Skip to main content
SpringerLink
Log in

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

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.-K. Yang, S.-T. Wu, Fundamentals of Liquid Crystal Devices (John Wiley, New Jersey, 2006)

  2. R. Baetens, B.P. Jelle, A. Gustavsen, Solar Energy Mater. Solar Cells 94, 87 (2010)

    Article  Google Scholar 

  3. J. Doane, Liquid Crystals: Their Applications and Uses (World Scientific, New Jersey, 1990)

  4. P. Oswald, P. Pieranski, Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments (CRC Press, 2005)

  5. D.S. Miller, N.L. Abbott, Soft Matter 9, 374 (2013)

    Article  ADS  Google Scholar 

  6. G. Crawford, D.W. Allender, J. Doane, Phys. Rev. A 45, 8693 (1992)

    Article  ADS  Google Scholar 

  7. P. Boltenhagen, O. Lavrentovich, M. Kleman, J. Phys. II 1, 1233 (1991)

    Google Scholar 

  8. P. Boltenhagen, M. Kleman, O.D. Lavrentovich, J. Phys. II 4, 1439 (1994)

    Google Scholar 

  9. P. Boltenhagen, O. Lavrentovich, M. Kleman, Phys. Rev. A 46, R1743 (1992)

    Article  ADS  Google Scholar 

  10. A. Sparavigna, O.D. Lavrentovich, A. Strigazzi, Phys. Rev. E 49, 1344 (1994)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  12. P. Cladis, M. Kleman, J. Phys. (Paris) 33, 591 (1972)

    Article  Google Scholar 

  13. M. Kleman, O.D. Lavrentovich, Soft Matter Physics: An Introduction (Springer-Verlag, New York, 2003)

  14. P.A. Kossyrev, G.P. Crawford, Mol. Cryst. Liq. Cryst. 351, 379 (2000)

    Article  Google Scholar 

  15. R.D. Polak, G.P. Crawford, B.C. Kostival, J.W. Doane, S. Zumer, Phys. Rev. E 49, R978 (1994)

    Article  ADS  Google Scholar 

  16. C. Sátiro, F. Moraes, Eur. Phys. J. E 20, 173 (2006)

    Article  Google Scholar 

  17. E. Pereira, F. Moraes, Liq. Cryst. 38, 295 (2011)

    Article  Google Scholar 

  18. E.R. Pereira, F. Moraes, Cent. Eur. J. Phys. 9, 1100 (2011)

    Google Scholar 

  19. E. Pereira, S. Fumeron, F. Moraes, Phys. Rev. E 87, 022506 (2013)

    Article  ADS  Google Scholar 

  20. S. Fumeron, B. Berche, F. Santos, E. Pereira, F. Moraes, Phys. Rev. A 92, 063806 (2015)

    Article  ADS  Google Scholar 

  21. S. Fumeron, E. Pereira, F. Moraes, Physica B 476, 19 (2015)

    Article  ADS  Google Scholar 

  22. S. Fumeron, E. Pereira, F. Moraes, Int. J. Therm. Sci. 67, 64 (2013)

    Article  Google Scholar 

  23. S. Fumeron, E. Pereira, F. Moraes, Phys. Rev. E 89, 020501 (2014)

    Article  ADS  Google Scholar 

  24. D. Melo, I. Fernandes, F. Moraes, S. Fumeron, E. Pereira, Phys. Lett. A 380, 3121 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  25. A.A. Joshi, J.K. Whitmer, O. Guzman, N.L. Abbott, J.J. de Pablo, Soft Matter 10, 882 (2014)

    Article  ADS  Google Scholar 

  26. R.R. A.J. Leadbetter, C. Colling, J. Phys. C1 36, 37 (1975)

    Google Scholar 

  27. M. Kleman, L. Michel, Phys. Rev. Lett. 40, 1387 (1978)

    Article  ADS  Google Scholar 

  28. M. Kleman, G. Toulouse, J. Phys. (Paris) Lett. 37, 149 (1976)

    Article  Google Scholar 

  29. G. Volovik, V. Mineev, Sov. Phys. JETP 45, 1186 (1977)

    ADS  MathSciNet  Google Scholar 

  30. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd edition (Claredon Press, Oxford, 1992)

  31. S. Burylov, Sov. Phys. JETP 85, 873 (1997)

    Article  ADS  Google Scholar 

  32. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999)

  33. W. Gordon, Ann. Phys. (Berlin) 377, 421 (1923)

    Article  ADS  Google Scholar 

  34. P. Alsing, Am. J. Phys. 66, 779 (1998)

    Article  ADS  Google Scholar 

  35. M. Novello, J.M. Salim, Phys. Rev. D 63, 083511 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  36. U. Leonhardt, P. Piwnicki, Phys. Rev. Lett. 84, 822 (2000)

    Article  ADS  Google Scholar 

  37. S.M. Carroll, Spacetime and Geometry (Addison Wesley, San Francisco, 2003)

  38. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W. H. Freeman and Company, San Francisco, 1973)

  39. R. D’Inverno, Introducing Einstein’s Relativity (Oxford University Press, Oxford, 1998)

  40. A. Vilenkin, E. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, 1994)

  41. G.P. Crawford, J.A. Mitcheltree, E.P. Boyko, W. Fritz, S. Zumer, J.W. Doane, Appl. Phys. Lett. 60, 3226 (1992)

    Article  ADS  Google Scholar 

  42. D.W. Allender, G. Crawford, J. Doane, Phys. Rev. Lett. 67, 1442 (1991)

    Article  ADS  Google Scholar 

  43. C. Cohen-Tannnoudji, B. Diu, F. Laloe, Quantum Mechanics, Vol. 2 (Wiley-Interscience, New York, 1982)

  44. G.B. Arfken, H.J. Weber, F.E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, 7th edition (Academic Press, 2013)

  45. R.B. Meyer, Philos. Mag. 27, 405 (1973)

    Article  ADS  Google Scholar 

  46. C. Williams, P. Pieranski, P.E. Cladis, Phys. Rev. Lett. 29, 90 (1972)

    Article  ADS  Google Scholar 

  47. C.E. Williams, P.E. Cladis, M. Kleman, Mol. Cryst. Liq. Cryst. 21, 355 (1973)

    Article  Google Scholar 

  48. A. Saupe, Mol. Cryst. Liq. Cryst. 21, 211 (1973)

    Article  Google Scholar 

  49. M. Kleman, Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Ordered Media (Wiley, New York, 1988)

  50. M. Kuzma, M.M. Labes, Mol. Cryst. Liq. Cryst. 100, 103 (1983)

    Article  Google Scholar 

  51. A. Scharkowski, G.P. Crawford, S. Zumer, J.W. Doane, J. Appl. Phys. 73, 7280 (1993)

    Article  ADS  Google Scholar 

  52. S.-W. Tam-Chang, L. Huang Chem. Commun., 1957 (2008), DOI:10.1039/B714319B

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  55. V.R. Horowitz, L.A. Janowitz, A.L. Modic, P.A. Heiney, P.J. Collings, Phys. Rev. E 72, 041710 (2005)

    Article  ADS  Google Scholar 

  56. J. Ericksen, Phys. Fluids (1958-1988) 9, 1205 (1966)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Jean Lamour, Université de Lorraine, Boulevard des Aiguillettes, BP 239, 54506, Vandæuvre les Nancy, France

    Sébastien Fumeron

  2. Laboratoire dÉnergétique et de Mécanique Théorique et Appliquée, CNRS UMR 7563, Nancy Université, 54506, Vandoeuvre Cedex, France

    Sébastien Fumeron

  3. Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa, PB, Brazil

    Fernando Moraes

  4. Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil

    Fernando Moraes

  5. Escola Politécnica de Pernambuco, Universidade de Pernambuco, Rua Benfíca, 455, Madalena, 50720-001, Recife, PE, Brazil

    Erms Pereira

Authors
  1. Sébastien Fumeron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fernando Moraes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Erms Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erms Pereira.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fumeron, S., Moraes, F. & Pereira, E. Retrieving the saddle-splay elastic constant K24 of nematic liquid crystals from an algebraic approach. Eur. Phys. J. E 39, 83 (2016). https://doi.org/10.1140/epje/i2016-16083-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2016-16083-8

Keywords

Search

Navigation