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Phase behaviour of colloidal superballs mixed with non-adsorbing polymers

  • Álvaro González García
  • Joeri Opdam
  • Remco TuinierEmail author
Open Access
Regular Article

Abstract.

Inspired by experimental work on colloidal cuboid-polymer dispersions (Rossi et al., Soft Matter, 7, 4139 (2011)) we have theoretically studied the phase behaviour of such mixtures. To that end, free volume theory (FVT) was applied to predict the phase behaviour of mixtures of superballs and non-adsorbing polymer chains in a common solvent. Closed expressions for the thermodynamic properties of a suspension of hard colloidal superballs have been derived, accounting for fluid (F), face-centred cubic (FCC) and simple cubic (SC) phase states. Even though the considered solid phases are approximate, the hard superballs phase diagram semi-quantitatively matches with more evolved methods. The theory developed for the cuboid-polymer mixture reveals a rich phase behaviour, which includes not only isostructural F1-F2 coexistence, but also SC1-SC2 coexistence, several triple coexistences, and even a quadruple-phase coexistence region (F1-F2-SC-FCC). The model proposed offers a tool to asses the stability of cuboid-polymer mixtures in terms of the colloid-to-polymer size ratio.

Graphical abstract

Keywords

Soft Matter: Colloids and Nanoparticles 

References

  1. 1.
    D. Frenkel, Physica A 263, 26 (1999) (Proceedings of the 20th IUPAP International Conference on Statistical PhysicsCrossRefADSGoogle Scholar
  2. 2.
    M. Dijkstra, Entropy-Driven Phase Transitions in Colloids: From Spheres to Anisotropic Particles, Vol. 156, (John Wiley & Sons, Inc., 2014) Chapt. 2, pp. 35--71Google Scholar
  3. 3.
    L. Onsager, Ann. N. Y. Acad. Sci. 51, 627 (1949)CrossRefADSGoogle Scholar
  4. 4.
    G.J. Vroege, H.N.W. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992)CrossRefADSGoogle Scholar
  5. 5.
    S. Varga, A. Galindo, G. Jackson, Mol. Phys. 101, 817 (2003)CrossRefADSGoogle Scholar
  6. 6.
    J.A.C. Veerman, D. Frenkel, Phys. Rev. A 45, 5632 (1992)CrossRefADSGoogle Scholar
  7. 7.
    A. Haji-Akbari, M. Engel, A.S. Keys, X. Zheng, R.G. Petschek, P. Palffy-Muhoray, S.C. Glotzer, Nature 462, 773 (2009)CrossRefADSGoogle Scholar
  8. 8.
    A.P. Gantapara, J. de Graaf, R. van Roij, M. Dijkstra, J. Chem. Phys. 142, 054904 (2015)CrossRefADSGoogle Scholar
  9. 9.
    S. Asakura, F. Oosawa, J. Chem. Phys. 22, 1255 (1954)CrossRefADSGoogle Scholar
  10. 10.
    S. Asakura, F. Oosawa, J. Polym. Sci. 33, 183 (1958)CrossRefADSGoogle Scholar
  11. 11.
    R. Tuinier, H.N.W. Lekkerkerker, Colloids and the Depletion Interaction (Springer Netherlands, 2011)Google Scholar
  12. 12.
    G. van Anders, N.K. Ahmed, R. Smith, M. Engel, S.C. Glotzer, ACS Nano 8, 931 (2014)CrossRefGoogle Scholar
  13. 13.
    J. Glaser, A.S. Karas, S.C. Glotzer, J. Chem. Phys. 143, 184110 (2015)CrossRefADSGoogle Scholar
  14. 14.
    A.S. Karas, J. Glaser, S.C. Glotzer, Soft Matter 12, 5199 (2016)CrossRefADSGoogle Scholar
  15. 15.
    A.V. Petukhov, R. Tuinier, G.J. Vroege, Curr. Opin. Colloid Interface Sci. 30, 54 (2017)CrossRefGoogle Scholar
  16. 16.
    Á. González García, H.H. Wensink, H.N.W. Lekkerkerker, R. Tuinier, Sci. Rep. 7, 17058 (2017)CrossRefADSGoogle Scholar
  17. 17.
    Y.A. Vlasov, X.-Z. Bo, J.C. Sturm, D.J. Norris, Nature 414, 289 (2001)CrossRefADSGoogle Scholar
  18. 18.
    J.-M. Meijer, A. Pal, S. Ouhajji, H.N.W. Lekkerkerker, A.P. Philipse, A.V. Petukhov, Nat. Commun. 8, 14352 (2017)CrossRefADSGoogle Scholar
  19. 19.
    J.W.J. de Folter, E.M. Hutter, S.I.R. Castillo, K.E. Klop, A.P. Philipse, W.K. Kegel, Langmuir 30, 955 (2014)CrossRefGoogle Scholar
  20. 20.
    B.G. Prevo, E.W. Hon, O.D. Velev, J. Mater. Chem. 17, 791 (2007)CrossRefGoogle Scholar
  21. 21.
    S.I.R. Castillo, D.M.E. Thies-Weesie, A.P. Philipse, Phys. Rev. E 91, 022311 (2015)CrossRefADSGoogle Scholar
  22. 22.
    L. Rossi, S. Sacanna, W.T.M. Irvine, P.M. Chaikin, D.J. Pine, A.P. Philipse, Soft Matter 7, 4139 (2011)CrossRefADSGoogle Scholar
  23. 23.
    J.R. Royer, G.L. Burton, D.L. Blair, S.D. Hudson, Soft Matter 11, 5656 (2015)CrossRefADSGoogle Scholar
  24. 24.
    A.H. Barr, IEEE Comput. Graph. Appl. 1, 11 (1981)CrossRefGoogle Scholar
  25. 25.
    Y. Jiao, F.H. Stillinger, S. Torquato, Phys. Rev. E 79, 041309 (2009)MathSciNetCrossRefADSGoogle Scholar
  26. 26.
    R. Ni, A.P. Gantapara, J. de Graaf, R. van Roij, M. Dijkstra, Soft Matter 8, 8826 (2012)CrossRefADSGoogle Scholar
  27. 27.
    J.-M. Meijer, F. Hagemans, L. Rossi, D.V. Byelov, S.I. Castillo, A. Snigirev, I. Snigireva, A.P. Philipse, A.V. Petukhov, Langmuir 28, 7631 (2012)CrossRefGoogle Scholar
  28. 28.
    R.D. Batten, F.H. Stillinger, S. Torquato, Phys. Rev. E 81, 061105 (2010)CrossRefADSGoogle Scholar
  29. 29.
    U. Agarwal, F.A. Escobedo, Nat. Mater. 10, 230 (2011)CrossRefADSGoogle Scholar
  30. 30.
    L. Rossi, V. Soni, D.J. Ashton, D.J. Pine, A.P. Philipse, P.M. Chaikin, M. Dijkstra, S. Sacanna, W.T.M. Irvine, Proc. Natl. Acad. Sci. U.S.A. 112, 5286 (2015)CrossRefADSGoogle Scholar
  31. 31.
    S.M. Oversteegen, R. Roth, J. Chem. Phys. 122, 214502 (2005)CrossRefADSGoogle Scholar
  32. 32.
    E. Herold, R. Hellmann, J. Wagner, J. Chem. Phys. 147, 204102 (2017)CrossRefADSGoogle Scholar
  33. 33.
    A. Isihara, T. Hayashida, J. Phys. Soc. Jpn. 6, 40 (1951)CrossRefADSGoogle Scholar
  34. 34.
    H. Hadwiger, Experientia 7, 395 (1951)CrossRefGoogle Scholar
  35. 35.
    R. Gibbons, Mol. Phys. 17, 81 (1969)CrossRefADSGoogle Scholar
  36. 36.
    T. Boublík, Mol. Phys. 27, 1415 (1974)CrossRefADSGoogle Scholar
  37. 37.
    T. Boublík, J. Chem. Phys. 63, 4084 (1975)CrossRefADSGoogle Scholar
  38. 38.
    T. Boublík, Mol. Phys. 42, 209 (1981)CrossRefADSGoogle Scholar
  39. 39.
    N.F. Carnahan, J. Chem. Phys. 51, 635 (1969)CrossRefADSGoogle Scholar
  40. 40.
    J.E. Lennard-Jones, A.F. Devonshire, Proc. R. Soc. London, Ser. A 163, 53 (1937)CrossRefADSGoogle Scholar
  41. 41.
    M. Baus, C.F. Tejero, Equilibrium Statistical Physics, 1st edition (Springer-Verlag Berlin Heidelberg, 2008)Google Scholar
  42. 42.
    E. Velasco, L. Mederos, G. Navascués, Langmuir 14, 5652 (1998)CrossRefGoogle Scholar
  43. 43.
    S.K. Kwak, T. Park, Y.-J. Yoon, J.-M. Lee, Mol. Sim. 38, 16 (2012)CrossRefGoogle Scholar
  44. 44.
    A. Cuetos, M. Dennison, A. Masters, A. Patti, Soft Matter 13, 4720 (2017)CrossRefADSGoogle Scholar
  45. 45.
    F. Smallenburg, L. Filion, M. Marechal, M. Dijkstra, Proc. Natl. Acad. Sci. U.S.A. 109, 17886 (2012)CrossRefADSGoogle Scholar
  46. 46.
    A.P. Gantapara, J. de Graaf, R. van Roij, M. Dijkstra, Phys. Rev. Lett. 111, 015501 (2013)CrossRefADSGoogle Scholar
  47. 47.
    H.N.W. Lekkerkerker, W.C.-K. Poon, P.N. Pusey, A. Stroobants, P.B. Warren, Europhys. Lett. 20, 559 (1992)CrossRefADSGoogle Scholar
  48. 48.
    A. Vrij, Pure Appl. Chem. 48, 471 (1976)CrossRefGoogle Scholar
  49. 49.
    Y. Nema, R. Ohmura, I. Senaha, K. Yasuda, Fluid Phase Equilib. 441, 49 (2017)CrossRefGoogle Scholar
  50. 50.
    J. Edwards, D.H. Everett, T. O’Sullivan, I. Pangalou, B. Vincent, J. Chem. Soc., Faraday Trans. 1 80, 2599 (1984)CrossRefGoogle Scholar
  51. 51.
    S.M. Ilett, A. Orrock, W.C.K. Poon, P.N. Pusey, Phys. Rev. E 51, 1344 (1995)CrossRefADSGoogle Scholar
  52. 52.
    R. Tuinier, G.J. Fleer, J. Phys. Chem. B 110, 20540 (2006)CrossRefGoogle Scholar
  53. 53.
    Á. González García, R. Tuinier, Phys. Rev. E 94, 062607 (2016)CrossRefADSGoogle Scholar
  54. 54.
    B. Widom, J. Chem. Phys. 39, 2808 (1963)CrossRefADSGoogle Scholar
  55. 55.
    E. Helfand, H. Reiss, H.L. Frisch, J.L. Lebowitz, J. Chem. Phys. 33, 1379 (1960)MathSciNetCrossRefADSGoogle Scholar
  56. 56.
    J.L. Lebowitz, E. Helfand, E. Praestgaard, J. Chem. Phys. 43, 774 (1965)CrossRefADSGoogle Scholar
  57. 57.
    M.L. Connolly, J. Appl. Crystallogr. 16, 548 (1983)CrossRefGoogle Scholar
  58. 58.
    W.R. Inc., Mathematica, Version 11.2 Champaign, IL, 2017. Google Scholar
  59. 59.
    W.G. Hoover, F.H. Ree, J. Chem. Phys. 49, 3609 (1968)CrossRefADSGoogle Scholar
  60. 60.
    M. Dijkstra, R. van Roij, R. Roth, A. Fortini, Phys. Rev. E 73, 041404 (2006)CrossRefADSGoogle Scholar
  61. 61.
    A.G. García, R. Tuinier, J.V. Maring, J. Opdam, H.H. Wensink, H.N.W. Lekkerkerker, Mol. Phys. 116, 2757 (2018)CrossRefADSGoogle Scholar
  62. 62.
    F.M. van der Kooij, M. Vogel, H.N.W. Lekkerkerker, Phys. Rev. E 62, 5397 (2000)CrossRefADSGoogle Scholar
  63. 63.
    P.G. Bolhuis, M. Hagen, D. Frenkel, Phys. Rev. E 50, 4880 (1994)CrossRefADSGoogle Scholar
  64. 64.
    C.F. Tejero, A. Daanoun, H.N.W. Lakkerkerker, M. Baus, Phys. Rev. E 51, 558 (1995)CrossRefADSGoogle Scholar
  65. 65.
    D.J. Audus, A.M. Hassan, E.J. Garboczi, J.F. Douglas, Soft Matter 11, 3360 (2015)CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Álvaro González García
    • 1
    • 2
  • Joeri Opdam
    • 1
    • 2
  • Remco Tuinier
    • 1
    • 2
    Email author
  1. 1.Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems (ICMS)Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Van ’t Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry, & Debye InstituteUtrecht UniversityUtrechtThe Netherlands

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