Small-angle light scattering symmetry breaking in polymer-dispersed liquid crystal films with inhomogeneous electrically controlled interface anchoring

  • V. A. LoikoEmail author
  • A. V. Konkolovich
  • V. Ya. Zyryanov
  • A. A. Miskevich
Atoms, Molecules, Optics


We have described the method of analyzing and reporting on the results of calculation of the small-angle structure of radiation scattered by a polymer-dispersed liquid crystal film with electrically controlled interfacial anchoring. The method is based on the interference approximation of the wave scattering theory and the hard disk model. Scattering from an individual liquid crystal droplet has been described using the anomalous diffraction approximation extended to the case of droplets with uniform and nonuniform interface anchoring at the droplet–polymer boundary. The director field structure in an individual droplet is determined from the solution of the problem of minimizing the volume density of the free energy. The electrooptical effect of symmetry breaking in the angular distribution of scattered radiation has been analyzed. This effect means that the intensities of radiation scattered within angles +θ s and–θ s relative to the direction of illumination in the scattering plane can be different. The effect is of the interference origin and is associated with asymmetry of the phase shift of the wavefront of an incident wave from individual parts of the droplet, which appears due to asymmetry of the director field structure in the droplet, caused by nonuniform anchoring of liquid crystal molecules with the polymer on its surface. This effect is analyzed in the case of normal illumination of the film depending on the interfacial anchoring at the liquid crystal–polymer interface, the orientation of the optical axes of droplets, their concentration, sizes, anisometry, and polydispersity.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. M. Zharkova and A. S. Sonin, Liquid Crystal Composites (Nauka, Moscow, 1994) [in Russian].Google Scholar
  2. 2.
    F. Simoni, Nonlinear Properties of Liquid Crystals and Polymer Dispersed Liquid Crystals (World Scientific, Singapore, 1997).CrossRefGoogle Scholar
  3. 3.
    M. G. Tomilin and S. M. Pestov, Properties of Liquid Crystal Materials (Politekhnika, St. Petersburg, 2005) [in Russian].Google Scholar
  4. 4.
    Display Systems, Ed. by L. W. MacDonald and A. C. Lowe (Wiley, New York, 1997).Google Scholar
  5. 5.
    V. G. Chigrinov, Liquid Crystal Devices: Physics and Application (Artech House, Boston, 1999).Google Scholar
  6. 6.
    V. Ya. Zyryanov, S. L. Smorgon, and V. F. Shabanov, Mol. Eng. 1, 305 (1992).CrossRefGoogle Scholar
  7. 7.
    F. Basile, F. Bloisi, L. Vicari, and F. Simoni, Phys. Rev. E 48, 432 (1993).ADSCrossRefGoogle Scholar
  8. 8.
    V. V. Presnyakov and T. V. Galstian, Mol. Cryst. Liq. Cryst. 413, 435 (2004).CrossRefGoogle Scholar
  9. 9.
    V. A. Loiko and A. V. Konkolovich, J. Exp. Theor. Phys. 96, 489 (2003).ADSCrossRefGoogle Scholar
  10. 10.
    V. A. Loiko and A. V. Konkolovich, J. Exp. Theor. Phys. 99, 343 (2004).ADSCrossRefGoogle Scholar
  11. 11.
    V. A. Loiko and A. V. Konkolovich, J. Exp. Theor. Phys. 103, 935 (2006).ADSCrossRefGoogle Scholar
  12. 12.
    P. G. Lisinetskaya, A. V. Konkolovich, and A. V. Loiko, Appl. Opt. 48, 3144 (2009).ADSCrossRefGoogle Scholar
  13. 13.
    A. Khan, I. Shiyanovskaya, T. Schneider, et al., J. SID 15, 9 (2007).Google Scholar
  14. 14.
    G. E. Volovik and O. D. Lavrentovich, Sov. Phys. JETP 58, 1159 (1983).Google Scholar
  15. 15.
    P. S. Drzaic, Liquid Crystal Dispersions (World Sci., Singapore, 1995).CrossRefGoogle Scholar
  16. 16.
    J. L. West, J. W. Doane, and S. Zumer, US Patent No. 4685771, Int. Cl. G02F 1/13 (1987).Google Scholar
  17. 17.
    V. K. Freedericksz and V. Zolina, Trans. Faraday Soc. 29, 919 (1933).CrossRefGoogle Scholar
  18. 18.
    V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, and A. V. Shabanov, JETP Lett. 86, 383 (2007).ADSCrossRefGoogle Scholar
  19. 19.
    E. Dubois-Violette and P. G. de Gennes, J. Phys. Lett. 36, L–255 (1975).CrossRefGoogle Scholar
  20. 20.
    L. M. Blinov, E. I. Kats, and A. A. Sonin, Sov. Phys. Usp. 30, 604 (1987).ADSCrossRefGoogle Scholar
  21. 21.
    S. Zumer and J. W. Doane, Phys. Rev. A 34, 3373 (1986).ADSCrossRefGoogle Scholar
  22. 22.
    S. Zumer, Phys. Rev. A 37, 4006 (1988).ADSCrossRefGoogle Scholar
  23. 23.
    D. A. Yakovlev and O. A. Afonin, Opt. Spectrosc. 82, 78 (1997).ADSGoogle Scholar
  24. 24.
    V. A. Loiko, P. G. Maksimenko, and A. V. Konkolovich, Opt. Spectrosc. 105, 791 (2008).ADSCrossRefGoogle Scholar
  25. 25.
    V. A. Loiko, A. V. Konkolovich, and A. A. Miskevich, J. Exp. Theor. Phys. 122, 176 (2016).ADSCrossRefGoogle Scholar
  26. 26.
    V. A. Loiko, V. Ya. Zyryanov, A. V. Konkolovich and A. A. Miskevich, Opt. Spectrosc. 120, 143 (2016).ADSCrossRefGoogle Scholar
  27. 27.
    V. A. Loiko, U. Mashke, V. Ya. Zyryanov, A. V. Konkolovich, and A. A. Miskevich, Opt. Spectrosc. 111, 866 (2011).CrossRefGoogle Scholar
  28. 28.
    V. A. Loiko, V. Ya. Zyryanov, U. Maschke, et al., J. Quant. Spectrosc. Rad. Transfer 113, 2585 (2012).ADSCrossRefGoogle Scholar
  29. 29.
    V. A. Loiko, V. Ya. Zyryanov, A. V. Konkolovich, et al., Mol. Cryst. Liq. Cryst. 561, 194 (2012).CrossRefGoogle Scholar
  30. 30.
    V. A. Loiko and A. V. Konkolovich, J. Phys. D 33, 2201 (2000).ADSCrossRefGoogle Scholar
  31. 31.
    M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1964; Nauka, Moscow, 1970).Google Scholar
  32. 32.
    C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998; Mir, Moscow, 1986).Google Scholar
  33. 33.
    V. I. Iveronova and G. P. Revkevich, Theory of X-ray Scattering (Mosk. Gos. Univ., Moscow, 1978) [in Russian].Google Scholar
  34. 34.
    A. P. Ivanov, V. A. Loiko, and V. P. Dik, Light Propagation in Densely Packed Dispersed Media (Nauka Tekhnika, Minsk, 1988) [in Russian].Google Scholar
  35. 35.
    J. Ziman, Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems (Cambridge Univ., Cambridge, 1979; Mir, Moscow, 1982).Google Scholar
  36. 36.
    M. S. Wertheim, Phys. Rev. Lett. 10, 321 (1963).ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Y. Rosenfeld, Phys. Rev. A 42, 5978 (1990).ADSCrossRefGoogle Scholar
  38. 38.
    K. H. Ding, C. E. Mandt, L. Tsang, and J. A. Kong, J. Electromagn. Waves Appl. 6, 1015 (1992).Google Scholar
  39. 39.
    K. M. Hong, J. Opt. Soc. Am. 70, 821 (1980).ADSCrossRefGoogle Scholar
  40. 40.
    Scattering of Electromagnetic Waves: Numerical Simulations, Ed. by J. Kong (Wiley, New York, 2001).Google Scholar
  41. 41.
    J. A. Lock and Chiu Chin-Lien, Appl. Opt. 33, 4663 (1994).ADSCrossRefGoogle Scholar
  42. 42.
    V. A. Loiko and A. V. Konkolovich, Opt. Spektrosc. 85, 623 (1998).Google Scholar
  43. 43.
    V. A. Loiko, U. Mashke, V. Ya. Zyryanov, et al., Opt. Spektrosc. 110, 116 (2011).ADSGoogle Scholar
  44. 44.
    V. A. Loiko, M. N. Krakhalev, A. V. Konkolovich et al., J. Quant. Spectrosc. Radiat. Transfer 178, 263 (2016).ADSCrossRefGoogle Scholar
  45. 45.
    H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981; Inostr. Liter., Moscow, 1961).Google Scholar
  46. 46.
    V. N. Lopatin and N. V. Shepelevich, Opt. Spectrosc. 81, 103 (1996).ADSGoogle Scholar
  47. 47.
    G. H. Meeten, Opt. Acta 29, 759 (1982).ADSCrossRefGoogle Scholar
  48. 48.
    R. Azzam and N. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977; Mir, Moscow, 1981).Google Scholar
  49. 49.
    E. V. Ishchenko and A. L. Sokolov, Polarization Optics (Mosk. Energet. Inst., Moscow, 2005) [in Russian].Google Scholar
  50. 50.
    L. M. Blinov, Structure and Properties of Liquid Crystals (Springer, New York, 2011).CrossRefGoogle Scholar
  51. 51.
    O. O. Prischepa, A. V. Shabanov, and V. Ya. Zyryanov, JETP Lett. 79, 257 (2004).ADSCrossRefGoogle Scholar
  52. 52.
    O. O. Prishchepa, A. V. Shabanov, and V. Ya. Zyryanov, Phys. Rev. E 72, 031712 (2005).ADSCrossRefGoogle Scholar
  53. 53.
    V. Ya. Zyryanov, M. N. Krakhalev, and O. O. Prishchepa, Mol. Cryst. Liq. Cryst. 489, 273 (2008).CrossRefGoogle Scholar
  54. 54.
    V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, and A. V. Shabanov, JETP Lett. 88, 597 (2008).ADSCrossRefGoogle Scholar
  55. 55.
    A. Walther and A. Muller, Soft Matter 4, 663 (2008).ADSCrossRefGoogle Scholar
  56. 56.
    A. Perro, S. Reculusa, S. Ravaine, et al., J. Mater. Chem. 15, 3745 (2005).CrossRefGoogle Scholar
  57. 57.
    V. A. Loiko, U. Mashke, V. Ya. Zyryanov, A. V. Konkolovich, and A. A. Misckevich, J. Exp. Theor. Phys. 107, 692 (2008).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  • V. A. Loiko
    • 1
    Email author
  • A. V. Konkolovich
    • 1
  • V. Ya. Zyryanov
    • 2
  • A. A. Miskevich
    • 1
  1. 1.Stepanov Institute of PhysicsNational Academy of Sciences of BelarusMinskBelarus
  2. 2.Kirensky Institute of Physics, Federal Research Center “Krasnoyarsk Scientific Center,” Siberian BranchRussian Academy of SciencesKraskoyarskRussia

Personalised recommendations