Advertisement

Phase Behaviour of Colloidal Superballs Mixed with Non-adsorbing Polymers

  • Álvaro González GarcíaEmail author
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

Inspired by experimental work on colloidal cuboid–polymer dispersions [Rossi et al., Soft Matter, 2011, 7, 4139–4142] we have theoretically studied the phase behaviour of such mixtures. To that end, free volume theory 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 these expressions are approximate for the solid phases, 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 F\(_1\)–F\(_2\) coexistence, but also SC\(_1\)–SC\(_2\) coexistence, several triple coexistences, and even a quadruple phase coexistence region (F\(_1\)–F\(_2\)–SC–FCC). The model proposed offers a tool to assess the stability of cuboid–polymer mixtures in terms of the colloid-to-polymer size ratio and superball shape.

References

  1. 1.
    Y.A. Vlasov, X.-Z. Bo, J.C. Sturm, D.J. Norris, Nature 414, 289 (2001).  https://doi.org/10.1038/35104529
  2. 2.
    J.-M. Meijer, A. Pal, S. Ouhajji, H.N.W. Lekkerkerker, A.P. Philipse, A.V. Petukhov, Nat. Commun. 8, 14352 (2017).  https://doi.org/10.1038/ncomms14352
  3. 3.
    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).  https://doi.org/10.1021/la402427q
  4. 4.
    B.G. Prevo, E.W. Hon, O.D. Velev, J. Mater. Chem. 17, 791 (2007).  https://doi.org/10.1039/B612734G
  5. 5.
    S.I.R. Castillo, D.M.E. Thies-Weesie, A.P. Philipse, Phys. Rev. E 91, 022311 (2015).  https://doi.org/10.1103/PhysRevE.91.022311
  6. 6.
    L. Rossi, S. Sacanna, W.T.M. Irvine, P.M. Chaikin, D.J. Pine, A.P. Philipse, Soft Matter 7, 4139 (2011).  https://doi.org/10.1039/C0SM01246G
  7. 7.
    J.R. Royer, G.L. Burton, D.L. Blair, S.D. Hudson, Soft Matter 11, 5656 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    F. Dekker, R. Tuinier, A.P. Philipse, Colloids Interfaces 2, 44 (2018), https://www.mdpi.com/2504-5377/2/4/44
  9. 9.
    A.H. Barr, IEEE Comput. Graph. Appl. 1, 11 (1981).  https://doi.org/10.1109/MCG.1981.1673799
  10. 10.
    Y. Jiao, F.H. Stillinger, S. Torquato, Phys. Rev. E 79, 041309 (2009).  https://doi.org/10.1103/PhysRevE.79.041309
  11. 11.
    R. Ni, A.P. Gantapara, J. de Graaf, R. van Roij, M. Dijkstra, Soft Matter 8, 8826 (2012).  https://doi.org/10.1039/C2SM25813G
  12. 12.
    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).  https://doi.org/10.1021/la3007052
  13. 13.
    R.D. Batten, F.H. Stillinger, S. Torquato, Phys. Rev. E 81, 061105 (2010).  https://doi.org/10.1103/PhysRevE.81.061105
  14. 14.
    U. Agarwal F.A. Escobedo, Nat. Mater. 10, 230 (2011).  https://doi.org/10.1038/nmat2959
  15. 15.
    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), https://www.pnas.org/content/112/17/5286?sid=c9bec40f-0b6f-4a2b-baca-636cfc3e3038
  16. 16.
    S.M. Oversteegen R. Roth, J. Chem. Phys. 122, 214502 (2005).  https://doi.org/10.1063/1.1908765
  17. 17.
    E. Herold, R. Hellmann, J. Wagner, J. Chem. Phys. 147, 204102 (2017).  https://doi.org/10.1063/1.5004687
  18. 18.
    A. Isihara T. Hayashida, J. Phys. Soc. Jpn. 6, 40 (1951).  https://doi.org/10.1143/JPSJ.6.40
  19. 19.
    H. Hadwiger, Experientia 7, 395 (1951).  https://doi.org/10.1007/BF02168922
  20. 20.
  21. 21.
    T. Boublík, Mol. Phys. 27, 1415 (1974).  https://doi.org/10.1080/00268977400101191
  22. 22.
    T. Boublík, J. Chem. Phys. 63, 4084 (1975).  https://doi.org/10.1063/1.431882
  23. 23.
    T. Boublík, Mol. Phys. 42, 209 (1981), https://www.tandfonline.com/doi/abs/10.1080/00268978100100161
  24. 24.
    N.F. Carnahan K.E. Starling, J. Chem. Phys. 51, 635 (1969), https://aip.scitation.org/doi/10.1063/1.1672048
  25. 25.
    J.E. Lennard-Jones, A.F. Devonshire, Proc. R. Soc A 163, 53 (1937), https://www.jstor.org/stable/97067?seq=1#page_scan_tab_contents
  26. 26.
    M. Baus C.F. Tejero, Equilibrium Statistical Physics, 1st ed. (Springer, Heidelberg, 2008).  https://doi.org/10.1007/978-3-540-74632-4
  27. 27.
    E. Velasco, L. Mederos, G. Navascués, Langmuir 14, 5652 (1998).  https://doi.org/10.1021/la980126y
  28. 28.
    S.K. Kwak, T. Park, Y.-J. Yoon, J.-M. Lee, Mol. Sim. 38, 16 (2012).  https://doi.org/10.1080/08927022.2011.597397
  29. 29.
    H.N.W. Lekkerkerker R. Tuinier, Colloids and the Depletion Interaction (Springer, Heidelberg, 2011)Google Scholar
  30. 30.
    L. Onsager, Ann. N. Y. Acad. Sci. 51, 627 (1949).  https://doi.org/10.1111/j.1749-6632.1949.tb27296.x
  31. 31.
    A. Cuetos, M. Dennison, A. Masters, A. Patti, Soft Matter 13, 4720 (2017), https://pubs.rsc.org/en/Content/ArticleLanding/2017/SM/C7SM00726D#!divAbstract
  32. 32.
    F. Smallenburg, L. Filion, M. Marechal, M. Dijkstra, Proc. Natl. Acad. Sci. U.S.A. 109, 17886 (2012), https://www.pnas.org/content/109/44/17886
  33. 33.
    A.P. Gantapara, J. de Graaf, R. van Roij, M. Dijkstra, Phys. Rev. Lett. 111, 015501 (2013), https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.015501
  34. 34.
    W.G. Hoover F.H. Ree, J. Chem. Phys. 49, 3609 (1968), https://aip.scitation.org/doi/10.1063/1.1670641
  35. 35.
    H.N.W. Lekkerkerker, W.C.K. Poon, P.N. Pusey, A. Stroobants, P.B. Warren, Europhys. Lett. 20, 559 (1992).  https://doi.org/10.1209/0295-5075/20/6/015
  36. 36.
    M. Dijkstra, R. van Roij, R. Roth, A. Fortini, Phys. Rev. E 73, 041404 (2006), https://journals.aps.org/pre/abstract/10.1103/PhysRevE.73.041404
  37. 37.
    P.G. Bolhuis, M. Hagen, D. Frenkel, Phys. Rev. E 50, 4880 (1994), https://journals.aps.org/pre/abstract/10.1103/PhysRevE.50.4880
  38. 38.
    C.F. Tejero, A. Daanoun, H.N.W. Lekkerkerker, M. Baus, Phys. Rev. E 51, 558 (1995).  https://doi.org/10.1103/PhysRevE.51.558
  39. 39.
    D.J. Audus, A.M. Hassan, E.J. Garboczi, J.F. Douglas, Soft Matter 11, 3360 (2015).  https://doi.org/10.1039/C4SM02869D

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Van ’t Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry and Debye InstituteUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations