Skip to main content
SpringerLink
Log in

Surface Order Forces in Nematic Liquid Crystals

  • Chapter
Modeling of Soft Matter

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 141))

Abstract

The notion of surface order force in nematic liquid crystals is presented and contrasted with the notions of similar forces already introduced in the literature. We illustrate how a surface order force could in principle be measured and how it would convey the mechanical signature of an intrinsically nanoscopic phenomenon, often referred to as order reconstruction. The relationship between this force and the occurrence of biaxial states of the nematic order tensor is further illuminated.

This work has been partially funded by the Institute for Mathematics and its Applications (IMA).

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. R.G. Horn, J.N. Israelaschvili, and E. Perez, J. Phys. (Prance), 42, 39 (1981).

    Google Scholar 

  2. B.W. Ninham, J. Chem. Phys. 84, 1423 (1980).

    Article  Google Scholar 

  3. W. Maier and A. Saupe, Z. Naturforsch., 14a, 882 (1959).

    Google Scholar 

  4. C.W, Oseen, Trans. Faraday Soc., 29, 883 (1939).

    Article  Google Scholar 

  5. F.C. Frank, Discuss. Faraday Soc., 25, 19 (1958).

    Article  Google Scholar 

  6. H. Schröder, J. Chem. Phys. 67, 16 (1977).

    Article  Google Scholar 

  7. P. Sheng, Phys. Rev. Lett. 37, 1059 (1976).

    Article  Google Scholar 

  8. P. Richetti, L. Moreau, P. Barois, and P. Kékicheff, Phys. Rev E 54, 1749 (1996).

    Article  Google Scholar 

  9. K. Kočevar, R. Blinc, and I. Muševic, Phys. Rev. E 62, R3055 (2000).

    Article  Google Scholar 

  10. K. Kočevar and I. Muševic, Phys. Rev. E 65, 021703 (2002).

    Article  Google Scholar 

  11. B. Zappone, Films nanométriques de cristeaux liquides étudiés par mesure de force SFA et AFM, PhD. Thesis, University of Bordeaux, Prance (2004).

    Google Scholar 

  12. F. Bisi, E.G. Virga, and G.E. Durand, Phys. Rev. E 70, 042701 (2004).

    Article  Google Scholar 

  13. N. Schopohl and T.J. Sluckin, Phys. Rev. Lett. 59, 2582 (1987).

    Article  Google Scholar 

  14. P. Palffy-Muhoray, E.G. Gartland, and J. R. Kelly, Liq. Cryst. 16, 713 (1994).

    Article  Google Scholar 

  15. P.G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford 1993), pp. 56–57.

    Google Scholar 

  16. P. Kaiser, N. Wiese, and S. Hess, J. Non-Equilib. Themodyn. 17, 153 (1992).

    Article  MATH  Google Scholar 

  17. F. Bisi, E.G. Gartland, R. Rosso, and E.G. Virga, Phys. Rev. E 68, 021707 (2003).

    Article  Google Scholar 

  18. S. Kralj, E. G. Virga, and S. Žumer, Phys. Rev. E 60, 1858 (1999).

    Article  Google Scholar 

  19. H.J. Coles, Mol. Cryst. Liq. Cryst. Lett. 49, 67 (1978).

    Article  Google Scholar 

  20. R. Barberi, F. Ciuchi, G.E. Durand, M. Iovane, D. Sikharulidze, A.M. Sonnet, and E.G. virga, Eur. Phys. J. E 13, 61 (2004).

    Article  Google Scholar 

  21. K. Miyano, Phys. Rev. Lett. 43, 51 (1979).

    Article  Google Scholar 

  22. E.G. Gartland and E.G. Virga, in preparation (2005).

    Google Scholar 

  23. J. L. Ericksen, Arch. Rational Mech. Anal. 9, 371 (1962).

    MATH  MathSciNet  Google Scholar 

  24. A.M. Sonnet, P.L. Maffettone, and E.G. Virga, J. Non-Newtonian Fluid Mech. 119, 51 (2004).

    Article  MATH  Google Scholar 

  25. MATLAB is a registered trademark of The MathWorks, Inc. http://www.mathworks.com.

    Google Scholar 

  26. See http://sourceforge.net/projects/auto2000.

    Google Scholar 

  27. J.N. Israelaschvili and D. Tabor, Proc. R. Soc. London A, 331, 19 (1972).

    Article  Google Scholar 

  28. J.N. Israelaschvili and G.E. Adams, J. Chem. Soc. Faraday TVans. I 74, 975 (1978).

    Article  Google Scholar 

  29. J.N. Israelaschvili, Intermolecular and surface forces (Academic Press, London, 1992).

    Google Scholar 

  30. G. Barbero, Z. Gabbasova, and M. A. Osipov, J. Phys. II 1, 691 (1991).

    Article  Google Scholar 

  31. M.A. Osipov and S. Hess, J. Chem. Phys. 99(5), 4181 (1993).

    Article  Google Scholar 

  32. M. Cagnon and G. Durand, Phys. Rev. Lett. 73, 3556 (1993).

    Google Scholar 

  33. J.S. Foster and J. E. Frommer, Nature (London) 333, 542 (1988).

    Article  Google Scholar 

  34. J.K. Spong, H. M. Mizes, J. R. L. J. Lacomb, M. M. Dovek, J.E. Frommer, and J.S. Foster, Nature (London) 338, 137 (1989).

    Article  Google Scholar 

  35. D.P.E. Smith, J. K. H. Hörber, G. Binnig, and N. Nejoh, Nature (London) 344, 641 (1990).

    Article  Google Scholar 

  36. B. Jérôme, Rep. Prog. Phys. 54, 391 (1991).

    Article  Google Scholar 

  37. B. Zappone, Ph. Richetti, R. Barberi, R. Bartolino, and H. T. Nguyen, Phys, Rev E 71, 041703 (2005).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Istituto Nazionale di Fisica della Materia, Università di Pavia, via Ferrata 1, 27100, Pavia, Italy

    Fulvio Bisi & Epifanio G. Virga

Authors
  1. Fulvio Bisi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Epifanio G. Virga
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, USA

    Maria-Carme T. Calderer

  2. Cavendish Laboratory, Cambridge University, Cambridge

    Eugene M. Terentjev

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

Bisi, F., Virga, E.G. (2005). Surface Order Forces in Nematic Liquid Crystals. In: Calderer, MC.T., Terentjev, E.M. (eds) Modeling of Soft Matter. The IMA Volumes in Mathematics and its Applications, vol 141. Springer, New York, NY. https://doi.org/10.1007/0-387-32153-5_5

Download citation

Publish with us

Policies and ethics

Search

Navigation