Elasticity Tensors in Nematic Liquid Crystals

Elasticity Tensors in Nematic Liquid Crystals

Loading document ...
Loading page ...


Author(s): Amelia Carolina Sparavigna

Download Full PDF Read Complete Article

DOI: 10.18483/ijSci.1117 229 692 54-65 Volume 5 - Jul 2016


The paper is discussing the contributions to the free energy of elastic distortions in a nematic liquid crystal. These contributions are here given by tensors, which are represented by means of the components of the director, the unit vector indicating the local average alignment of molecules, and by Kronecker and Levi-Civita symbols. The paper is also discussing the elasticity of the second order and its contribution in threshold phenomena.


Liquid Crystals, Nematics, Elasticity, Continuum Theories


  1. Oseen, C. W. (1933). The theory of liquid crystals. Transactions of the Faraday Society, 29(140), 883-899. DOI: http://dx.doi.org/10.1039/tf9332900883
  2. Frank, F. C. (1958). I. Liquid crystals. On the theory of liquid crystals. Discussions of the Faraday Society, 25, 19-28. DOI: http://dx.doi.org/10.1039/df9582500019
  3. Nehring, J., & Saupe, A. (1972). Calculation of the elastic constants of nematic liquid crystals. J. Chem. Phys. 56, 5527-5529 DOI: http://dx.doi.org/10.1063/1.1677071
  4. Sparavigna, A., Lavrentovich, O. D., & Strigazzi, A. (1994). Periodic stripe domains and hybrid-alignment regime in nematic liquid crystals: Threshold analysis. Physical Review E, 49(2), 1344. DOI: http://dx.doi.org/10.1103/physreve.49.1344
  5. Sparavigna, A., Komitov, L., Stebler, B., & Strigazzi, A. (1991). Static splay-stripes in a hybrid aligned nematic layer. Molecular Crystals and Liquid Crystals 207(1), 265-280. DOI: http://dx.doi.org/10.1080/10587259108032105
  6. Sparavigna, A., Komitov, L., Lavrentovich, O. D., & Strigazzi, A. (1992). Saddle-splay and periodic instability in a hybrid aligned nematic layer subjected to a normal magnetic field. Journal de Physique II, 2(10), 1881-1888. DOI: http://dx.doi.org/10.1051/jp2:1992241
  7. Barbero, G., Sparavigna, A., & Strigazzi, A. (1990). The structure of the distortion free-energy density in nematics: second-order elasticity and surface terms. Il Nuovo Cimento D, 12(9), 1259-1272. DOI: http://dx.doi.org/10.1007/bf02450392
  8. Sparavigna, A., Komitov, L., & Strigazzi, A. (1991). Hybrid Aligned Nematics and second order elasticity. Physica Scripta, 43(2), 210. DOI: http://dx.doi.org/10.1088/0031-8949/43/2/017
  9. Stephen, M. J., & Straley, J. P. (1974). Physics of liquid crystals. Reviews of Modern Physics, 46(4), 617-704. DOI: http://dx.doi.org/10.1103/revmodphys.46.617
  10. De Gennes, P. G., & Prost, J. (1995). The Physics of Liquid Crystals, Clarendon Press. ISBN: 0198517858, 9780198517856
  11. Sparavigna, A. C. (2012). Distortional Lifshitz vectors and helicity in nematic free energy density. arXiv preprint arXiv:1207.2918.
  12. Sparavigna, A. C. (2013). Distortional Lifshitz vectors and Helicity in nematic free energy density, International Journal of Sciences 07(2013):54-59. DOI: http://dx.doi.org/10.18483/ijsci.211
  13. Lavrentovich, O. D., & Pergamenshchik, V. M. (1995). Patterns in thin liquid crystal films and the divergence (“surfacelike”) elasticity. International Journal of Modern Physics B, 9, 2389-2437. DOI: http://dx.doi.org/10.1142/9789812831101_0008
  14. Pergamenshchik, V. M., Subacius, D., & Lavrentovich, O. D. (1997). K13-induced deformations in a nematic liquid crystal: Experimental test of the first-order theory. Molecular Crystals and Liquid Crystals, 292(1), 25-37. DOI: http://dx.doi.org/10.1080/10587259708031918

Cite this Article:

  • BibTex
  • RIS
  • APA
  • Harvard
  • IEEE
  • MLA
  • Vancouver
  • Chicago

International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Author(s) retain the copyrights of this article, though, publication rights are with Alkhaer Publications.

Search Articles

Issue July 2020

Volume 9, July 2020

Table of Contents

Order Print Copy

World-wide Delivery is FREE

Share this Issue with Friends:

Submit your Paper