Abstract
Configuration properties of layer orientation in smectic C* type ferroelectric liquid crystals are theoretically described for constant temperature. The proposed model in this letter admits both symmetric and asymmetric configurations of smectic layers [chevron structures] in surface-stabilized liquid crystal cells, which [chevron structures] perturb ordering of smectic C* molecules in the so-called bookshelf geometry. The investigated model reasonably disregards mass transfer between the smectic molecular layers. Since the length of smectic layers is permanent for any coordinate of the chevron tip [because the polar angle \theta is fixed], then the locus of the chevron tip can be represented by ellipse. By using the continuum approach, we derived the functional of the free energy density, where we do not neglect the quadratic term of the electric field density. To determine energetically favorable structures of molecular layers, we solve the Euler-Lagrange equation, which is the φ-dependence of the director’s azimuthal angle versus the direction perpendicular the cell plates. It is shown that only symmetric chevron structures exhibit minimum of free energy in the absence of electric field as well as the electric field is applied. The reason of this effect is splay deformation of smectic layers. The stability analysis of the Euler-Lagrange equation for typical values of electric field and smectic C* parameters shows that the theoretical results are in agreement with experimental data. The proposed approach for studying chevron configurations can explain the abundance of textures in smectic C* liquid crystal cells.
References (12)
1. N. Ul Islam, N. J. Mottram, S. J. Elston. Liquid Crystals. 26, 1059 (1999).
2. N. Vaupotic, S. Kralj, M. Copic, T. J. Sluckin. Phys. Rev. E. 54, 3783 (1996).
3. N. A. Clark, T. P. Rieker. Phys. Rev. A. 37 (3), 1053 (1988).
4. P. C. Willis, N. A. Clark, C. R. Safinya. Liquid Crystals. 11, 581 (1992).
5. J. Sabater, J. M. S. Pena, J. M. Otón. J. Appl. Phys. 77 3023 (1995).
6. A. D. Kiselev, V. G. Chigrinov, E. P. Pozhidaev. Phys. Rev. E. 75 061706 (2007).
7. M. Oh-e, M. Isogai, T. Kitamura. Liquid Crystals. 11, 101 (1992).
8. R. E. Webster, N. J. Mottram, D. J. Cleaver. Phys. Rev. E. 68. 021706 (2003).
9. I. W. Stewart. The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, London, Taylor & Francis (2004) 360 p.
10. S. T. Lagerwall. Ferroelectric and Antiferroelectric Liquid Crystals, Weinheim, Wiley-VCH (1999) 427 p.
11. V. P. Romanov, S. V. Ul’yanov, K. G. Chernyak, Physics of the Solid State. 52 (9) 1985 (2010).
12. J. C. Jones. Liquid Crystals. 42, 732 (2015).