Strongly nonlinear dynamics of ferroelectric liquid crystals

Open Access
Regular Article

Abstract

Molecular reorientation processes induced in thin ferroelectric liquid crystal systems by strong alternating external electric fields are studied both by solving numerically the equation of reorientation motion of molecules and by measuring the electro-optic response of thin samples. It is shown that the occurrence of a wide band in nonlinear response spectra above the Goldstone-mode frequency is a consequence of complex partially uncorrelated molecular reorientations enforced within smectic layers by sufficiently high fields of high enough frequencies. Such nonlinear reorientational motions of molecules are argued to have a character of weakly chaotic long-lasting transients, related to almost periodic modulations of the amplitude of rotational oscillations performed by molecules with the field frequency. These modulations have been numerically proved to proceed with lower frequencies than the field frequency and with space-dependent depths of temporal changes. The occurrence of the modulations has experimentally been confirmed by registering distinct contributions to electro-optic response spectra at frequencies less than the running frequency of the applied electric field.

Graphical abstract

Keywords

Soft Matter: Liquid crystals 

References

  1. 1.
    J.R. Lalanne, J. Buchert, S. Kielich, in Modern Nonlinear Optics, Part 1, edited by M. Evans, S. Kielich (Wiley, New York, 1993).Google Scholar
  2. 2.
    M. Buscalia, T. Bellini, V. Degiorgio, F. Mantegazza, F. Simoni, Europhys. Lett. 48, 634 (1999).ADSCrossRefGoogle Scholar
  3. 3.
    G. Russo, V. Carbone, G. Cipparrone, Phys. Rev. E 62, 5036 (2000).ADSCrossRefGoogle Scholar
  4. 4.
    G. Cipparrone, G. Russo, C. Versace, G. Strangi, V. Carbone, Opt. Commun. 173, 1 (2000).ADSCrossRefGoogle Scholar
  5. 5.
    Y. Kimura, H. Isono, R. Hayakawa, Eur. Phys. J. E 9, 3 (2002).Google Scholar
  6. 6.
    S.M. Morris, A.D. Ford, M.N. Pivnenko, H.J. Coles, J. Opt. A 7, 215 (2005).ADSCrossRefGoogle Scholar
  7. 7.
    B. Piccirillo, A. Vella, A. Setaro, E. Santamato, Phys. Rev. E 73, 062701 (2006).ADSCrossRefGoogle Scholar
  8. 8.
    L. Lucchetti, M. Gentili, F. Simoni, S. Pavliuchenko, S. Subota, V. Reshetnyak, Phys. Rev. E 78, 061706 (2008).ADSCrossRefGoogle Scholar
  9. 9.
    S.T. Lagerwall, Ferroelectric and Antiferroelectric Liquid Crystals (Wiley-VCH, Weinheim, 1999). .Google Scholar
  10. 10.
    L. Lam, Z.C. Ou-Yang, M. Lax, Phys. Rev. A 37, 3469 (1988).ADSCrossRefGoogle Scholar
  11. 11.
    H. Orihara, A. Fukase, S. Izumi, Y. Ishibashi, Ferroelectrics 147, 411 (1993).CrossRefGoogle Scholar
  12. 12.
    Y. Ishibashi, H. Orihara, Frerroelectrics 156, 185 (1994).CrossRefGoogle Scholar
  13. 13.
    H. Orihara, Y. Isibashi, J. Phys. Soc. Jpn. 64, 3775 (1995).ADSCrossRefGoogle Scholar
  14. 14.
    Y. Ishibashi, H. Orihara, Physica B 219-220, 626 (1996).Google Scholar
  15. 15.
    G. Demeter, L. Kramer, Phys. Rev. Lett. 83, 4744 (1999).ADSCrossRefGoogle Scholar
  16. 16.
    Y. Kimura, S. Hara, R. Hayakawa, Ferroelectrics 245, 61 (2000).CrossRefGoogle Scholar
  17. 17.
    Y. Kimura, S. Hara, R. Hayakawa, Phys. Rev. E 62, R5907 (2000).ADSCrossRefGoogle Scholar
  18. 18.
    T.D. Frank, Phys. Rev. E 72, 041703 (2005).ADSCrossRefGoogle Scholar
  19. 19.
    J.M. Leblond, R. Douali, C. Legrand, R. Dabrowski, Eur. Phys. J. Appl. Phys. 36, 157 (2006).ADSCrossRefGoogle Scholar
  20. 20.
    C. Thibierge, D. L’ote, F. Ladieu, R. Tourbot, Rev. Sci. Instrum. 79, 103905 (2008).ADSCrossRefGoogle Scholar
  21. 21.
    N.A. Clark, S.T. Lagerwall, in Ferroelectric Liquid Crystals, Principles, Properties and Applications, edited by J.W. Goodbye, R. Blinc, N.A. Clark, S.T. Lagerwall, M.A. Osipov, S.A. Pikin, T. Sakurai, K. Yoshino, B. Žekš (Gordon and Breach, Philadelphia, 1991).Google Scholar
  22. 22.
    W. Jezewski, W. Kuczyński, J. Hoffmann, Phys. Rev. E 83, 042701 (2011).ADSCrossRefGoogle Scholar
  23. 23.
    R.E. Amritkar, N. Gupte, Phys. Rev. A 44, R3403 (1991).ADSCrossRefGoogle Scholar
  24. 24.
    M.D. LaMar, G.D. Smith, Phys. Rev. E 2010 81, 046206 (2010).MathSciNetCrossRefGoogle Scholar
  25. 25.
    W. Kuczyński, J. Hoffmann, J. Małecki, Ferroelectrics 150, 279 (1993).CrossRefGoogle Scholar
  26. 26.
    W. Jezewski, W. Kuczyński, J. Hoffmann, Liq. Cryst. 34, 1299 (2007).CrossRefGoogle Scholar
  27. 27.
    W. Jezewski, W. Kuczyński, J. Hoffmann, Phys. Rev. E 73, 061702 (2006).ADSCrossRefGoogle Scholar
  28. 28.
    W. Jezewski, W. Kuczyński, J. Hoffmann, Phys. Rev. B 77, 094101 (2008).ADSCrossRefGoogle Scholar
  29. 29.
    W. Jezewski, W. Kuczyński, Phys. Rev. B 79, 214206 (2009).ADSCrossRefGoogle Scholar
  30. 30.
    M.A. Handschy, N.A. Clark, S.T. Lagerwall, Phys. Rev. Lett. 51, 471 (1983).ADSCrossRefGoogle Scholar
  31. 31.
    J.E. Maclennan, M.A. Handschy, N.A. Clark, Liq. Cryst. 7, 787 (1990).CrossRefGoogle Scholar
  32. 32.
    P.J. Davies, I. Polonsky, in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by M. Abramowitz, I.A. Stegun (Dover, New York, 1972) p. 896.Google Scholar
  33. 33.
    E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993).Google Scholar
  34. 34.
    R.C.L. Wolf, J. R. Stat. Soc. B 54, 353 (1992).Google Scholar
  35. 35.
    F. Ali, M. Menzinger, Chaos 9, 348 (1999).MathSciNetADSCrossRefMATHGoogle Scholar
  36. 36.
    A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985).MathSciNetADSCrossRefMATHGoogle Scholar
  37. 37.
    G.M. Zaslavsky, R.Z. Sagdeev, D.A. Usikov, A.A. Chernikov, Weak Chaos and Quasi-Regular Patterns (Cambridge University Press, Cambridge, 1991).Google Scholar
  38. 38.
    R.C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, Oxford, 2000).Google Scholar
  39. 39.
    I.W. Stewart, T. Carlsson, F.M. Leslie, Ferroelectrics 148, 41 (1993).CrossRefGoogle Scholar
  40. 40.
    H. Katz, P. Grassberger, Physica D 17, 75 (1985).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.Institute of Molecular PhysicsPolish Academy of SciencesPoznańPoland

Personalised recommendations