The European Physical Journal E

, Volume 25, Issue 3, pp 277–289 | Cite as

Lehmann effect in a compensated cholesteric liquid crystal: Experimental evidence with fixed and gliding boundary conditions

Regular Article

Abstract.

In a recent letter (Europhys. Lett. 80, 26001 (2007)), we have shown that a compensated cholesteric liquid crystal (in which the macroscopic helix completely unwinds) may be subjected to a thermomechanical torque (the so-called Lehmann effect), in agreement with previous findings of Éber and Jánossy (Mol. Cryst. Liq. Cryst. Lett. 72, 233 (1982)). These results prove that one must take into account the chirality of the molecules and the absence of inversion symmetry at the macroscopic scale when deriving the constitutive equations of the phase at the compensation temperature. In this paper, we present the details of our experimental work and a new experiment performed in a sample treated for planar gliding anchoring. The latter experiment, coupled with a numerical simulation, supports the existence of a thermomechanical coupling in a compensated cholesteric.

PACS.

61.30.-v Liquid crystals 05.70.Ln Nonequilibrium and irreversible thermodynamics 65.40.De Thermal expansion; thermomechanical effects 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P.-G. de Gennes, J. Prost, The Physics of Liquid Crystals (Oxford University Press, Oxford, 1995).Google Scholar
  2. 2.
    P. Oswald, P. Pieranski, Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments (Taylor & Francis, CRC press, Boca Raton, 2005).Google Scholar
  3. 3.
    O. Lehmann, Ann. Phys. (Leipzig) 2, 649 (1900). ADSGoogle Scholar
  4. 4.
    O. Lehmann, Flüssige Kristalle und ihr Scheinbares Leben (Verlag von Leopold Voss, Leipzig, 1921).Google Scholar
  5. 5.
    F.M. Leslie, Proc. R. Soc. London, Ser. A 307, 359 (1968).Google Scholar
  6. 6.
    N. Éber, I. Jánossy, Mol. Cryst. Liq. Cryst. Lett. 72, 233 (1982).CrossRefGoogle Scholar
  7. 7.
    N. Éber, I. Jánossy, Mol. Cryst. Liq. Cryst. Lett. 102, 311 (1984).CrossRefGoogle Scholar
  8. 8.
    H. Pleiner, H.R. Brand, Mol. Cryst. Liq. Cryst. Lett. 5, 61 (1987).Google Scholar
  9. 9.
    H. Pleiner, H.R. Brand, Mol. Cryst. Liq. Cryst. Lett. 5, 183 (1988).Google Scholar
  10. 10.
    N. Éber, I. Jánossy, Mol. Cryst. Liq. Cryst. Lett. 5, 81 (1988).Google Scholar
  11. 11.
    A. Dequidt, P. Oswald, Europhys. Lett. 80, 26001 (2007).CrossRefADSGoogle Scholar
  12. 12.
    P. Oswald, J. Baudry, S. Pirkl, Phys. Rep. 337, 67 (2000).CrossRefADSGoogle Scholar
  13. 13.
    F.J. Kahn, Appl. Phys. Lett. 22, 386 (1973).CrossRefADSGoogle Scholar
  14. 14.
    P. Oswald, P.M. Moulin, P. Metz, J.-C. Géminard, P. Sotta, J. Phys. III 3, 1891 (1993).CrossRefGoogle Scholar
  15. 15.
    K.C. Lim, J.T. Ho, Mol. Cryst. Liq. Cryst. 47, 173 (1978).CrossRefGoogle Scholar
  16. 16.
    As pointed out by Pawel Pieranski, convection must develop in the sample as long as it is submitted to a horizontal temperature gradient. As a result, the director field must distort in homeotropic samples because of the shear flow. It can be checked that this effect should lead to a phase shift $\Phi_{\ab{H}}$ proportional to $d^9$. This dependence is very different from that observed experimentally ($\Phi_{\ab{H}}\propto d^5$), suggesting that hydrodynamic effects are negligible in our experiments. This conclusion agrees with the experimental results of Éber and Jánossy eber1 who found that $\Phi_{\ab{H}}= 0$ at all temperature gradients in a pure nematic (8CB).Google Scholar
  17. 17.
    We emphasize that in the planar geometry the convection does not destabilize the director field as the director is perpendicular to the shear plane.Google Scholar
  18. 18.
    S.W. Morris, P. Palffy-Muhoray, D.A. Balzarini, Mol. Cryst. Liq. Cryst. 139, 263 (1986).CrossRefGoogle Scholar
  19. 19.
    C.V. Brown, N.J. Mottram, Phys. Rev. E 68, 031702 (2003).CrossRefADSGoogle Scholar
  20. 20.
    A. Dequidt, P. Oswald, Eur. Phys. J. E 24, 157 (2007).CrossRefGoogle Scholar
  21. 21.
    E.P. Raynes, Mol. Cryst. Liq. Cryst. Lett. 4, 1 (1986).Google Scholar
  22. 22.
    D. Taupin, Probabilities Data Reduction and Error Analysis in the Physical Sciences (Les Editions de Physique, Les Ulis, 1988).Google Scholar
  23. 23.
    Note that we have implicitly assumed that $\nu_{eff}$ is positive as in the mixture 8CB+CC, for which this result was proved experimentally by Éber and Jánossy in reference eber2. We emphasize that taking $\nu_{eff}<0$ would have lead to $\nu=-10.4\times10^{-7}$kg K^-1 s^-2, which is more than three times larger in absolute value than the retained value. The conclusion is that, in all cases, $\nu$ is different from 0, which is the main result of this article.Google Scholar
  24. 24.
    I. Dozov, D.N. Stoenescu, S. Lamarque-Forget, Ph. Martinot-Lagarde, E. Polossat, Appl. Phys. Lett. 77, 4124 (2000).CrossRefADSGoogle Scholar
  25. 25.
    C. Blanc, D. Svensek, S. Zumer, M. Nobili, Phys. Rev. Lett. 95, 097802 (2005).CrossRefADSGoogle Scholar
  26. 26.
    N.V. Madhusudana, R. Pratibha, H.P. Padmini, Mol. Cryst. Liq. Cryst. 202, 35 (1991).CrossRefGoogle Scholar
  27. 27.
    H.P. Padmini, N.V. Madhusudana, Liq. Cryst. 14, 497 (1993).CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2008

Authors and Affiliations

  1. 1.Laboratoire de Physique, École Normale Supérieure de Lyon, CNRSUniversité de LyonLyonFrance
  2. 2.Department III, Institute of Physical ChemistryPolish Academy of SciencesWarsawPoland

Personalised recommendations