Skip to main content
SpringerLink
Log in

Analytical description of 2D magnetic Freedericksz transition in a rectangular cell of a nematic liquid crystal

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

We study the Freedericksz transition induced by a magnetic field in a rectangular cell filled with a nematic liquid crystal. In the initial state the director of the nematic liquid crystal is uniformly aligned in the cross section plane of the cell with rigid anchoring of the director at cell walls: planar on the top and bottom walls, and homeotropic on the left and right ones. The magnetic field is directed perpendicular to the cell cross section plane. We consider two-dimensional (2D) orientational deformations of the nematic liquid crystal in the rectangular cell and determine the critical value of the Freedericksz transition field above which these orientational deformations occur. The 2D expression for the director alignment profile above the threshold of Freedericksz transition is analytically found and the profile shapes as functions of cell sizes, values of the Frank elastic constants of the nematic liquid crystal and the magnetic field are studied.

Graphical abstract

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I.W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction (Taylor & Francis, London, 2004)

  2. V.G. Chigrinov, V.M. Kozenkov, H.S. Kwok, Photoalignment of Liquid Crystalline Materials: Physics and Applications (Wiley, New York, 2008)

  3. L.M. Blinov, Structure and Properties of Liquid Crystals (Springer, London, 2011)

  4. D-K. Yang, S-T. Wu, Fundamentals of liquid crystal devices (John Wiley & Sons, New York, 2006)

  5. G.P. Crawford, S. Zumer (Editors), Liquid crystals in complex geometries: formed by polymer and porous networks (Taylor & Francis, London, 1996)

  6. E.L. Aero, J. Appl. Math. Mech. 60, 75 (1996)

    Article  MathSciNet  Google Scholar 

  7. S.V. Burylov, JETP 85, 873 (1997)

    Article  ADS  Google Scholar 

  8. S.V. Burylov, Zh. Eksp. Teor. Phys. 112, 1603 (1997)

    Google Scholar 

  9. S.V. Burylov, Ukr. J. Phys. 42, 1219 (1997)

    Google Scholar 

  10. S.W. Leonard, J.P. Mondia, H.M. van Driel, O. Toader, S. John, K. Busch, V. Lehmann, Phys. Rev. B 61, R2389 (2000)

    Article  ADS  Google Scholar 

  11. A.H. Lewis, I. Garlea, J. Alvarado, O.J. Dammone, P.D. Howell, A. Majumdar, B.M. Mulder, M.P. Lettinga, G.H. Koenderink, D.G.A.L. Aarts, Soft Matter 10, 7865 (2014)

    Article  ADS  Google Scholar 

  12. D.C. Zografopoulos, E.E. Kriezis, T.D. Tsiboukis, J. Lightwave Technol. 24, 3427 (2006)

    Article  ADS  Google Scholar 

  13. I.C. Garlea, B.M. Mulder, Soft Matter 11, 608 (2015)

    Article  ADS  Google Scholar 

  14. S. Kralj, A. Majumdar, Proc. R. Soc. A 470, 20140276 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  15. M. González-Pinto, Y. Martínez-Ratón, E. Velasco, Phys. Rev. E 88, 032506 (2013)

    Article  ADS  Google Scholar 

  16. T. Geigenfeind, S. Rosenzweig, M. Schmidt, D. de las Heras, J. Chem. Phys. 142, 174701 (2015)

    Article  ADS  Google Scholar 

  17. N. Éber, J. Heuer, R. Stannarius, G. Tátrai, Á. Buka, Phys. Rev. E 81, 051702 (2010)

    Article  ADS  Google Scholar 

  18. D. de las Heras, L. Mederos, E. Velasco, Liq. Cryst. 37, 45 (2009)

    Article  Google Scholar 

  19. D. de las Heras, E.Velasco, Soft Matter 10, 1758 (2014)

    Article  ADS  Google Scholar 

  20. A. Lorenz, H.-S. Kitzerow, A. Schwuchow, J. Kobelke, H. Bartelt, Opt. Express 16, 19375 (2008)

    Article  ADS  Google Scholar 

  21. M. Wahle, H.S. Kitzerow, Appl. Phys. Lett. 107, 201114 (2015)

    Article  ADS  Google Scholar 

  22. A.J. Davidson, N.J. Mottram, Eur. J. Appl. Math. 23, 99 (2012)

    Article  MathSciNet  Google Scholar 

  23. R.M.W. van Bijnen, R.H.J. Otten, P. van der Schoot, Phys. Rev. E 86, 051703 (2012)

    Article  ADS  Google Scholar 

  24. D.C. Zografopoulos, R. Beccherelli, E.E. Kriezis, Phys. Rev. E 90, 042503 (2014)

    Article  ADS  Google Scholar 

  25. S.V. Burylov, Ukr. J. Phys. 54, 1094 (2009)

    Google Scholar 

  26. S. Zhou, Y.A. Nastishin, M.M. Omelchenko, L. Tortora, V.G. Nazarenko, O.P. Boiko, T. Ostapenko, T. Hu, C.C. Almasan, S.N. Sprunt, J.T. Gleeson, O.D. Lavrentovich, Phys. Rev. Lett. 109, 037801 (2012)

    Article  ADS  Google Scholar 

  27. S. Zhou, K. Neupane, Y.A. Nastishin, A.R. Baldwin, S.V. Shiyanovskii, O.D. Lavrentovich, S. Sprunt, Soft Matter 10, 6571 (2014)

    Article  Google Scholar 

  28. J. Jeong, L. Kang, Z.S. Davidson, P.J. Collings, T.C. Lubensky, A.G. Yodh, Proc. Nat. Acad. Sci. U.S.A. 112, E1837 (2015)

    Article  ADS  Google Scholar 

  29. J.L. Lamb, jr., Elements of Soliton Theory (John Wiley & Sons, New York, 1980)

  30. E. Jahnke, F. Emde, F. Lösch, Tafeln höherer Funktionen (B.G. Teubnër Verlagsgesellschaft, Stuttgart, 1960)

Download references

Author information

Authors and Affiliations

  1. Institute of Transport Systems and Technologies, Ukrainian National Academy of Science, 5 Pisargevsky St., 49005, Dnepropetrovsk, Ukraine

    S. V. Burylov

  2. Physics of Phase Transitions Department, Perm State University, 15 Bukirev St., 614990, Perm, Russia

    A. N. Zakhlevnykh

Authors
  1. S. V. Burylov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Zakhlevnykh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Burylov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Burylov, S.V., Zakhlevnykh, A.N. Analytical description of 2D magnetic Freedericksz transition in a rectangular cell of a nematic liquid crystal. Eur. Phys. J. E 39, 65 (2016). https://doi.org/10.1140/epje/i2016-16065-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2016-16065-x

Keywords

Search

Navigation