Defects and Undulation in Layered Liquid Crystals

  • T. Ishikawa
  • O. D. Lavrentovich
Chapter
Part of the NATO Science Series book series (NAII, volume 43)

Abstract

Many systems, such as lamellar liquid crystals, block copolymers, ferrofluids and ferromagnets posses a one-dimensional periodic order. Cholesteric liquid crystals with large periodicity (say, 10 microns) represent a model system that allows one to directly determine layer configurations under a polarizing microscope and thus to study various elastic phenomena. We review recent studies of the so-called cholesteric “fingerprint textures” as an experimental model of two elastic effects: (1) distortions of the order parameter around an elementary edge dislocation and (2) undulations of layers in the magnetic field. Elastic distortions caused by the edge dislocation can be properly described only when the elastic free energy is supplemented by a non-linear term. Fitting the dislocation profile allows one to measure the penetration length of the system. With the known penetration length, one can verify the scenario of layers undulations in the magnetic field. The experiments reveal that the displacement of layers above the undulations threshold is much larger than the one expected from the Helfrich-Hurault theory which assumes that the boundaries impose infinitely strong surface anchoring. A revised theory that accounts for a finite surface anchoring for a bounded lamellar system fits the experimental data well. The feature of finite surface anchoring allows one to find an analytical description of undulations well above the threshold field, namely, the transformation of sinusoidal layer distortions into the saw-tooth distortions and reorientation of layers at the bounding substrates at very high fields.

Keywords

Liquid Crystal Edge Dislocation Free Energy Density Cholesteric Liquid Crystal Penetration Length 
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.
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References

  1. 1.
    Landau, L.D. and Lifshitz, E.M., Course of Theoretical Physics, Statistical Mechanics, Part1, (Pergamon Press, Oxford, 1980)Google Scholar
  2. 2.
    Chaikin, P.M. and Lubensky, T.C., (1995) Principles of Condensed Matter Physics. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  3. 3.
    Holyst, R. (1991) Phys. Rev. A, 44, 3692.ADSCrossRefGoogle Scholar
  4. 4.
    Helfrich, W. (1971) J. Chem. Phys. 55, 839; Hurault, J.P. (1973) J. Chem. Phys. 59, 2068.ADSCrossRefGoogle Scholar
  5. 5.
    Kleman, M. and Lavrentovich, O.D. (2001) Soft Matter Physics: An Introduction. Springer Verlag, New York.Google Scholar
  6. 6.
    Weatherburn, C.E., (1961) Differential Geometry of Three Dimensions, vol. 1. Cambridge University Press, Cambridge.Google Scholar
  7. 7.
    Grinstein, G. and Pelcovits, R.A. (1982) Phys. Rev. A, 26, 915.ADSCrossRefGoogle Scholar
  8. 8.
    Brener, E.A. and Marchenko, V.I. (1999) Phys. Rev. E, 59, R4752.MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Nallet, F., Roux, D. and Prost, J., (1989) Phys. Rev. Lett. 62, 276.ADSCrossRefGoogle Scholar
  10. 10.
    de Gennes, P.G. and Prost, J., (1992) Physics of Liquid Crystals, 2nd ed., Clarendon Press, Oxford.Google Scholar
  11. 11.
    Lubensky, T.C. (1972) Phys. Rev. A, 6, 452.ADSCrossRefGoogle Scholar
  12. 12.
    Kats, E.I. and Lebedev, V.V. (1993) Fluctuational Effects in the Dynamics of Liquid Crystals. Springer-Verlag, New York, 170pp.Google Scholar
  13. 13.
    Sonin, A.A. (1950) The Surface Physics of Liquid Crystals. Gordon and Breach Publishers, Luxembourg, 180pp.Google Scholar
  14. 14.
    Quilliet, C., Blanc, C. and Kleman, M. (1996) Phys. Rev. Lett., 77, 522.ADSCrossRefGoogle Scholar
  15. 15.
    Lavrentovich, O.D., Quilliet, C. and Kleman, M.,J. (1997) Phys. Chem. B, 101, 420.CrossRefGoogle Scholar
  16. 16.
    Sutton, A.P. and Balluffi, R.W. (1996) Interfaces in Crystalline Materials. Oxford Science Publications, Clarendon Press, 820pp.Google Scholar
  17. 17.
    Durand, G. (1993) Liq. Cryst., 14, 159.CrossRefGoogle Scholar
  18. 18.
    Li, Z. and Lavrentovich, O.D. (1994) Phys. Rev. Lett., 73, 280.ADSCrossRefGoogle Scholar
  19. 19.
    Lavrentovich, O.D. and Yang, D.-K. (1998) Phys. Rev. E, 57, R6269.ADSCrossRefGoogle Scholar
  20. 20.
    Lavrentovich, O.D. (1986) Zh. Eksp. Teor. Fiz., 91, 1666 [(1986) Sov. Phys. JETP, 64, 984.]Google Scholar
  21. 21.
    Fournier, J.B. and Durand, G. (1991) J. Phys. II France, 1, 845.CrossRefGoogle Scholar
  22. 22.
    Friedel, J. (1964) Dislocations. Pergamon press, Oxford.MATHGoogle Scholar
  23. 23.
    Kleman, M. (1983) Points, Lines and Walls. John-Wiley and Sons, New York.Google Scholar
  24. 24.
    Holyst, R. and Oswald, P. (1995) Int. J. Mod. Phys. B, 9, 1515.ADSCrossRefGoogle Scholar
  25. 25.
    de Gennes, P.G. (1972) C. R. Seances Acad. Sci. Ser. B, 275, 939.Google Scholar
  26. 26.
    Maaloum, M., Ausserre, D., Chatenay, D., Coulon, G. and Gallot, Y. (1992) Phys. Rev. Lett. 68, 1575.ADSCrossRefGoogle Scholar
  27. 27.
    Turner, M. S., Maaloum, M., Ausserre, D., Joanny, J-F. and Kunz, M. (1994) J. Phys. II France, 4, 689.CrossRefGoogle Scholar
  28. 28.
    Wethank M. Kleman for the illuminating consultations on the available results about the dislocation structures. See also reference [31] for the discussion of dislocation in materials with small and large rigidity.Google Scholar
  29. 29.
    Ishikawa, T. and Lavrentovich, O.D. (1999) Phys. Rev. E, 60, R5037.ADSCrossRefGoogle Scholar
  30. 30.
    Subacius, D., Shiyanovskii, S.V., Bos, P. and Lavrentovich, O.D. (1997) Appl. Phys. Lett. 71, 3323.ADSCrossRefGoogle Scholar
  31. 31.
    Kleman, M. (1988) Liq. Cryst., 3, 1355.CrossRefGoogle Scholar
  32. 32.
    Williams, C.E. and Kleman, M. (1974) J. Phys. Lett France, 35, L33.Google Scholar
  33. 33.
    Clark, N.A. and Meyer, R.B (1973) Appl. Phys. Lett., 22, 493.ADSCrossRefGoogle Scholar
  34. 34.
    Fukuda, J. and Onuki, A. (1995) J. Phys. II France, 5, 1107.CrossRefGoogle Scholar
  35. 35.
    Ribotta, R. and Durand, G. (1977) J. Physique, 38, 179.CrossRefGoogle Scholar
  36. 36.
    Eq.17 is often written with a coefficient 4√2 instead of 8; we found the coefficient 8 to be correct.Google Scholar
  37. 37.
    Delaye, M., Ribotta, R. and Durand, G. (1973) Phys. Lett. A, 44, 139.ADSCrossRefGoogle Scholar
  38. 38.
    Rondelez, F. (1971) C.R. Acad. Sci. B, 273, 549.Google Scholar
  39. 39.
    Moncton, D. E., Pindak, R., Davey, S.C. and Brown, G. (1982) S., Phys. Rev. Lett., 49, 1865.ADSCrossRefGoogle Scholar
  40. 40.
    Gharbia, M., Cagnon, M. and Durand, G. (1985) J. Phys.Lett. France, 46, L683.Google Scholar
  41. 41.
    Molho, P., Porteseil, J.L., Souche, Y., Gouzerh, J. and Levy, J.C.S. (1987) Appl. Phys. Lett., 61, 4188.Google Scholar
  42. 42.
    Seul, M. and Wolfe, R. (1992) Phys. Rev. A, 46, 7519; (1992) Phys. Rev. Lett., 68, 2460; (1992) Phys. Rev. E, 46, 7519 and 7534.ADSCrossRefGoogle Scholar
  43. 43.
    Elias, F., Flament, C., Bacri, J.-C. and Neveu, S. (1997) J. Phys. I France, 7, 711.CrossRefGoogle Scholar
  44. 44.
    Wang, Z.G. (1994) J. Chem. Phys., 100, 2298.ADSCrossRefGoogle Scholar
  45. 45.
    Cohen, Y., Albalak, R.J., Dair, B.J., Capel, M.S. and Thomas, E.L. (2000) Macromolecules, 33, 6502.ADSCrossRefGoogle Scholar
  46. 46.
    Ishikawa, T. and Lavrentovich, O.D., Technical Reports 10 169pp, ALCOM Symposium Chiral Materials and Applications, February 18-19, 1999; (2001) Phys. Rev. E, 63, 030501 (R).Google Scholar
  47. 47.
    Flament, C., Bacri, J.C., Cebers, A., Elias, F. and Perzynski, R. (1996) Europhys Lett., 34, 225.ADSCrossRefGoogle Scholar
  48. 48.
    Singer, S.J. (1993) Phys. Rev. E, 48, 2796.ADSCrossRefGoogle Scholar
  49. 49.
    Abramowitz, M. and Stegun, I.A. (1965) Handbook of Mathematical Functions. Dover, New York.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • T. Ishikawa
    • 1
  • O. D. Lavrentovich
    • 1
  1. 1.Liquid Crystal Institute and Chemical Physics Interdisciplinary ProgramKent State UniversityKentUSA

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