Journal of Experimental and Theoretical Physics

, Volume 127, Issue 5, pp 939–944 | Cite as

Effect of Polydispersity on the Phase Diagram of Colloid Systems

  • E. I. Kats


A theoretical model is proposed that describes the experimentally observed phase diagram of colloidal dispersions of disk-shaped polydisperse particles. In the framework of the phenomenological theory of phase transitions, it is shown that if disk-shaped particles have polydispersity comparable in thickness and disk diameter, then the following sequence of phase transitions should be expected with increasing volume fraction of ϕ particles: an isotropic liquid (I); a nematic liquid crystal (N), in which the director n sets the preferred orientation of the disk normal; and the discotic (columnar) phase (C), in which the disklike molecules aggregate into liquid columns, and the latter form a two-dimensional hexagonal crystal consisting of liquid columns. However, when the particles forming the colloidal dispersion do not have any polydispersity in thickness (but the polydispersity in the particle diameter is preserved), another sequence of phase transitions takes place, in which the columnar phase is replaced by a smectic liquid crystal (S); that is, particles form a system of equidistant liquid layers. This work proposes and discusses the mechanisms of this behavior and new predictions that follow from this consideration.



I am grateful to Zhengdong Cheng for discussing the current state of the problem of phase diagrams of polydisperse colloidal dispersions. The work was started during the author’s stay at Tohoku University (Sendai, Japan), and I am grateful to T. Nakanishi and N. Yoshinaga for their hospitality and useful questions when I reported this topic.


  1. 1.
    D. Sun, Hung-Jue Sue, Zh. Cheng, Yu. Martinez-Raton, and E. Velasco, Phys. Rev. E 80, 041704 (2009).ADSCrossRefGoogle Scholar
  2. 2.
    M. Dijkstra, Curr. Opin. Colloid Interface Sci. 6, 372 (2001).CrossRefGoogle Scholar
  3. 3.
    D. Frenkel and B. Smit, in Algorithms to Applications (Academic, New York, 2001).zbMATHGoogle Scholar
  4. 4.
    D. Frenkel, Phys. A (Amsterdam, Neth.) 313, 1 (2002).Google Scholar
  5. 5.
    H. N. W. Lekkerkerker and R. Tuiner, Colloids and the Depletion Interaction (Springer, Berlin, 2011).CrossRefGoogle Scholar
  6. 6.
    A. Mertelj, D. Lisjak, M. Drofenik, and M. Copic, Nature (London, U.K.) 504, 237 (2013).ADSCrossRefGoogle Scholar
  7. 7.
    Q. Liu, P. J. Ackerman, T. C. Lubensky, and I. I. Smalyukh, Proc. Natl. Acad. Sci. (U.S.A.) 113, 1601235 (2016).Google Scholar
  8. 8.
    F. Brochard and P. G. de Gennes, J. Phys. 31, 691 (1970).CrossRefGoogle Scholar
  9. 9.
    E. I. Kats and V. V. Lebedev, Sov. Phys. JETP 69, 1155 (1989).Google Scholar
  10. 10.
    A. B. D. Brown, C. Ferrero, T. Narayanan, and A. R. Rennie, Eur. Phys. J. B 11, 481 (1999).ADSCrossRefGoogle Scholar
  11. 11.
    F. M. var der Kooij, K. Kassapidon, and M. N. W. Lekkerker, Nature (London, U.K.) 406, 868 (2000).Google Scholar
  12. 12.
    M. Bates and D. Frenkel, J. Chem. Phys. 110, 6553 (1999).ADSCrossRefGoogle Scholar
  13. 13.
    P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1993).Google Scholar
  14. 14.
    P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge Univ. Press, Cambridge, 2000).Google Scholar
  15. 15.
    T. Odagaki and K. Okazuki, J. Phys.: Condens. Matter 17, 4531 (2005).ADSGoogle Scholar
  16. 16.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1995; Pergamon, Oxford, 1980). Google Scholar
  17. 17.
    L. G. Fel, Phys. Rev. E 52, 702 (1995).ADSCrossRefGoogle Scholar
  18. 18.
    E. V. Gurovich, E. I. Kats, and V. V. Lebedev, Sov. Phys. JETP 73, 473 (1991).Google Scholar
  19. 19.
    P. G. Bolhuis and H. N. W. Lekkerkerer, Phys. A (Amsterdam, Neth.) 196, 375 (1993).Google Scholar
  20. 20.
    P. Woolston and J. S. van Duijneveldt, J. Chem. Phys. 142, 184901 (2015).ADSCrossRefGoogle Scholar
  21. 21.
    S. A. Brazovskii, Sov. Phys. JETP 41, 85 (1975).ADSGoogle Scholar
  22. 22.
    E. I. Kats and A. R. Muratov, Sov. Phys. JETP 67, 89 (1988).Google Scholar
  23. 23.
    E. I. Kats, V. V. Lebedev, and A. R. Muratov, Phys. Rep. 228, 1 (1993).ADSCrossRefGoogle Scholar
  24. 24.
    V. V. Brazhkin, A. G. Lyapin, V. N. Ryzhov, K. Trachenko, Yu. D. Fomin, and E. N. Tsiok, Phys. Usp. 55, 1061 (2012).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • E. I. Kats
    • 1
  1. 1.Landau Institute for Theoretical Physics, Russian Academy of SciencesChernogolovkaRussia

Personalised recommendations