Periodic Distortions In Nematics Caused By Flexoelectricity And Saddle-Splay Elasticity

Author(s): Amelia Carolina Sparavigna

In liquid crystal materials, the coupling between their elastic field and an external action, such as electric and magnetic fields or the confinement created by free surfaces or cell walls, can give rise to periodic domains. Here, some simple calculations are proposed for nematics in planar cells, where undulations are caused by flexoelectricity and saddle-splay elasticity.

Liquid Crystals, Nematics, Flexoelectricity, Saddle-Splay Elasticity

1. L.D. Landau and E.M. Lifshitz, Statistical physics, Pergamon Press, Oxford, UK, 1980
2. P. Oswald and P. Pieranski, Nematic and cholesteric liquid crystals: Concepts and physical properties illustrated by experiments, Taylor & Francis, 2005
3. S.A. Pikin, Structural transformations in liquid crystals, Gordon & Breach Science Publishers Ltd., 1991
4. A. Sparavigna, O.D. Lavrentovich and A. Strigazzi, Periodic stripe domains and hybrid-alignment regime in nematic liquid crystals: Threshold analysis. Phys. Rev. E 1994, 49, 1344-1352
5. A. Sparavigna, L. Komitov, O. Lavrentovich and A. Strigazzi, Saddle-splay and periodic instability in a hybrid aligned nematic layer subjected to a normal magnetic field. Journal de Physique II, EDP Sciences 1992, 2 (10), 1881-1888
6. L.K. Vistin, Electrostructural effect and optical properties of a certain class of liquid crystals and their binary mixtures, Sov. Phys. Crystallogr. 1970, 15(3) 514-515
7. Y.P. Bobylev, V.G. Chigrinov and S.A. Pikin, Threshold flexoelectric effect in nematic liquid crystals, Journal de Physique Colloques 1979, 40(C3), 331-333
8. O.D. Lavreontovich and V.M. Pergamenshchik, Periodic domain-structures in thin hybrid nematic layers, Mol. Cryst. Liquid Cryst. 1990, 179, 125-132
9. L.D. Landau and E.M. Lifsits, Fisica Teorica 8 - Elettrodinamica dei mezzi continui, Editori Riuniti, Roma, 1986
10. P.G. De Gennes and J. Prost, The Physics of Liquid Crystals, Oxford Science Publication, 1995
11. A.C. Sparavigna, Distortional Lifshitz vectors and helicity in nematic free energy density, International Journal of Sciences, 2013, 2(7), 54-59
12. A. Sparavigna, Role of Lifshitz invariants in liquid crystals, Materials 2009, 2, 674-698
13. R.B. Meyer, Piezoelectric effects in liquid crystals. Phys. Rev. Lett. 1969, 22, 918-921
14. D.L.G. Cheung, Structures and properties of liquid crystals and related molecules from computer simulation, Ph. D. Thesis, University of Durham, Durham, UK, 2002
15. D. Schmidt, M. Schadt and W.Z. Helfrich, Liquid-crystalline curvature electricity: The bending mode of MBBA. Z. Naturforschung, 1972, 27a, 277-280
16. S. Warrier and N.V. Madhusudana, An AC electrooptic technique for measuring the flexoelectric coefficient and anchoring energies of nematics, J. Phys. II 1997, 7, 1789-1803
17. J. Harden, B. Mbanga, N. Ėber, K. Fodor-Csorba, S. Sprunt, J.T. Gleeson and A. Jákli, Giant flexoelectricity of bent-core nematic liquid crystals, Phys. Rev. Lett. 2006, 97, 157802-1-157802-4
18. W.Z. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforschung, 1973, 28c, 693-703