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The European Physical Journal E

, Volume 20, Issue 3, pp 299–308 | Cite as

Energetics of 2D colloids in free-standing smectic-C films

  • C. Bohley
  • R. Stannarius
Regular Article

Abstract.

The formation of regular colloid patterns in free-standing smectic films at the transition from the smectic-C to the isotropic or nematic phase is well known experimentally. The self-organization of isotropic or nematic droplets is caused by their mutual interaction, mediated by elastic distortions of the local director in the surrounding liquid crystal. These distortions are related to the anchoring conditions of the director at the droplet border. We describe analytically the energetics of the liquid crystal environment of a single droplet in one-constant approximation. A method of complex analysis, Conformal Mapping, is employed. Following a suggestion of Dolganov et al. (Phys. Rev. E. 73, 041706 (2006)), energetics of chain and grid patterns built from the colloids are investigated numerically in order to explain experimentally observed formations and their director fields.

PACS.

61.30.Dk Continuum models and theories of liquid crystal structure 61.30.Jf Defects in liquid crystals 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions 

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References

  1. 1.
    P.S. Drzaic, Liquid Crystal Dispersions, Vol. 1 (World Scientific, Singapore, 1995).Google Scholar
  2. 2.
    P. Poulin, H. Stark, T.C. Lubensky, D.A. Weitz, Science 275, 1770 (1997).CrossRefGoogle Scholar
  3. 3.
    P. Poulin, D.A. Weitz, Phys. Rev. E 57, 626 (1998).CrossRefADSGoogle Scholar
  4. 4.
    H. Stark, Phys. Rep. 351, 387 (2001) and references therein.CrossRefADSGoogle Scholar
  5. 5.
    P.V. Dolganov, V.K. Dolganov, Phys. Rev. E 73, 041706 (2006).CrossRefADSGoogle Scholar
  6. 6.
    P. Cluzeau, P. Poulin, G. Joly, H.T. Nguyen, Phys. Rev. E 63, 031702 (2001).CrossRefADSGoogle Scholar
  7. 7.
    H. Schüring, R. Stannarius, Langmuir 18, 9735 (2002).CrossRefGoogle Scholar
  8. 8.
    P. Cluzeau, V. Bonnand, G. Joly, V. Dolganov, H.T. Nguyen, Eur. Phys. J. E 10, 231 (2003).CrossRefGoogle Scholar
  9. 9.
    C. Völtz, R. Stannarius, Phys. Rev. E 70, 061702 (2004).CrossRefADSGoogle Scholar
  10. 10.
    R. Stannarius, C. Völtz, Phys. Rev. E 72, 032701 (2005)MathSciNetCrossRefADSGoogle Scholar
  11. 11.
    P. Cluzeau, G. Joly, H.T. Nguyen, V.K. Dolganov, JETP Lett. 75, 482 (2002)CrossRefADSGoogle Scholar
  12. 12.
    D. Pettey, T.C. Lubensky, D. Link, Liq. Cryst. 25, 579 (1998).CrossRefGoogle Scholar
  13. 13.
    P. Patricio, M. Tasinkevych, M.M. Telo da Gama, Eur. Phys. J. 7, 117 (2002).Google Scholar
  14. 14.
    T.C. Lubensky, D. Pettey, N. Currier, H. Stark, Phys. Rev. E 57, 610 (1998).CrossRefADSGoogle Scholar
  15. 15.
    B.I. Lev, S.B. Chernyshuk, P.M. Tomchuk, H. Yokoyama, Phys. Rev. E 65, 021709 (2002).CrossRefADSGoogle Scholar
  16. 16.
    J. Fukuda, H. Stark, M. Yoneya, H. Yokoyama, Phys. Rev. E 69, 041706 (2004). CrossRefADSGoogle Scholar
  17. 17.
    J. Fukuda, H. Yokoyama, Eur. Phys. J. E 4, 389 (2001).CrossRefGoogle Scholar
  18. 18.
    M. Tasinkevych, N.M. Silvestre, P. Patricio, M.M. Telo da Gama, Eur. Phys. J. E 9, 341 (2002).CrossRefGoogle Scholar
  19. 19.
    P.V. Dolganov, E.I. Demikhov, V.K. Dolganov, B.M. Bolotin, K. Krohn, Eur. Phys. J. E 12, 593 (2003).CrossRefGoogle Scholar
  20. 20.
    P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).Google Scholar
  21. 21.
    R. Yamamoto, Phys. Rev. Lett. 87, 075502 (2001).CrossRefADSGoogle Scholar
  22. 22.
    R. Yamamoto, Y. Nakayama, K. Kim, J. Phys.: Condens. Matter 16, 1945 (2004).CrossRefGoogle Scholar
  23. 23.
    S.A. Langer, J.P. Sethna, Phys. Rev. A 34, 5035 (1986).CrossRefADSGoogle Scholar
  24. 24.
    I. Kraus, R.B. Meyer, Phys. Rev. Lett. 82, 3815 (1999).MathSciNetCrossRefADSGoogle Scholar
  25. 25.
    R. Courant, D. Hilbert, Methoden der Mathematischen Physik (Springer, Berlin, 1937).Google Scholar
  26. 26.
    A. Rapini, M. Papoular, J. Phys. (Paris), Colloq. C4 30, 54 (1969).Google Scholar
  27. 27.
    A. Sonnet, A. Kilian, S. Hess, Phys. Rev. E 52, 718 (1995).CrossRefADSGoogle Scholar
  28. 28.
    M.R. Spiegel, Komplexe Variablen (McGraw-Hill Book Company, London, 1997).Google Scholar
  29. 29.
    W.H. Westphal, Physik (Springer, Berlin, 1937).Google Scholar
  30. 30.
    C. Bohley, unpublished results.Google Scholar
  31. 31.
    C. Pozrikidis, Theoretical and Computational Fluid Dynamics (Oxford University Press, New York, 1997).Google Scholar
  32. 32.
    L. Lejček, Czech. J. Phys. 55, 1237 (2005).CrossRefADSGoogle Scholar
  33. 33.
    P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1997).Google Scholar
  34. 34.
    R.B. Meyer, Mol. Cryst. Liq. Cryst. 40, 355 (1972).Google Scholar
  35. 35.
    S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge University Press, Cambridge, 1992).Google Scholar
  36. 36.
    P.V. Dolganov, P.M. Bolotin, JETP Lett. 77, 429 (2003).CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2006

Authors and Affiliations

  1. 1.Institute of Experimental PhysicsNonlinear PhenomenaMagdeburgGermany

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