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Discotic Dispersions Mediated by Depletion

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

Abstract

In this Chapter we show how free volume theory (FVT) is an efficient and tractable thermodynamic framework capable of unravelling the complicated multi-phase behaviour of disc–polymer mixtures. Three principal reference phases for the hard platelets are considered: isotropic (I), nematic (N), and columnar (C). We derive analytical expressions that enable us to systematically trace the different types of phase coexistences revealed upon adding depletants, and confirm the predictive power of FVT by testing the calculated diagrams against phase stability scenarios from alternative approaches. A wide range of multi-phase equilibria is revealed, involving two-phase isostructural transitions of all phase symmetries (I, N, C) considered as well as the possible three-phase coexistences. Moreover, we identify the system parameters, relative disc shapes and colloid–polymer size ratios, at which four-phase equilibria are expected. These involve a remarkable coexistence of all three phase states commonly encountered in discotics including isostructural coexistences I\(_1\)–I\(_2\)–N–C, I–N\(_1\)–N\(_2\)–C, and I–N–C\(_1\)–C\(_2\). The isostructural C\(_1\)–C\(_2\) coexistence is analysed in detail and compared to direct-coexistence Monte Carlo computations. We improve FVT for disc–polymer mixtures, particularly accounting for a better depletant partitioning over the discotic columnar phases. From theory and simulations it is clear that in the C\(_1\) phase depletants are present between the flat faces of the discs, as opposed to the denser (C\(_2\)) phase. Consequently, the C\(_1\)–C\(_2\) coexistence is driven by the depletant partitioning in the intra-columnar direction. This study helps to understand the role of compartmentalisation in highly asymmetric, crowded systems.

References

  1. 1.
    L. Yuan, X.L. Weng, J.L. Xie, L.J. Deng, Mater. Res. Innov. 19, S1 (2015).  https://doi.org/10.1179/1432891715Z.0000000001497
  2. 2.
    L. Bailey, H.N.W. Lekkerkerker, G.C. Maitland, Soft Matter 11, 222 (2015).  https://doi.org/10.1039/C4SM01717J
  3. 3.
    T. Ye, N. Phan-Thien, C.T. Lim, J. Biomech. 49, 2255 (2016).  https://doi.org/10.1016/j.jbiomech.2015.11.050
  4. 4.
    E. Dickinson, Food Hydrocoll. 52, 497 (2016).  https://doi.org/10.1016/j.foodhyd.2015.07.029
  5. 5.
    F.M. Van der Kooij, M.  Vogel, H.N.W. Lekkerkerker, Phys. Rev. E 62, 5397 (2000). http://journals.aps.org/pre/abstract/10.1103/PhysRevE.62.5397
  6. 6.
    W. Zhu, D. Sun, S. Liu, N. Wang, J. Zhang, L. Luan, Colloids Surf. A 301, 106 (2007). http://www.sciencedirect.com/science/article/pii/S0927775706009666
  7. 7.
    L. Luan, W. Li, S. Liu, D. Sun, Langmuir 25, 6349 (2009).  https://doi.org/10.1021/la804023b
  8. 8.
    S.M. Oversteegen, C. Vonk, J.E.G.J. Wijnhoven, H.N.W. Lekkerkerker, Phys. Rev. E 71, 041406 (2005).  https://doi.org/10.1103/PhysRevE.71.041406
  9. 9.
    D. Kleshchanok, A.V. Petukhov, P. Holmqvist, D.V. Byelov, H.N.W. Lekkerkerker, Langmuir 26, 13614 (2010).  https://doi.org/10.1021/la101891e
  10. 10.
    D. Kleshchanok, J.-M. Meijer, A.V. Petukhov, G. Portale, H.N.W. Lekkerkerker, Soft Matter 7, 2832 (2011).  https://doi.org/10.1039/C0SM01206H
  11. 11.
    N. Doshi, G. Cinacchi, J.S. van Duijneveldt, T. Cosgrove, S.W. Prescott, I. Grillo, J. Phipps, D.I. Gittins, J. Phys.: Condens. Matter 23, 194109 (2011). http://stacks.iop.org/0953-8984/23/i=19/a=194109
  12. 12.
    D. Kleshchanok, J.-M. Meijer, A.V. Petukhov, G. Portale, H.N.W. Lekkerkerker, Soft Matter 8, 191 (2012).  https://doi.org/10.1039/C1SM06535A
  13. 13.
    D. de las Heras, N. Doshi, T. Cosgrove, J. Phipps, D.I. Gittins, J.S. van Duijneveldt, M. Schmidt, Sci. Rep. 2, 789 (2012).  https://doi.org/10.1038/srep00789
  14. 14.
    J. Landman, E. Paineau, P. Davidson, I. Bihannic, L.J. Michot, A.-M. Philippse, A.V. Petukhov, H.N.W. Lekkerkerker, J. Phys. Chem. B 118, 4913 (2014).  https://doi.org/10.1021/jp500036v
  15. 15.
    M. Chen, H. Li, Y. Chen, A.F. Mejia, X. Wang, Z. Cheng, Soft Matter 11, 5775 (2015).  https://doi.org/10.1039/C5SM00615E
  16. 16.
    T. Nakato, Y. Yamashita, E. Mouri, K. Kuroda, Soft Matter 10, 3161 (2014).  https://doi.org/10.1039/C3SM52311J
  17. 17.
    M.A. Bates, D. Frenkel, Phys. Rev. E 62, 5225 (2000).  https://doi.org/10.1103/PhysRevE.62.5225
  18. 18.
    S.-D. Zhang, P.A. Reynolds, J.S. van Duijneveldt, J. Chem. Phys. 117, 9947 (2002).  https://doi.org/10.1063/1.1518007
  19. 19.
    S.-D. Zhang, P.A. Reynolds, J.S. van Duijneveldt, Mol. Phys. 100, 3041 (2002).  https://doi.org/10.1080/00268970210130146
  20. 20.
    L. Harnau, Mol. Phys. 106, 1975 (2008).  https://doi.org/10.1080/00268970802032301
  21. 21.
    D. de las Heras, M. Schmidt, Philos. Trans. R. Soc. A 371, 20120259 (2013).  https://doi.org/10.1098/rsta.2012.0259
  22. 22.
    R. Aliabadi, M. Moradi, S. Varga, J. Chem. Phys. 144, 074902 (2016).  https://doi.org/10.1063/1.4941981
  23. 23.
    A. Vrij, Pure Appl. Chem. 48, 471 (1976).  https://doi.org/10.1351/pac197648040471
  24. 24.
    R. Tuinier, G.J. Fleer, Macromolecules 37, 8754 (2004).  https://doi.org/10.1021/ma0485742
  25. 25.
    S.M. Oversteegen, R. Roth, J. Chem. Phys. 122, 214502 (2005).  https://doi.org/10.1063/1.1908765
  26. 26.
    H.H. Wensink, H.N.W. Lekkerkerker, Mol. Phys. 107, 2111 (2009).  https://doi.org/10.1080/00268970903160605
  27. 27.
    M.A. Bates, D. Frenkel, Phys. Rev. E 57, 4824 (1998). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.57.4824
  28. 28.
    M. Marechal, A. Cuetos, B. Martínez-Haya, M. Dijkstra, J. Chem. Phys. 134, 094501 (2011).  https://doi.org/10.1063/1.3552951
  29. 29.
    R. Tuinier, Adv. Condens. Matter Phys. (2016). https://www.hindawi.com/journals/acmp/2016/5871826/cta/
  30. 30.
    R. Tuinier, G.J. Fleer, J. Phys. Chem. B 110, 20540 (2006).  https://doi.org/10.1021/jp063650j
  31. 31.
    B. Widom, J. Phys. Chem. 77, 2196 (1973).  https://doi.org/10.1021/j100637a008
  32. 32.
    P.G. Bolhuis, M. Hagen, D. Frenkel, Phys. Rev. E 50, 4880 (1994). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.50.4880
  33. 33.
    M. Dijkstra, J.M. Brader, R. Evans, J. Phys.: Condens. Matter 11, 10079 (1999)ADSGoogle Scholar
  34. 34.
    K. Akahane, J. Russo, H. Tanaka, Nat. Commun. 7, 12599 (2016).  https://doi.org/10.1038/ncomms12599
  35. 35.
    V.F.D. Peters, M. Vis, Á. González García, R. Tuinier, in preparation (n.a.a)Google Scholar
  36. 36.
    M.A. Bates, D.  Frenkel, J. Chem. Phys 110, 6553 (1999).  https://doi.org/10.1063/1.478558
  37. 37.
    H.H. Wensink, G.J. Vroege, J. Phys.: Condens. Matter 16, S2015 (2004). http://stacks.iop.org/0953-8984/16/i=19/a=013
  38. 38.
    H.H. Wensink, H.N.W. Lekkerkerker, Europhys. Lett. 66, 125 (2004).  https://doi.org/10.1209/epl/i2003-10140-1
  39. 39.
    D. de las Heras, M. Schmidt, Soft Matter 9, 8636 (2013).  https://doi.org/10.1039/C3SM51491A
  40. 40.
    F.M. van der Kooij, K. Kassapidou, H.N.W. Lekkerkerker, Nature 406, 868 (2000).  https://doi.org/10.1038/35022535
  41. 41.
    S. Liu, J. Zhang, N. Wang, W. Liu, C. Zhang, D. Sun, Chem. Mater. 15, 3240 (2003).  https://doi.org/10.1021/cm034201o
  42. 42.
    V.F.D. Peters, M. Vis, H.H. Wensink, R. Tuinier, in preparation (n.a.b)Google Scholar
  43. 43.
    H.H. Wensink, Phys. Rev. Lett. 93, 157801 (2004). https://doi.org/10.1103/PhysRevLett.93.157801
  44. 44.
    C.F. Tejero, A. Daanoun, H.N.W. Lekkerkerker, M. Baus, Phys. Rev. Lett. 73, 752 (1994). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.73.752
  45. 45.
    G. Foffi, G.D. McCullagh, A. Lawlor, E. Zaccarelli, K.A. Dawson, F. Sciortino, P. Tartaglia, D. Pini, G. Stell, Phys. Rev. E 65, 031407 (2002).  https://doi.org/10.1103/PhysRevE.65.031407
  46. 46.
    C. Fernandes, A. Senos, Int. J. Refract. Met. Hard Mater. 29, 405 (2011). http://www.sciencedirect.com/science/article/pii/S0263436811000333
  47. 47.
    D. Marenduzzo, K. Finan, P.R. Cook, J. Cell. Biol. 175, 681 (2006). http://jcb.rupress.org/content/175/5/681
  48. 48.
    L. Sapir, D. Harries, Bunsen-Mag. 19, 152 (2017). https://scholars.huji.ac.il/danielharries/publications/wisdom-crowd#
  49. 49.
    G. van Anders, D. Klotsa, N.K. Ahmed, M. Engel, S.C. Glotzer, Proc. Natl. Acad. Sci. USA 111, E4812 (2014).  https://doi.org/10.1073/Proc.Natl.Acad.Sci.U.S.A..1418159111
  50. 50.
    M. Dijkstra, in Advances in Chemical Physics, ed. by S.A. Rice, A.R. Dinner, vol. 156 (Wiley, Hoboken, 2014), Chap.  2. https://onlinelibrary.wiley.com/doi/10.1002/9781118949702.ch2
  51. 51.
    L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).  https://doi.org/10.1111/j.1749-6632.1949.tb27296.x
  52. 52.
    H.H. Wensink, G.J. Vroege, H.N.W. Lekkerkerker, J. Phys. Chem B 105, 10610 (2001).  https://doi.org/10.1021/jp0105894
  53. 53.
    R. van Roij, Eur. J. Phys. 26, S57 (2005). http://stacks.iop.org/0143-0807/26/i=5/a=S07
  54. 54.
    J.D. Parsons, Phys. Rev. A 19, 1225 (1979).  https://doi.org/10.1103/PhysRevA.19.1225
  55. 55.
    S.-D. Lee, J. Chem. Phys. 87, 4972 (1987).  https://doi.org/10.1063/1.452811
  56. 56.
    T. Odijk, Macromolecules 19, 2313 (1986).  https://doi.org/10.1021/ma00163a001
  57. 57.
    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
  58. 58.
    A.Z. Panagiotopoulos, Mol. Phys. 61, 813 (1987).  https://doi.org/10.1080/00268978700101491

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

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