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Director reorientation and order reconstruction: competing mechanisms in a nematic cell

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Abstract

We propose a model to explore the competition between two mechanisms possibly at work in a nematic liquid crystal confined within a flat cell with strong uniaxial planar conditions on the bounding plates and subject to an external field. To obtain an electric field perpendicular to the plates, a voltage is imposed across the cell; no further assumption is made on the electric potential within the cell, which is therefore calculated together with the nematic texture. The Landau-de Gennes theory of liquid crystals is used to derive the equilibrium nematic order tensor Q. When the voltage applied is low enough, the equilibrium texture is nearly homogeneous. Above a critical voltage, there exist two different possibilities for adjusting the order tensor to the applied field within the cell: plain director reorientation, i.e., the classical Freedericksz transition, and order reconstruction. The former mechanism entails the rotation of the eigenvectors of Q and can be described essentially by the orientation of the ordinary uniaxial nematic director, whilst the latter mechanism implies a significant variation of the eigenvalues of Q within the cell, virtually without any rotation of its eigenvectors, but with the intervention of a wealth of biaxial states. Either mechanism can actually occur, which yields different nematic textures, depending on material parameters, temperature, cell thickness and the applied potential. The equilibrium phase diagram illustrating the prevailing mechanism is constructed for a significant set of parameters.

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References

  1. Schopohl N., Sluckin T.J.: Defect core structure in nematic liquid crystals. Phys. Rev. Lett. 59, 2582–2584 (1987)

    Article  Google Scholar 

  2. Palffy-Muhoray P., Gartland E.C., Kelly J.R.: A new configurational transition in inhomogeneous nematics. Liq. Cryst. 16, 713–718 (1994)

    Article  Google Scholar 

  3. Bisi F., Gartland E.C., Rosso R., Virga E.G.: Order reconstruction in frustrated nematic twist cells. Phys. Rev. E 68, 021707 (2003)

    Article  Google Scholar 

  4. Martinot-Lagarde Ph., Dreyfus-Lambez H., Dozov I.: Biaxial melting of the nematic order under a strong electric field. Phys. Rev. E 67, 015710 (2003)

    Article  Google Scholar 

  5. Barberi R., Ciuchi F., Durand G.E., Iovane M., Sikharulidze D., Sonnet A.M., Virga E.G.: Electric field induced order reconstruction in a nematic cell. Eur. Phys. J. E 13, 61–71 (2004)

    Article  Google Scholar 

  6. Barberi R., Ciuchi F., Lombardo G., Bartolino R., Durand G.E.: Time resolved experimental analysis of the electric field induced biaxial order reconstruction in nematics. Phys. Rev. Lett. 93, 137801 (2004)

    Article  Google Scholar 

  7. Richetti Ph., Moreau L., Barois P., Kékicheff P.: Measurement of the interactions between two ordering surfaces under symmetric and asymmetric boundary conditions. Phys. Rev. E 54, 1749–1762 (1996)

    Article  Google Scholar 

  8. Kočevar K., Blinc R., Muševic I.: Atomic force microscope evidence for the existence of smecticlike surface layers in the isotropic phase of a nematic liquid crystal. Phys. Rev. E 62, R3055–R3058 (2000)

    Article  Google Scholar 

  9. Kočevar K., Muševic I.: Surface-induced nematic and smectic order at a liquid-crystalsilanated-glass interface observed by atomic force spectroscopy and Brewster angle ellipsometry. Phys. Rev. E 65, 021703 (2002)

    Article  Google Scholar 

  10. Zappone, B.: Films nanométriques de cristaux liquides étudiés par mesure de force SFA et AFM. PhD Thesis, University of Bordeaux, France (2004)

  11. Zappone B., Richetti Ph., Barberi R., Bartolino R., Nguyen H.T.: Forces in nematic liquid crystals constrained to the nanometer scale under hybrid anchoring conditions. Phys. Rev. E 71, 041703 (2005)

    Article  Google Scholar 

  12. Bisi F., Virga E.G., Durand G.E.: Nanomechanics of order reconstruction in nematic liquid crystals. Phys. Rev. E 70, 042701 (2004)

    Article  Google Scholar 

  13. Bisi, F., Virga, E.G.: Surface order forces in nematic liquid crystals. In: Calderer, M.C., Terentjev, E.M. (eds.) Modeling of Soft Matter (The IMA Volumes in Mathematics and its Applications, 141), pp. 111–132. Springer, New York (2005)

  14. Mirantsev L.V., Virga E.G.: Molecular dynamics simulation of a nanoscopic nematic twist cell. Phys. Rev. E 76, 021703 (2007)

    Article  Google Scholar 

  15. Ambrožič M., Kralj S., Virga E.G.: Defect-enhanced nematic surface order reconstruction. Phys. Rev. E 75, 031708 (2007)

    Article  MathSciNet  Google Scholar 

  16. Lombardo G., Ayeb H., Ciuchi F., De Santo M.P., Barberi R., Bartolino R., Virga E.G., Durand G.E.: Inhomogeneous bulk nematic order reconstruction. Phys. Rev. E 77, 020702(R) (2008)

    Google Scholar 

  17. Fréedericksz W., Repiewa A.: Theoretisches und Experimentelles zur Frage nach der Natur der anisotropen Flüssigkeiten. Z. Phys. 42, 532–546 (1927)

    Article  Google Scholar 

  18. Fréedericksz W., Zolina V.: Forces causing the orientation of an anisotropic liquid. Trans Faraday Soc. 29, 919–930 (1933)

    Article  Google Scholar 

  19. Zocher, H.: The effect of a magnetic field on the nematic state. Trans Faraday Soc. 29, 945–957 (1933). Also available in: Sluckin, T.J., Dunmur, D.A., Stegemeyer, H.: Crystals that flow, pp. 289–301. Taylor & Francis, London (2004)

  20. Gruler H., Meier G.: Electric field-induced deformations in oriented liquid crystals of the nematic type. Mol. Cryst. Liq. Cryst. 16, 299–310 (1972)

    Article  Google Scholar 

  21. Carr E.F.: Influence of electric fields on the molecular alignment in the liquid crystal p − (Anisalamino)-phenyl Acetate. Mol. Cryst. Liq. Cryst. 7, 253–268 (1969)

    Article  Google Scholar 

  22. Gruler H., Scheffer T.J., Meier G.: Elastic constants of nematic liquid crystals. I. Theory of the normal deformation. Z. Naturforsch 27a, 966–976 (1972)

    Google Scholar 

  23. Bradshaw M.J., Raynes E.P., Bunning J.D., Faber T.E.: The Frank constants of some nematic liquid crystals. J. Phys. (Paris) 46, 1513–1520 (1985)

    Google Scholar 

  24. de Gennes P.G., Prost J.: The Physics of Liquid Crystals. Clarendon Press, Oxford (1993)

    Google Scholar 

  25. Kaiser P., Wieser W., Hess S.: Stability and instability of an uniaxial alignment against biaxial distortions in the isotropic and nematic phases of liquid crystals. J. Non-Equilib. Thermodyn. 17, 153–169 (1992)

    Article  MATH  Google Scholar 

  26. Coles H.: Laser and electric field induced birefringence studies on the cyanobiphenyl homologues. Mol. Cryst. Liq. Cryst. Lett. 49, 67–74 (1978)

    Article  Google Scholar 

  27. Madhusudana N., Pratibha R.: Elasticity and orientational order in some cyanobiphenyls: Part IV. reanalysis of the data. Mol. Cryst. Liq. Cryst. 89, 249–257 (1982)

    Article  Google Scholar 

  28. Ratna B., Shasidhar R.: Dielectric studies on liquid crystals of strong positive dielectric anisotropy. Mol. Cryst. Liq. Cryst. 42, 113–125 (1977)

    Article  Google Scholar 

  29. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P.: Numerical Recipes. The Art of Scientific Computing. Cambridge University Press, Cambridge (2007)

    MATH  Google Scholar 

  30. Dhooge, A., Govaerts, W., Kuznetsov, Yu.A., Mestrom, W., Riet, A.M., Sautois, B.: matcont, http://www.matcont.ugent.be/matcont.html (2004–2008). Accessed 8 May 2008

  31. matlab is a registered trademark of The MathWorks, Inc. http://www.mathworks.com/products/matlab/ (1994–2008) Accessed 8 May 2008

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Authors and Affiliations

  1. Engineering Ceramics Department, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia

    Milan Ambrožič

  2. Dipartimento di Matematica and CNISM, Università di Pavia, via Ferrata 1, 27100, Pavia, Italy

    Fulvio Bisi & Epifanio G. Virga

Authors
  1. Milan Ambrožič
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  2. Fulvio Bisi
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  3. Epifanio G. Virga
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Correspondence to Fulvio Bisi.

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Communicated by S. Roux

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Ambrožič, M., Bisi, F. & Virga, E.G. Director reorientation and order reconstruction: competing mechanisms in a nematic cell. Continuum Mech. Thermodyn. 20, 193–218 (2008). https://doi.org/10.1007/s00161-008-0077-x

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  • DOI: https://doi.org/10.1007/s00161-008-0077-x

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