Skip to main content
SpringerLink
Log in

Defects in Liquid Crystals: Surface and Interfacial Anchoring Effects

  • Conference paper
Patterns of Symmetry Breaking

Part of the book series: NATO Science Series ((NAII,volume 127))

Abstract

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.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kleman, M. and Lavrentovich, O.D. (2003) Soft Matter Physics: An Introduction. Springer-Verlag, New York.

    Google Scholar 

  2. deGennes, P.G., and Prost, J. The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).

    Google Scholar 

  3. Chaikin, P.M. and Lubensky, T. (1995) Principles of Condensed Matter Physics. Cambridge University Press, Cambridge.

    Book  Google Scholar 

  4. Pieranski, P.and Oswald, P. (2000) Les Cristaux Liquides, Tomes 1 et 2. Gordon and Breach Science Publishers, Paris.

    Google Scholar 

  5. Kleman, M. (1983) Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Various Ordered Media. Wiley, Chichester.

    Google Scholar 

  6. Kurik, M.V. and Lavrentovich, O.D. (1988) Usp. Fiz. Nauk, 154, 381–431 [Sov.Phys.Usp. 31, 196-224]

    Article  MathSciNet  Google Scholar 

  7. Faetti, S., and Palleschi, V. (1984) Phys. Rev. A 30, 3241–3251.

    Google Scholar 

  8. Bradshaw, M.J, Raynes, E.P., Bunning, J.D., and Faber, T.E. (1985) J. Physique 46, 1513–1520.

    Google Scholar 

  9. Bowick, M.J., Chandar, L., Schiff, E.A., and Srivastava, A.M. (1994) Science 263, 943–945.

    Google Scholar 

  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. 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. 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. Smalyukh, I.I., Shiyanovskii, S.V. and Lavrentovich, O.D. (2001) Chem. Phys. Lett., 336, 88–96.

    Article  ADS  Google Scholar 

  15. Shiyanovskii, S.V., Smalyukh, I.I., and Lavrentovich, O.D. (2001), see Ref.[12], p. 229–270.

    Google Scholar 

  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.

    Article  ADS  Google Scholar 

  17. Smalyukh, I.I., and Lavrentovich, O.D. (2003) Phys. Rev. Lett., 90, 085503

    Article  ADS  Google Scholar 

  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.

    Article  Google Scholar 

  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. Volovik, G.E. (1978) Pis’ ma Zh. Eksp. Teor. Fiz (USSR) 28, 65–67 [JETP Lett. (USA) 28, 59-61].

    Google Scholar 

  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. Toulouse, G. (1977) J. Phys. Lett. (Paris) 3, L-67-L-68.

    Google Scholar 

  23. Chiccoli, C, Feruli, I., Lavrentovich, O.D., Pasini, P., Shiyanovskii, S.V., Zannoni, C. (2002) Phys. Rev. E 66, 030701R.

    Article  ADS  Google Scholar 

  24. Madhusudana, N.V. and Pratibha, R. (1983) Mol. Cryst.Liq.Cryst. 103, 31–47.

    Article  Google Scholar 

  25. Lavrentovich, O.D. and Nastishin, Yu.A. (1990) Europhys. Lett. 12, 135–141.

    Article  ADS  Google Scholar 

  26. Frank, F.C. (1958) On the theory of liquid crystals, Disc. Faraday Soc. 25, 19–28.

    Article  Google Scholar 

  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. Cladis, P.E. and Kleman M. (1972) J. Physique (Paris) 33, 591.

    Article  Google Scholar 

  29. Meyer, R.B. ( 1973) Phil. Mag. 27,405–424.

    Article  ADS  Google Scholar 

  30. Mori, H. and Nakanishi, H. (1988) J. Phys. Soc. Japan 57, 1281.

    Article  ADS  Google Scholar 

  31. Lavrentovich, O.D., Ishikawa T., and Terentjev, E.M. (1997) Mol. Cryst. Liq. Cryst. 299, 301.

    Article  Google Scholar 

  32. Ishikawa, T. and Lavrentovich, O.D. (1998) Europhys. Lett. 41, 171–176.

    Article  ADS  Google Scholar 

  33. Lavrentovich, O.D. (1992) Phys. Rev. A 46, R722–725.

    Article  ADS  Google Scholar 

  34. Lavrentovich, O.D. (1998) Liq. Cryst. 24, 117–125.

    Article  Google Scholar 

  35. Poulin, P. Stark, H., Lubensky, T.C., and Weitz, D.A. (1997) Science 275, 1770–1773.

    Article  Google Scholar 

  36. Nastishin, Yu.A., Polak, R.D., Shiyanovskii, S.V., Bodnar, V.H. and Lavrentovich, O.D. (1999) J. Appl. Phys. 86, 4199.

    Article  ADS  Google Scholar 

  37. Rapini, A. and Papoular, M. (1969) /. Phys. (Paris) Colloq. 30, C-4.

    Google Scholar 

  38. Shiyanovskii, S.V., Glushchenko, A., Reznikov, Yu., Lavrentovich, O.D. and West, J.L.(2000) Phys. Rev. E, 62, R1477.

    Google Scholar 

  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. Yokoyama, H. (1988) J. Chem. Soc. Faraday Trans. 2, 84, 1023.

    Google Scholar 

  41. Pershan, P.S. (1974) J. Appl. Phys. 45, 1590.

    Article  ADS  Google Scholar 

  42. Holyst, R. and Oswald, P. (1995) Int. J. Mod. Phys. B 9, 1515.

    Article  ADS  Google Scholar 

  43. Brener, E. A. and Marchenko, V.I. (1999) Phys. Rev. E 59, R4752.

    Article  MathSciNet  ADS  Google Scholar 

  44. Ishikawa, T., and Lavrentovich, O.D. (1999) Phys. Rev. E 60, R5037.

    Article  ADS  Google Scholar 

  45. Kleman, M., and Friedel, J. (1969) J. Physique Colloq. 30, C4–43.

    Google Scholar 

  46. Smalyukh, I.I., and Lavrentovich, O.D., (2002) Phys. Rev. E 66, 051703.

    Article  ADS  Google Scholar 

  47. Lubensky, T. C. (1972) Phys. Rev. A 6, 452.

    Article  ADS  Google Scholar 

  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.

    Book  Google Scholar 

  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. Ishikawa, T. and Lavrentovich, O.D. (2001) Phys. Rev. E 63, R030501.

    Article  ADS  Google Scholar 

  51. Lavrentovich, O.D. and Yang, D.-K. (1998) Phys. Rev. E 57, R6269.

    Article  ADS  Google Scholar 

  52. Lavrentovich, O.D. (1986) Zh. Eksp. Teor. Fiz. 91, 1666–1676 [Sov.Phys. JETP 64, 984-990]

    Google Scholar 

  53. Kleman, M. and Lavrentovich, O.D. (2000) Eur. Phys. J E 2, 47–57.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA

    O. D. Lavrentovich

Authors
  1. O. D. Lavrentovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Jagiellonian University, Cracow, Poland

    Henryk Arodz  & Jacek Dziarmaga  & 

  2. Los Alamos National Laboratory, Los Alamos, USA

    Wojciech Hubert Zurek

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Lavrentovich, O.D. (2003). Defects in Liquid Crystals: Surface and Interfacial Anchoring Effects. In: Arodz, H., Dziarmaga, J., Zurek, W.H. (eds) Patterns of Symmetry Breaking. NATO Science Series, vol 127. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1029-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-1029-0_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1745-2

  • Online ISBN: 978-94-007-1029-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation