google Scholar 

  58. M. Martinsons, M. Schmiedeberg, J. Phys.: Condens. Matter 30, 255403 (2018)

    ADS  Google Scholar 

  59. J. Hermisson, C. Richard, M. Baake, J. Phys. I 7, 1003 (1997)

    Google Scholar 

  60. T.A. Witten Jr., L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)

    Article  ADS  Google Scholar 

  61. M. Oxborrow, C.L. Henley, Phys. Rev. B 48, 6966 (1993)

    Article  ADS  Google Scholar 

  62. E. Tondl, M. Ramsay, P. Harrowell, A. Widmer-Cooper, J. Chem. Phys. 140, 104503 (2014)

    Article  ADS  Google Scholar 

  63. L. Korkidi, K. Barkan, R. Lifshitz, in Aperiodic Crystals (Springer, Berlin, 2013) pp. 117--124

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik I, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany

    Anja Gemeinhardt, Miriam Martinsons & Michael Schmiedeberg

Authors
  1. Anja Gemeinhardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miriam Martinsons
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Schmiedeberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miriam Martinsons.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gemeinhardt, A., Martinsons, M. & Schmiedeberg, M. Growth of two-dimensional dodecagonal colloidal quasicrystals: Particles with isotropic pair interactions with two length scales vs. patchy colloids with preferred binding angles. Eur. Phys. J. E 41, 126 (2018). https://doi.org/10.1140/epje/i2018-11737-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2018-11737-1

Keywords

Search

Navigation