Skip to main content
Log in

Spatially modulated structures in nematic colloids: Statistical thermodynamics and kinetics

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract

We examine the spatial distribution of rigid-sphere-like particles in a nematic host. Using a continuum model we analyse the conditions necessary for the appearance of a modulated lamellar structure. There is a long-range effective interaction between the particles, which can lead to the formation of superstructures. In general, this interaction includes several contributions: van der Waals-type direct interaction and indirect interaction via the director field distortions. The latter depends on the temperature of the sample, the coupling energy between a colloidal particle and a nematic host, and the particle concentration. This effective interaction controls the spatial structure and the kinetic properties of the system. We obtained the analytical expression for the temperature when the system loses the stability with respect to the modulated structure formation. Typical contours of the diffuse light scattering are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. Poulin, H. Stark, T.C. Lubensky, D.A. Weitz, Science 275, 1770 (1997)

    Article  Google Scholar 

  2. T.C. Lubensky, D. Pettey, N. Currier, H. Stark, Phys. Rev. E 57, 610 (1998)

    Article  ADS  Google Scholar 

  3. H. Stark, Phys. Rep. 351, 387 (2001)

    Article  ADS  Google Scholar 

  4. C. Lapointe, T. Mason, I.I. Smalyukh, Science 326, 1083 (2009)

    Article  ADS  Google Scholar 

  5. O.P. Pishnyak, S. Tang, J.R. Kelly, S.V. Shiyanovskii, O.D. Lavrentovich, Phys. Rev. Lett. 99, 127802 (2007)

    Article  ADS  Google Scholar 

  6. Akihiko Matsuyama, J. Chem. Phys. 131, 204904 (2009)

    Article  Google Scholar 

  7. P. van der Schoot, V. Popa-Nita, S. Kralj, J. Phys. Chem. B 112, 4512 (2008)

    Article  Google Scholar 

  8. V. Popa-Nita, S. Kralj, J. Chem. Phys. 132, 024902 (2010)

    Article  ADS  Google Scholar 

  9. W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge 1989)

  10. I. Musevic, M. Skarabot, M. Ravnik, U. Tkalec, S. Zumer, Science 313, 954 (2006)

    Article  ADS  Google Scholar 

  11. S.L. Lopatnikov, V.A. Namiot, Sov. Phys. JETP 48, 181 (1978)

    ADS  Google Scholar 

  12. I. Musevic, M. Skarabot, M. Ravnik, U. Tkalec, S. Zumer, Soft Matter 5, 269 (2009)

    Article  Google Scholar 

  13. V.I. Zadorozhnii, T.J. Sluckin, V.Yu. Reshetnyak, K.S. Thomas, SIAM J. Appl. Math. 68, 1688 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. V.M. Pergamenshchik, V.A. Uzunova, Phys. Rev. E 79, 021704 (2009)

    Article  ADS  Google Scholar 

  15. B.I. Lev, P.M. Tomchuk, Phys. Rev. E 59, 591 (1999)

    Article  ADS  Google Scholar 

  16. S.B. Chernyshuk, B.I. Lev, Phys. Rev. E 81, 041701 (2010)

    Article  ADS  Google Scholar 

  17. B. Zhou, G.S. Iannacchione, C.W. Garland, T. Bellini, Phys. Rev. E 55, 2962 (1997)

    Article  ADS  Google Scholar 

  18. Karatairi et al., Phys. Rev. E 81, 041703 (2010)

    Article  ADS  Google Scholar 

  19. A.V. Kleshchonok, V.Yu. Reshetnyak, V.A. Tatarenko, Ukr. J. Phys. 55, 524 (2010)

    Google Scholar 

  20. H.S. Tsien, Physical Mechanics (Science Press, Bejing, 1962)

  21. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993)

  22. P. Oswald, P. Pieranski, Nematic and Cholesteric Liquid Crystals (Taylor & Francis Group, Boca Raton, 2005)

  23. G. Barbero, V.M. Pergamenshchik, Phys. Rev. E 66, 051706 (2002)

    Article  ADS  Google Scholar 

  24. N.A. Smirnova, Molecular Theories of Solutions (Khimiya, Leningrad, 1987) (in Russian)

  25. D.L. Cheung, M.P. Allen, Phys. Rev. E 74, 021701 (2006)

    Article  ADS  Google Scholar 

  26. Denis Andrienko, Michael P. Allen, Gregor Skacej, Slobodan Zumer, Phys. Rev. E 65, 041702 (2002)

    Article  ADS  Google Scholar 

  27. A.G. Khachaturyan, Theory of Structural Transformations in Solids (John Wiley & Sons, New York, 1983)

  28. D.A. Badalyan, A.G. Khachaturyan, J. Phys. Chem. Solids 39, 711 (1978)

    Article  ADS  Google Scholar 

  29. T.G. Sokolovska, R.O. Sokolovskii, G.N. Patey, Phys. Rev. E 77, 041701 (2008)

    Article  ADS  Google Scholar 

  30. A. Korn, T. Korn, Mathematical Handbook (McGraw-Hill Book Company, New York, 1968)

  31. S. Faetti, M. Gatti, V. Palleschi, J. Phys. (Paris) Lett. 46, 881 (1985)

    Google Scholar 

  32. O.V. Kuksenok, R.W. Ruhwandl, S.V. Shiyanovskii, E.M. Terentjev, Phys. Rev. E 54, 5198 (1996)

    Article  ADS  Google Scholar 

  33. T. Kishita, K. Takahashi, M. Ichikawa, J. Fukuda, Y. Kimura, Phys. Rev. E 81, 010701 (2010)

    Article  ADS  Google Scholar 

  34. A.R. Alnatt, A.B. Lidiard, Atomic Transport in Solids (Cambridge University Press, Cambridge, 1993).

  35. J.M. Ziman, Models of Disorder (Cambridge University Press, Cambridge, 1979)

  36. A.I. Kitaigorodsky, Mixed Crystals (Nauka, Moscow, 1983) (in Russian)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Kleshchonok.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kleshchonok, A.V., Reshetnyak, V.Y. & Tatarenko, V.A. Spatially modulated structures in nematic colloids: Statistical thermodynamics and kinetics. Eur. Phys. J. E 34, 33 (2011). https://doi.org/10.1140/epje/i2011-11033-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2011-11033-8

Keywords

Navigation