Advertisement

The European Physical Journal Special Topics

, Volume 222, Issue 11, pp 3039–3052 | Cite as

Mixtures of anisotropic and spherical colloids: Phase behavior, confinement, percolation phenomena and kinetics

  • T. Schilling
  • S. Dorosz
  • M. Radu
  • M. Mathew
  • S. Jungblut
  • K. Binder
Review Confining Geometries

Abstract

Purely entropic systems such as suspensions of hard rods, platelets and spheres show rich phase behavior. Rods and platelets have successfully been used as models to predict the equilibrium properties of liquid crystals for several decades. Over the past years hard particle models have also been studied in the context of non-equilibrium statistical mechanics, in particular regarding the glass transition, jamming, sedimentation and crystallization. Recently suspensions of hard anisotropic particles also moved into the focus of materials scientists who work on conducting soft matter composites. An insulating polymer resin that is mixed with conductive filler particles becomes conductive when the filler percolates. In this context the mathematical topic of connectivity percolation finds an application in modern nano-technology. In this article, we briefly review recent work on the phase behavior, confinement effects, percolation transition and phase transition kinetics in hard particle models. In the first part, we discuss the effects that particle anisotropy and depletion have on the percolation transition. In the second part, we present results on the kinetics of the liquid-to-crystal transition in suspensions of spheres and of ellipsoids.

Keywords

Monte Carlo European Physical Journal Special Topic Percolation Threshold Hard Sphere Perc 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W.C.K. Poon, P.N. Pusey, in Observation, prediction and simulation of phase transitions in complex fluids, edited by M. Baus, L.F. Rull, J.P. Ryckaert (Kluwer Acad. Publ., Dordrecht, 1995), p. 3Google Scholar
  2. 2.
    A.K. Arora, B.V.R. Tata, Advanc. Colloid Interface Sci. 78, 49 (1998)CrossRefGoogle Scholar
  3. 3.
    H.N.W. Lekkerkerker, P. Bruning, J. Bintenhuis, C.G. Kroope, A. Stroobants, in Observation, Prediction and Simulation of Phase Transitions in Complex Fluids, edited by M. Baus, L.F. Rull, J.P. Ryckaert (Kluwer Acad. Publ., Dordrecht, 1995), p. 53Google Scholar
  4. 4.
    P. Bolhuis, D. Frenkel, J. Chem. Phys. 106, 666 (1997)ADSCrossRefGoogle Scholar
  5. 5.
    F.M. van der Kooij, K. Kassapidou, H.N.W. Lekkerkerker, Nature 406, 868 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    P. Davidson, J.C.P. Gabriel, Curr. Opinion Colloid Interface Sci. 9, 377 (2005)CrossRefGoogle Scholar
  7. 7.
    H. Löwen, J. Phys.: Condens. Matter 13, R415 (2001)CrossRefGoogle Scholar
  8. 8.
    D. van der Beek, H. Reich, P. van der Schoot, M. Dijkstra, T. Schilling, R. Vink, M. Schmidt, R. van Roij, H. Lekkerkerker, Phys. Rev. Lett. 97, 087801 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    G. Vroege, H.N.W. Lekkerkerker, Rep. Progr. Phys. 55, 1241 (1992)ADSCrossRefGoogle Scholar
  10. 10.
    K. Binder, J. Horbach, R.L.C. Vink, A. De Virgiliis, Soft. Matter 4, 1555 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    N. Grossiord, J. Loos, D. Regev, C.E. Koning, Chem. Mater. 18, 1089 (2006)CrossRefGoogle Scholar
  12. 12.
    Q. Cao, J.A. Rogers, Adv. Mater. 21, 29 (2009)CrossRefGoogle Scholar
  13. 13.
    A.V. Kyrylyuk, M.C. Hermant, T. Schilling, B. Klumperman, C.E. Koning, P. van der Schoot, Nature Nanotech. 6, 364 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    M. Moniruzzaman, K.I. Winey, Macromolecules 39, 5194 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    S. Stankovich, D. Dikin, G. Commett, K. Kohlhaas, E. Zimney, E. Stach, R. Piner, S. Nguyen, R. Ruoff, Nature 442, 282 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    B. Li, W. Zhong, J. Math. Sci. 46, 5595 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    J. Potts, D. Dreyer, C. Bielanski, R. Ruoff, Polymer 52, 5 (2011)CrossRefGoogle Scholar
  18. 18.
    P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Oxford Univ. Press, Oxford, 1993)Google Scholar
  19. 19.
    M. Radu, T. Schilling, [arXiv:1301.5592] [cond-mat.soft] (2013)
  20. 20.
    A. Winkler, P. Virnau, K. Binder, R.G. Winkler, G. Gompper, J. Chem. Phys. 138 054901 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    S. Dorosz, T. Schilling, J. Chem. Phys. 139, 124508 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    D. Stauffer, A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor & Francis, London, 1994)Google Scholar
  23. 23.
    R. Meester, R. Roy, Continuum Percolation (Cambridge Univ. Press, Cambridge, 1996)Google Scholar
  24. 24.
    T. Schilling, S. Jungblut, M.A. Miller, Phys. Rev. Lett. 98, 108303 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    S. Jungblut, Mixtures of Colloidal Rods and Spheres in Bulk and in Confinement (Dissertation, Johannes Gutenberg Universität Mainz, 2008) (unpublished)Google Scholar
  26. 26.
    F Oosawa, S. Asakura, J. Chem. Phys. 22, 1255 (1954)ADSGoogle Scholar
  27. 27.
    W.C.K. Poon, J. Phys.: Condens. Matter 14, R859 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    S. Jungblut, R. Tuinier, K. Binder, T. Schilling, J. Chem. Phys. 127, 244909 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    M. Mathew, T. Schilling, M. Oettel, Phys. Rev. E 85, 061407 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    K. Binder, W. Kob, Glassy Materials and Disordered Solids: An Introduction to Their Statstical Mechanics, Revised Edition (World Scientific, Singapore, 2011)Google Scholar
  31. 31.
    S. Jungblut, K. Binder, T. Schilling, Computer Phys. Commun. 179, 13 (2008)MathSciNetADSCrossRefzbMATHGoogle Scholar
  32. 32.
    S. Jungblut, K. Binder, T. Schilling, J. Phys.: Condens. Matter 20, 404223 (2008)CrossRefGoogle Scholar
  33. 33.
    P.G.Bolhuis, A. Stroobants, D. Frenkel, H.N.W. Lekkerkerker, J. Chem. Phys. 107, 1551 (1997)ADSCrossRefGoogle Scholar
  34. 34.
    S.V. Savenko, M. Dijkstra, J. Chem. Phys. 124, 234902 (2006)ADSCrossRefGoogle Scholar
  35. 35.
    R.L.C. Vink, J. Horbach, J. Chem. Phys. 121, 3253 (2004)ADSCrossRefGoogle Scholar
  36. 36.
    P. Virnau, M. Müller, J. Chem. Phys. 120, 10925 (2004)ADSCrossRefGoogle Scholar
  37. 37.
    K. Binder, D.P. Landau, Phys. Rev. B 30, 1477 (1984)ADSCrossRefGoogle Scholar
  38. 38.
    H. Müller-Krumbhaar, Phys. Lett. 50, 27 (1974)CrossRefGoogle Scholar
  39. 39.
    K. Binder, Solid State Commun. 34, 191 (1980)ADSCrossRefGoogle Scholar
  40. 40.
    K. Binder, P. Fratzl, in Phase Transformations in Materials, edited by G. Kostorz (Wiley-VCH, Weinheim, 2001), p. 409Google Scholar
  41. 41.
    K. Binder, D. Stauffer, Adv. Phys. 25, 343 (1976)ADSCrossRefGoogle Scholar
  42. 42.
    K. Binder, Rep. Progr. Phys. 50, 783 (1987)ADSCrossRefGoogle Scholar
  43. 43.
    M. Foygel, R. Morris, D. Anez, S. French, V. Sobolev, Phys. Rev. B 71, 104201 (2005)ADSCrossRefGoogle Scholar
  44. 44.
    K. Leung, D. Chandler, J. Stat. Phys. 63, 837 (1991)MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    R. Otten, P. van der Schoot, J. Chem. Phys. 134, 094902 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    K. Schätzel, B.J. Ackerson, Phys. Rev. E 48, 3766 (1993)ADSCrossRefGoogle Scholar
  47. 47.
    J.L. Harland, W. van Megen, Phys. Rev. E 55, 8054 (1997)CrossRefGoogle Scholar
  48. 48.
    S. Iacopini, T. Palberg, H.J. Schöpe, J. Chem. Phys. 130, 084502 (2009)ADSCrossRefGoogle Scholar
  49. 49.
    S. Auer, D. Frenkel, Nature 409, 1020 (2001)ADSCrossRefGoogle Scholar
  50. 50.
    L. Filion, R. Ni, D. Frenkel, M. Dijkstra, J. Chem. Phys. 134, 134901 (2011)ADSCrossRefGoogle Scholar
  51. 51.
    T. Schilling, S. Dorosz, H.J. Schöpe, G. Opletal, J. Phys.: Condens. Matter 25, 194129 (2011)Google Scholar
  52. 52.
    D.C. Rapaport, The Art of Molecular Dynamics Simulation, 2nd ed. (Cambridge Univ. Press, Cambridge, 2004)Google Scholar
  53. 53.
    I.K. Snook, The Langevin and Generalized Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems (Elsevier, Amsterdam, 2007)Google Scholar
  54. 54.
    M.G. McPhie, P.J. Davies, I.K. Snook, Phys. Rev. E 74, 031201 (2006)ADSCrossRefGoogle Scholar
  55. 55.
    A. Malevanets, R. Kapral, J. Chem. Phys. 110, 8605 (1999)ADSCrossRefGoogle Scholar
  56. 56.
    A. Malevanets, R. Kapral, J. Chem. Phys. 112, 7260 (2000)ADSCrossRefGoogle Scholar
  57. 57.
    T. Ihle, D. M. Kroll, Phys. Rev. E 63, 020201 (2001)ADSCrossRefGoogle Scholar
  58. 58.
    R. Kapral, Adv. Chem. Phys. 140, 89 (2008)CrossRefGoogle Scholar
  59. 59.
    G. Gompper, T. Ihle, D.M. Kroll, R.G. Winkler, Adv. Polym. Sci. 221, 1 (2009)Google Scholar
  60. 60.
    B.J. Alder, T.E. Wainwright, J. Chem. Phys. 31, 459 (1995)MathSciNetADSCrossRefGoogle Scholar
  61. 61.
    M. Marin, P. Cordero, Computer Phys. Commun. 92, 214 (1995)ADSCrossRefGoogle Scholar
  62. 62.
    A. Krantz, ACM Trans. Modeling Computer Sim. 6, 185 (1983)CrossRefGoogle Scholar
  63. 63.
    M. Radu, Ph.D. thesis (Univ. Luxembourg, 2013) (unpublished)Google Scholar
  64. 64.
    P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Phys. Rev. B 28, 784 (1983)ADSCrossRefGoogle Scholar
  65. 65.
    P.R. ten Wolde, M.J. Ruiz-Montero, D. Frenkel, Phys. Rev. Lett. 75, 2714 (1995)ADSCrossRefGoogle Scholar
  66. 66.
    P. Pfleiderer, T. Schilling, Phys. Rev. E 75, 020402(R) (2007)ADSCrossRefGoogle Scholar
  67. 67.
    M. Radu, P. Pfleiderer, T. Schilling, J. Chem. Phys. 131, 164513 (2009)ADSCrossRefGoogle Scholar
  68. 68.
    G. Odriozola, J. Chem. Phys. 136, 134505 (2012)ADSCrossRefGoogle Scholar
  69. 69.
    D. Frenkel, B.M. Mulder, J.P. Mctague, Molec. Cryst. Liquid Cryst. 123, 119 (1985)CrossRefGoogle Scholar
  70. 70.
    P. Pfleiderer, K. Milinkovic, T. Schilling, EPL 84, 16003 (2008)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • T. Schilling
    • 1
  • S. Dorosz
    • 1
  • M. Radu
    • 1
  • M. Mathew
    • 2
  • S. Jungblut
    • 3
  • K. Binder
    • 2
  1. 1.Theory of Soft MatterUniversité du LuxembourgLuxembourgLuxembourg
  2. 2.KOMET Institut für PhysikJohannes Gutenberg-Universität MainzMainzGermany
  3. 3.Fakultät für PhysikUniversität WienWienAustria

Personalised recommendations