Defects in Liquid Crystals: Surface and Interfacial Anchoring Effects

  • O. D. Lavrentovich
Conference paper
Part of the NATO Science Series book series (NAII, volume 127)


This review discusses static properties of topological defects, such as line defectsdisclinations and dislocations, point defects — hedgehogs (monopoles) and boojums; focal conic domains and tilt grain boundaries in basic types of liquid crystals: uniaxial and biaxial nematics, cholesterics and smectics. We present the most popular experimental techniques to study defects in soft matter, namely, polarizing microscopy and fluorescence confocal polarizing microscopy. The role of bounding surfaces and the so-called surface anchoring that lifts the degeneracy of the order parameter in stability of defects is discussed. Because of the surface anchoring, the equilibrium state of a bounded liquid crystal might contain topological defects. For example, nematic bubbles nucleating during the first-order phase transition from the isotropic melt, might contain point defects (hedgehogs and boojums) and disclination loops when their size is larger than the anchoring extrapolation length defined by the ratio of the Frank elastic constant of the director curvature and the (polar) anchoring coefficient. Depending on the strength of surface anchoring, an edge dislocation might be expelled from the system with ID positional order or be stabilized in the bulk. Furthermore, focal conic domains play the role of “surface anchoring facets” by providing the necessary orientation of the liquid crystal director at the smectic boundary.


Liquid Crystal Point Defect Edge Dislocation Easy Axis Topological Defect 
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  1. [1]
    Kleman, M. and Lavrentovich, O.D. (2003) Soft Matter Physics: An Introduction. Springer-Verlag, New York.Google Scholar
  2. [2]
    deGennes, P.G., and Prost, J. The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).Google Scholar
  3. [3]
    Chaikin, P.M. and Lubensky, T. (1995) Principles of Condensed Matter Physics. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  4. [4]
    Pieranski, P.and Oswald, P. (2000) Les Cristaux Liquides, Tomes 1 et 2. Gordon and Breach Science Publishers, Paris.Google Scholar
  5. [5]
    Kleman, M. (1983) Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Various Ordered Media. Wiley, Chichester.Google Scholar
  6. [6]
    Kurik, M.V. and Lavrentovich, O.D. (1988) Usp. Fiz. Nauk, 154, 381–431 [Sov.Phys.Usp. 31, 196-224]MathSciNetCrossRefGoogle Scholar
  7. [7]
    Faetti, S., and Palleschi, V. (1984) Phys. Rev. A 30, 3241–3251.Google Scholar
  8. [8]
    Bradshaw, M.J, Raynes, E.P., Bunning, J.D., and Faber, T.E. (1985) J. Physique 46, 1513–1520.Google Scholar
  9. [9]
    Bowick, M.J., Chandar, L., Schiff, E.A., and Srivastava, A.M. (1994) Science 263, 943–945.Google Scholar
  10. [10]
    Chuang, I., Durrer, R., Turok, N., and Yurke, B. (1991) Science 251, 1336–1342. Yokoyama: Yokoyama, H. (1988) J. Chem. Soc. Faraday Trans. 2, 84, 1023.Google Scholar
  11. [11]
    Lavrentovich, O.D. and Kleman, M. (2001), Ch.5: Cholesteric Liquid Crystals: Defects and Topology, in: Chirality in Liquid Crystals, Bahr, C. and Kitzerow, H. (eds.), Springer-Verlag, New York.Google Scholar
  12. [12]
    Lavrentovich, O.D., Pasini, P., Zannoni, C, and Zumer, S. (editors) (2001 ) Defects in Liquid Crystals: Computer Simulations, Theory and Experiments. Kluwer Academic Publishers, the Netherlands.Google Scholar
  13. Hartshorn, N.H. (1974) The Microscopy of Liquid Crystals. Microscope Publications, London.Google Scholar
  14. [14]
    Smalyukh, I.I., Shiyanovskii, S.V. and Lavrentovich, O.D. (2001) Chem. Phys. Lett., 336, 88–96.ADSCrossRefGoogle Scholar
  15. [15]
    Shiyanovskii, S.V., Smalyukh, I.I., and Lavrentovich, O.D. (2001), see Ref.[12], p. 229–270.Google Scholar
  16. [16]
    See, e.g., R.H. Webb, Rep. Prog. Phys. 59, 427 (1996); W.T. Mason, (ed.) (1999) Fluorescent and Luminescent Probes for Biological Activity: a Practical Guide to Technology for Quantitative Real Time Analysis. Calif.:Academic Press, San Diego; Pawley, J.B. (ed.) (1995) Handbook of Biological Confocal Microscopy. Plenum Press, New York.ADSCrossRefGoogle Scholar
  17. [17]
    Smalyukh, I.I., and Lavrentovich, O.D. (2003) Phys. Rev. Lett., 90, 085503ADSCrossRefGoogle Scholar
  18. [18]
    Toulouse, G. and Kleman, M. (1976) J. Phys. lett. (Paris) 37, L-149–151; Kleman, M. (1977) J. Phys. Lett. (Paris) 38, L-199; Kleman M. and Michel L. ( 1978) Phys. Rev. Lett. 40, 1387.CrossRefGoogle Scholar
  19. [19]
    Volovik, G.E. and Mineev, V.P. (1976) Pis’ ma Zh. Eksp. Teor. Fiz. 24, 605 [JETP Lett. 24, 595]; (1977) Zh. Eksper. Teor. Fiz. 72, 2256-2274 [Sov. Phys. JETP 45, 1186-1196].Google Scholar
  20. [20]
    Volovik, G.E. (1978) Pis’ ma Zh. Eksp. Teor. Fiz (USSR) 28, 65–67 [JETP Lett. (USA) 28, 59-61].Google Scholar
  21. [21]
    Volovik, G.E. and Lavrentovich, O.D. (1983) Zh. Eksper. Teor. Fiz.(USSR) 85, 1997 (1983) [Sov.Phys.JETP (USA) 58, 1159 (1983)]Google Scholar
  22. [22]
    Toulouse, G. (1977) J. Phys. Lett. (Paris) 3, L-67-L-68.Google Scholar
  23. [23]
    Chiccoli, C, Feruli, I., Lavrentovich, O.D., Pasini, P., Shiyanovskii, S.V., Zannoni, C. (2002) Phys. Rev. E 66, 030701R.ADSCrossRefGoogle Scholar
  24. [24]
    Madhusudana, N.V. and Pratibha, R. (1983) Mol. Cryst.Liq.Cryst. 103, 31–47.CrossRefGoogle Scholar
  25. [25]
    Lavrentovich, O.D. and Nastishin, Yu.A. (1990) Europhys. Lett. 12, 135–141.ADSCrossRefGoogle Scholar
  26. [26]
    Frank, F.C. (1958) On the theory of liquid crystals, Disc. Faraday Soc. 25, 19–28.CrossRefGoogle Scholar
  27. [27]
    Anisimov S.I. and Dzyaloshinskii, I.E. (1972) Zh. Eksp. Teor. Fiz. 63, 1460–1471 [Sov. Phys. JETP 36, 774-783].Google Scholar
  28. [28]
    Cladis, P.E. and Kleman M. (1972) J. Physique (Paris) 33, 591.CrossRefGoogle Scholar
  29. [29]
    Meyer, R.B. ( 1973) Phil. Mag. 27,405–424.ADSCrossRefGoogle Scholar
  30. [30]
    Mori, H. and Nakanishi, H. (1988) J. Phys. Soc. Japan 57, 1281.ADSCrossRefGoogle Scholar
  31. [31]
    Lavrentovich, O.D., Ishikawa T., and Terentjev, E.M. (1997) Mol. Cryst. Liq. Cryst. 299, 301.CrossRefGoogle Scholar
  32. [32]
    Ishikawa, T. and Lavrentovich, O.D. (1998) Europhys. Lett. 41, 171–176.ADSCrossRefGoogle Scholar
  33. [33]
    Lavrentovich, O.D. (1992) Phys. Rev. A 46, R722–725.ADSCrossRefGoogle Scholar
  34. [34]
    Lavrentovich, O.D. (1998) Liq. Cryst. 24, 117–125.CrossRefGoogle Scholar
  35. [35]
    Poulin, P. Stark, H., Lubensky, T.C., and Weitz, D.A. (1997) Science 275, 1770–1773.CrossRefGoogle Scholar
  36. [36]
    Nastishin, Yu.A., Polak, R.D., Shiyanovskii, S.V., Bodnar, V.H. and Lavrentovich, O.D. (1999) J. Appl. Phys. 86, 4199.ADSCrossRefGoogle Scholar
  37. [37]
    Rapini, A. and Papoular, M. (1969) /. Phys. (Paris) Colloq. 30, C-4.Google Scholar
  38. [38]
    Shiyanovskii, S.V., Glushchenko, A., Reznikov, Yu., Lavrentovich, O.D. and West, J.L.(2000) Phys. Rev. E, 62, R1477.Google Scholar
  39. [39]
    Kurik, M.V., and Lavrentovich, O.D. (1983) Zh. Eksp. Teor. Fiz. 85, 511–526 [Sov.Phys. JETP 58, 299-307]Google Scholar
  40. [40]
    Yokoyama, H. (1988) J. Chem. Soc. Faraday Trans. 2, 84, 1023.Google Scholar
  41. [41]
    Pershan, P.S. (1974) J. Appl. Phys. 45, 1590.ADSCrossRefGoogle Scholar
  42. [42]
    Holyst, R. and Oswald, P. (1995) Int. J. Mod. Phys. B 9, 1515.ADSCrossRefGoogle Scholar
  43. [43]
    Brener, E. A. and Marchenko, V.I. (1999) Phys. Rev. E 59, R4752.MathSciNetADSCrossRefGoogle Scholar
  44. [44]
    Ishikawa, T., and Lavrentovich, O.D. (1999) Phys. Rev. E 60, R5037.ADSCrossRefGoogle Scholar
  45. [45]
    Kleman, M., and Friedel, J. (1969) J. Physique Colloq. 30, C4–43.Google Scholar
  46. [46]
    Smalyukh, I.I., and Lavrentovich, O.D., (2002) Phys. Rev. E 66, 051703.ADSCrossRefGoogle Scholar
  47. [47]
    Lubensky, T. C. (1972) Phys. Rev. A 6, 452.ADSCrossRefGoogle Scholar
  48. [48]
    E.I. Kats and V.V. Lebedev, Fluctuational Effects in the Dynamics of Liquid Crystals, (Springer-Verlag, New York, 1994), Chapter 5, p. 170.CrossRefGoogle Scholar
  49. [49]
    The result is obtained by collecting the terms with (t x curlt)2, (divt)2, etc., and neglecting the divergence (surface-like) terms in Eqs. (5.1.27, 33) of Ref.[48].Google Scholar
  50. [50]
    Ishikawa, T. and Lavrentovich, O.D. (2001) Phys. Rev. E 63, R030501.ADSCrossRefGoogle Scholar
  51. [51]
    Lavrentovich, O.D. and Yang, D.-K. (1998) Phys. Rev. E 57, R6269.ADSCrossRefGoogle Scholar
  52. [52]
    Lavrentovich, O.D. (1986) Zh. Eksp. Teor. Fiz. 91, 1666–1676 [Sov.Phys. JETP 64, 984-990]Google Scholar
  53. [53]
    Kleman, M. and Lavrentovich, O.D. (2000) Eur. Phys. J E 2, 47–57.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

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

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