Parity of the weak Fréedericksz transition

  • Giuseppe Bevilacqua
  • Gaetano NapoliEmail author
Regular Article


Motivated by the recent experimental findings by Kumar et al. (Phys. Rev. E., 82, 011701 (2010)) in which the inverse Fréedericksz transition is observed, we have theoretically investigated the parity and the stability of the equilibrium configurations of a Fréedericksz cell with weak planar boundary conditions. Within the one-constant approximation of the Frank theory, the bulk equilibrium equation reduces to the nonlinear pendulum equation. Its solutions, when combined with boundary conditions deriving by the energy anchoring, lose uniqueness, exhibiting various symmetries. Thus, at a given anchoring strength and applied field, the cell becomes a system with metastable discrete energy levels. Our analysis proposes an explanation of the experimental results.

Graphical abstract


Soft Matter: Liquid crystals 


  1. 1.
    P.-G. de Gennes, J. Prost, The physics of liquid crystals (Oxford University Press, 1995)Google Scholar
  2. 2.
    E.G. Virga, Variational Theories For Liquid Crystals (Chapman-Hall, London, 1994)Google Scholar
  3. 3.
    G. Napoli, J. Phys. A: Math. Gen. 39, 11 (2006)CrossRefADSGoogle Scholar
  4. 4.
    F.P. da Costa, M. Grinfeld, N.J. Mottram, J.T. Pinto, J. Differ. Equ. 246, 2590 (2009)CrossRefADSGoogle Scholar
  5. 5.
    T.A. Kumar, P. Sathyanarayana, V.S.S. Sastry, H. Takezoe, N.V. Madhusudana, S. Dhara, Phys. Rev. E 82, 011701 (2010)CrossRefADSGoogle Scholar
  6. 6.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1964)Google Scholar
  7. 7.
    G. Barbero, L.R. Evangelista, An Elementary Course on the Continuum Theory for Nematic Liquid Crystals (World Scientific, 2001)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.CNISM and Dipartimento di FisicaUniversità di SienaSienaItaly
  2. 2.Dipartimento di Ingegneria dell’InnovazioneUniversità del SalentoLecceItaly

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