Metallurgy of soft spheres with hard core: From BCC to Frank-Kasper phases

Regular Article

Abstract.

Understanding how soft particles can fill the space is still an open question. Structures far from classical FCC or BCC phases are now commonly experimentally observed in many different systems. Models based on pair interaction between soft particles are at present much studied in 2D. Pair interactions with two different lengths have been shown to lead to quasicrystalline architectures. It is also the case for a hard core with a square repulsive shoulder potential. In 3D, global approaches have been proposed for instance by minimizing the interface area between the deformed objects in the case of foams or micellar systems or using a self-consistent mean-field theory in copolymer melts. In this paper we propose to compare a strong van der Waals attraction between spherical hard cores and an elastic energy associated to the deformation of the soft corona. This deformation is measured as the shift between the deformed shell compared to a corona with a perfect spherical symmetry. The two main parameters in this model are: the hard-core volume fraction and the weight of the elastic energy compared to the van der Waals one. The elastic energy clearly favours the BCC structure but large van der Waals forces favor Frank and Kasper phases. This result opens a route towards controlling the building of nanoparticle superlattices with complex structures and thus original physical properties.

Graphical abstract

Keywords

Soft Matter: Colloids and Nanoparticles 

References

  1. 1.
    M. Dzugutov, Phys. Rev. Lett. 70, 2924 (1993)ADSCrossRefGoogle Scholar
  2. 2.
    P.F. Damasceno, M. Engel, S.C. Glotzer, Science 337, 453 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    F.C. Frank, J.S. Kasper, Acta Crystallogr. 11, 184 (1958)CrossRefGoogle Scholar
  4. 4.
    G. Ungar, X. Zeng, Soft Matter 1, 95 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    D.V. Talapin, E.V. Shevchenko, M.I. Bodnarchuk1, X. Ye, J. Chen, C.B. Murray, Nature 461, 964 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    P. Ziherl, R.D. Kamien, J. Phys. Chem. B 105, 10147 (2001)CrossRefGoogle Scholar
  7. 7.
    C.R. Iacovella, A.S. Keys, S.C. Glotzer, Proc. Natl. Acad. Sci. U.S.A. 108, 20935 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    J. Seddon, R. Templer, Polymorphism of Lipid-Water Systems (Elsevier Science, 1995) pp. 97--160Google Scholar
  9. 9.
    G. Ungar, Y. Liu, X. Zeng, V. Percec, W.D. Cho, Science 299, 1208 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    S. Lee, M.J. Bluemle, F.S. Bates, Science 330, 349 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    L. Sangwoo, C. Leighton, F.S. Bates, Proc. Natl. Acad. Sci. U.S.A. 111, 17723 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    F. Laves, Crystal Chemistry: Structure of Metals, Metalloids and their Compounds (Butterworth, London, 1949)Google Scholar
  13. 13.
    S.A. Kim, K.J. Jeong, A. Yethiraj, M.K. Mahanthappa, Proc. Natl. Acad. Sci. U.S.A. 114, 4072 (2017)CrossRefGoogle Scholar
  14. 14.
    K. Yue, M. Huang, R.L. Marson, J. He, J. Huang, Z. Zhou, J. Wang, C. Liu, X. Yan, K. Wu et al., Proc. Natl. Acad. Sci. U.S.A. 113, 14195 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    B. Cabane, J. Li, F. Artzner, R. Botet, C. Labbez, G. Bareigts, M. Sztucki, L. Goehring, Phys. Rev. Lett. 116, 208001 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    K. Kim, M.W. Schulze, A. Arora, R.M. Lewis, M.A. Hillmyer, K.D. Dorfman, F.S. Bates, Science 356, 520 (2017)ADSCrossRefGoogle Scholar
  17. 17.
    M.A. Boles, M. Engel, D.V. Talapin, Chem. Rev. 116, 11220 (2016)CrossRefGoogle Scholar
  18. 18.
    U. Landman, W.D. Luedtke, Faraday Discuss. 125, 1 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    R.L. Whetten, M.N. Shafigullin, J.T. Khoury, T.G. Schaaff, I. Vezmar, M.M. Alvarez, A. Wilkinson, Acc. Chem. Res. 32, 397 (1999)CrossRefGoogle Scholar
  20. 20.
    B.W. Goodfellow, M.R. Rasch, C.M. Hessel, R.N. Patel, D.M. Smilgies, B.A. Korgel, Nano Lett. 13, 5710 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    S. Hajiw, B. Pansu, J.F. Sadoc, ACS Nano 9, 8116 (2015)CrossRefGoogle Scholar
  22. 22.
    P.D. Olmsted, S.T. Milner, Phys. Rev. Lett. 72, 936 (1994)ADSCrossRefGoogle Scholar
  23. 23.
    G.M. Grason, Phys. Rep. 433, 1 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    J.N. Israelachvili (Editor), Intermolecular and Surface Forces, 3rd edition (Academic Press, San Diego, 2011)Google Scholar
  25. 25.
    J.F. Sadoc, J. Charvolin, N. Rivier, J. Phys. A: Math. Theor. 46, 295202 (2013)CrossRefGoogle Scholar
  26. 26.
    G.M. Grason, B.A. DiDonna, R.D. Kamien, Phys. Rev. Lett. 91, 058304 (2003)ADSCrossRefGoogle Scholar
  27. 27.
    J. Schmitt, S. Hajiw, A. Lecchi, J. Degrouard, A. Salonen, M. Impéror-Clerc, B. Pansu, J. Phys. Chem. B 120, 5759 (2016)CrossRefGoogle Scholar
  28. 28.
    A. Travesset, ACS Nano 11, 5375 (2017)CrossRefGoogle Scholar
  29. 29.
    G.M. Grason, R.D. Kamien, Phys. Rev. E 71, 051801 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    Denis Weaire (Editor), The Kelvin Problem: Foam Structures of Minimal Surface Area (Taylor and Francis, London, Bristol, PA, 1996)Google Scholar
  31. 31.
    J.F. Sadoc, R. Jullien, N. Rivier, Eur. Phys. J. B 33, 355 (2003)ADSCrossRefGoogle Scholar
  32. 32.
    P.G. Born, PhD Thesis, Universität des Saarlandes, Saarbrücken (2011)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Laboratoire de Physique des Solides, Bât 510, UMR-CNRS 8502Université Paris-Sud, Université Paris-SaclayOrsayFrance

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