Effect of surface viscosity, anchoring energy, and cell gap on the response time of nematic liquid crystals

by Prof. Luiz Roberto Evangelista (Universidade Estadual de Maringa' - Brasil)

Tuesday 23 Dec 2014, 10:00 → 11:00 Europe/Rome

Aula Teorici (Dipartimento di Fisica e Astronomia)

In the continuum theory of nematics, the director's relaxation is Debye-like and described by a viscous process [1]. This relaxation has tremendous importance in liquid crystal (LC) devices, owing to the need for speed of modern displays [2]. In most textbooks, the decay response time is a function of elastic constant, rotational viscosity and the square of cell gap. As shown in [3] the anchoring strength, plays an important role when anchoring energy is finite and the thickness exponent in reality lies between 1 and 2. In addition to [3], the importance of the surface on the relaxation time has been discussed in several articles, with special attention given to thin cells in [4]. Interestingly, little is known about surface dynamics and the only aspect of the surface treated in such articles is the anchoring strength. A more complete description must take into account the balance of torque at the surfaces leading to the concept of surface viscosity. Introduced by Derzhanskii and Petrov [5], it accounts for the relaxation of the director at the surface with time. In a phenomenological perspective, the surface viscosity notion was introduced to take into account an extra dissipation at the surface arising when the director and the preferred anchoring direction change. Thus, there is a surface torque whose strength is measured by which describes the interaction between the surface treatment and the liquid crystal. It has attracted attention of the scientific community due to the relevance for displays and the mathematical difficulties faced in such problems [6,7]. Nonetheless, although it has been shown the importance of the surface on the response time of nematics, there are no explicit studies about the role of surface viscosity on molecular response time. In this work [8], an analytical expression for the relaxation time of a nematic liquid crystal is obtained for the first time by considering the influence of surface viscosity, anchoring energy strength and cell gap, validated numerically by using the so-called relaxation method. This general equation for the molecular response time, was derived for a vertical aligned cell and by solving an eigenvalue equation coming from the usual balance of torque equation in the Derzhanskii and Petrov formulation, recovering the usual equations in the appropriate limit. The results show that , where is observed only for strongly anchored cells, while for moderate to weak anchored cells, the exponent lies between 1 and 2, depending on both, surface viscosity and anchoring strength. We found that the surface viscosity is important when calculating the response time, especially for thin cells, critical for liquid crystal devices. The surface viscosity's effect on the optical response time with pretilt is also explored. Our results bring new insights about the role of surface viscosity and its effects in applied physics. [1] D. K. Yang and S. T. Wu, Fundamentals of Liquid Crystal Devices, Wiley-SID, Chichester, 2006. [2] H.C. Cheng, L.H. Rao, and S.-T. Wu. , J. of Disp. Tech. 6, 229 (2010). [3] X. Nie, R. Lu, H. Xianyu, T. X. Wu, and S.-T. Wu, J. Appl. Phys. 101, 103110 (͑2007). [4] M. Jiao, Z. Ge, Q. Song, and S-T. Wu, Appl. Phys. Lett. 92, 061102 ͑(2008). [5] A. I. Derzhanskii and A. G. Petrov, Acta Phys. Pol. A55, 747 (1979). [6]A Sonnet, E. G. Virga and G.E. Durand. Phys. Rev. E62, 3694 (2000) [7]A. T. Silva, M. A. F. dos Santos, E. K. Lenzi, L. R. Evangelista and R. S. Zola, Mol. Cryst. Liq. Cryst. 576, 32 (2013) [8] R. F. de Souza, D. K. Yang, E. K. Lenzi, L. R. Evangelista, and R. S. Zola, Ann. Phys. 346, 14 (2014)