Advertisement

Retrieving the saddle-splay elastic constant K24 of nematic liquid crystals from an algebraic approach

  • Sébastien Fumeron
  • Fernando Moraes
  • Erms Pereira
Regular Article

Abstract.

The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant K24. However, the usual methods to retrieve the latter involve adjusting of computational parameters through visual comparisons between the experimental light interference pattern or a 2 H-NMR spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparisons, we develop an algebraic method for obtaining of saddle-splay elastic constant K24. Considering an escaped-radial disclination inside a capillary tube with radius R0 of tens of micrometers, we use a metric approach to study the propagation of the light (in the scalar wave approximation), near the surface of the tube and to determine the light interference pattern due to the defect. The latter is responsible for the existence of a well-defined interference peak associated to a unique angle \( \phi_{0}\) . Since this angle depends on factors such as refractive indexes, curvature elastic constants, anchoring regime, surface anchoring strength and radius R0, the measurement of \( \phi_{0}\) from the interference experiments involving two different radii allows us to algebraically retrieve K24. Our method allowed us to give the first reported estimation of K24 for the lyotropic chromonic liquid crystal Sunset Yellow FCF: K 24 = 2.1 pN.

Graphical abstract

Keywords

Soft Matter: Liquid crystals 

References

  1. 1.
    D.-K. Yang, S.-T. Wu, Fundamentals of Liquid Crystal Devices (John Wiley, New Jersey, 2006)Google Scholar
  2. 2.
    R. Baetens, B.P. Jelle, A. Gustavsen, Solar Energy Mater. Solar Cells 94, 87 (2010)CrossRefGoogle Scholar
  3. 3.
    J. Doane, Liquid Crystals: Their Applications and Uses (World Scientific, New Jersey, 1990)Google Scholar
  4. 4.
    P. Oswald, P. Pieranski, Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments (CRC Press, 2005)Google Scholar
  5. 5.
    D.S. Miller, N.L. Abbott, Soft Matter 9, 374 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    G. Crawford, D.W. Allender, J. Doane, Phys. Rev. A 45, 8693 (1992)ADSCrossRefGoogle Scholar
  7. 7.
    P. Boltenhagen, O. Lavrentovich, M. Kleman, J. Phys. II 1, 1233 (1991)Google Scholar
  8. 8.
    P. Boltenhagen, M. Kleman, O.D. Lavrentovich, J. Phys. II 4, 1439 (1994)Google Scholar
  9. 9.
    P. Boltenhagen, O. Lavrentovich, M. Kleman, Phys. Rev. A 46, R1743 (1992)ADSCrossRefGoogle Scholar
  10. 10.
    A. Sparavigna, O.D. Lavrentovich, A. Strigazzi, Phys. Rev. E 49, 1344 (1994)ADSCrossRefGoogle Scholar
  11. 11.
    E. Pairam, J. Vallamkondu, V. Koning, B.C. van Zuiden, P.W. Ellis, M.A. Bates, V. Vitelli, A. Fernandez-Nieves, Proc. Natl. Acad. Sci. U.S.A. 110, 9295 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    P. Cladis, M. Kleman, J. Phys. (Paris) 33, 591 (1972)CrossRefGoogle Scholar
  13. 13.
    M. Kleman, O.D. Lavrentovich, Soft Matter Physics: An Introduction (Springer-Verlag, New York, 2003)Google Scholar
  14. 14.
    P.A. Kossyrev, G.P. Crawford, Mol. Cryst. Liq. Cryst. 351, 379 (2000)CrossRefGoogle Scholar
  15. 15.
    R.D. Polak, G.P. Crawford, B.C. Kostival, J.W. Doane, S. Zumer, Phys. Rev. E 49, R978 (1994)ADSCrossRefGoogle Scholar
  16. 16.
    C. Sátiro, F. Moraes, Eur. Phys. J. E 20, 173 (2006)CrossRefGoogle Scholar
  17. 17.
    E. Pereira, F. Moraes, Liq. Cryst. 38, 295 (2011)CrossRefGoogle Scholar
  18. 18.
    E.R. Pereira, F. Moraes, Cent. Eur. J. Phys. 9, 1100 (2011)Google Scholar
  19. 19.
    E. Pereira, S. Fumeron, F. Moraes, Phys. Rev. E 87, 022506 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    S. Fumeron, B. Berche, F. Santos, E. Pereira, F. Moraes, Phys. Rev. A 92, 063806 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    S. Fumeron, E. Pereira, F. Moraes, Physica B 476, 19 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    S. Fumeron, E. Pereira, F. Moraes, Int. J. Therm. Sci. 67, 64 (2013)CrossRefGoogle Scholar
  23. 23.
    S. Fumeron, E. Pereira, F. Moraes, Phys. Rev. E 89, 020501 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    D. Melo, I. Fernandes, F. Moraes, S. Fumeron, E. Pereira, Phys. Lett. A 380, 3121 (2016)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    A.A. Joshi, J.K. Whitmer, O. Guzman, N.L. Abbott, J.J. de Pablo, Soft Matter 10, 882 (2014)ADSCrossRefGoogle Scholar
  26. 26.
    R.R. A.J. Leadbetter, C. Colling, J. Phys. C1 36, 37 (1975)Google Scholar
  27. 27.
    M. Kleman, L. Michel, Phys. Rev. Lett. 40, 1387 (1978)ADSCrossRefGoogle Scholar
  28. 28.
    M. Kleman, G. Toulouse, J. Phys. (Paris) Lett. 37, 149 (1976)CrossRefGoogle Scholar
  29. 29.
    G. Volovik, V. Mineev, Sov. Phys. JETP 45, 1186 (1977)ADSMathSciNetGoogle Scholar
  30. 30.
    P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd edition (Claredon Press, Oxford, 1992)Google Scholar
  31. 31.
    S. Burylov, Sov. Phys. JETP 85, 873 (1997)ADSCrossRefGoogle Scholar
  32. 32.
    M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999)Google Scholar
  33. 33.
    W. Gordon, Ann. Phys. (Berlin) 377, 421 (1923)ADSCrossRefGoogle Scholar
  34. 34.
    P. Alsing, Am. J. Phys. 66, 779 (1998)ADSCrossRefGoogle Scholar
  35. 35.
    M. Novello, J.M. Salim, Phys. Rev. D 63, 083511 (2001)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    U. Leonhardt, P. Piwnicki, Phys. Rev. Lett. 84, 822 (2000)ADSCrossRefGoogle Scholar
  37. 37.
    S.M. Carroll, Spacetime and Geometry (Addison Wesley, San Francisco, 2003)Google Scholar
  38. 38.
    C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W. H. Freeman and Company, San Francisco, 1973)Google Scholar
  39. 39.
    R. D’Inverno, Introducing Einstein’s Relativity (Oxford University Press, Oxford, 1998)Google Scholar
  40. 40.
    A. Vilenkin, E. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, 1994)Google Scholar
  41. 41.
    G.P. Crawford, J.A. Mitcheltree, E.P. Boyko, W. Fritz, S. Zumer, J.W. Doane, Appl. Phys. Lett. 60, 3226 (1992)ADSCrossRefGoogle Scholar
  42. 42.
    D.W. Allender, G. Crawford, J. Doane, Phys. Rev. Lett. 67, 1442 (1991)ADSCrossRefGoogle Scholar
  43. 43.
    C. Cohen-Tannnoudji, B. Diu, F. Laloe, Quantum Mechanics, Vol. 2 (Wiley-Interscience, New York, 1982)Google Scholar
  44. 44.
    G.B. Arfken, H.J. Weber, F.E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, 7th edition (Academic Press, 2013)Google Scholar
  45. 45.
    R.B. Meyer, Philos. Mag. 27, 405 (1973)ADSCrossRefGoogle Scholar
  46. 46.
    C. Williams, P. Pieranski, P.E. Cladis, Phys. Rev. Lett. 29, 90 (1972)ADSCrossRefGoogle Scholar
  47. 47.
    C.E. Williams, P.E. Cladis, M. Kleman, Mol. Cryst. Liq. Cryst. 21, 355 (1973)CrossRefGoogle Scholar
  48. 48.
    A. Saupe, Mol. Cryst. Liq. Cryst. 21, 211 (1973)CrossRefGoogle Scholar
  49. 49.
    M. Kleman, Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Ordered Media (Wiley, New York, 1988)Google Scholar
  50. 50.
    M. Kuzma, M.M. Labes, Mol. Cryst. Liq. Cryst. 100, 103 (1983)CrossRefGoogle Scholar
  51. 51.
    A. Scharkowski, G.P. Crawford, S. Zumer, J.W. Doane, J. Appl. Phys. 73, 7280 (1993)ADSCrossRefGoogle Scholar
  52. 52.
    S.-W. Tam-Chang, L. Huang Chem. Commun., 1957 (2008), DOI:10.1039/B714319B CrossRefGoogle Scholar
  53. 53.
    S. Zhou, Y.A. Nastishin, M. Omelchenko, L. Tortora, V. Nazarenko, O. Boiko, T. Ostapenko, T. Hu, C. Almasan, S. Sprunt et al., Phys. Rev. Lett. 109, 037801 (2012)ADSCrossRefGoogle Scholar
  54. 54.
    J. Jeong, L. Kang, Z.S. Davidson, P.J. Collings, T.C. Lubensky, A. Yodh, Proc. Natl. Acad. Sci. U.S.A. 112, E1837 (2015)ADSCrossRefGoogle Scholar
  55. 55.
    V.R. Horowitz, L.A. Janowitz, A.L. Modic, P.A. Heiney, P.J. Collings, Phys. Rev. E 72, 041710 (2005)ADSCrossRefGoogle Scholar
  56. 56.
    J. Ericksen, Phys. Fluids (1958-1988) 9, 1205 (1966)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Sébastien Fumeron
    • 1
    • 2
  • Fernando Moraes
    • 3
    • 4
  • Erms Pereira
    • 5
  1. 1.Institut Jean LamourUniversité de LorraineVandæuvre les NancyFrance
  2. 2.Laboratoire dÉnergétique et de Mécanique Théorique et AppliquéeCNRS UMR 7563, Nancy UniversitéVandoeuvre CedexFrance
  3. 3.Departamento de Física, CCENUniversidade Federal da ParaíbaJoão Pessoa, PBBrazil
  4. 4.Departamento de FísicaUniversidade Federal Rural de PernambucoRecife, PEBrazil
  5. 5.Escola Politécnica de PernambucoUniversidade de PernambucoRecife, PEBrazil

Personalised recommendations