Issue
EPL
Volume 88, Number 5, December 2009
Article Number 58003
Number of page(s) 5
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/88/58003
Published online 15 December 2009
EPL, 88 (2009) 58003
DOI: 10.1209/0295-5075/88/58003

Influence of the anchoring energy on the relaxation of the nematic deformation

E. Kaminski Lenzi1, 2 and G. Barbero1

1   Dipartimento di Fisica del Politecnico - Corso Duca degli Abruzzi 24, 10129 Torino, Italia, EU
2   Departamento di Fisica, Universidade Estadual de Maringa - Avenida Colombo 5790, 87020-900 Maringa, Parana, Brazil

giovanni.barbero@polito.it

received 16 October 2009; accepted in final form 16 November 2009; published December 2009
published online 15 December 2009

Abstract
We analyze the influence of the anchoring energy strength on the relaxation of the nematic deformation, when the distorting field is removed, at t=0. The analysis is performed by assuming that the nematic sample is in the shape of a slab, the anchoring energy can be approximated by the form proposed by Rapini and Papoular, and the surface dissipation, responsible for the surface viscosity, is negligible with respect to the bulk one. The switching time of the distorting field is supposed finite, to avoid the non-physical discontinuity of the time derivative of the tilt angle at t=0. We show that the relaxation time of the nematic deformation is a multi-relaxation phenomenon. For large t, the relaxation phenomenon is simple, and the relaxation time is proportional to the diffusion time $\tau _{D}=\eta d^{2}/k$, where d is the thickness of the sample, $\eta $ the viscosity and k the elastic constant of the nematic liquid crystal. For $t\ll \tau _{D}$, the time dependence of the tilt angle is well approximated by few exponential terms. The relation between the effective relaxation time and the anchoring energy strength is deduced. A critical discussion on the standard analysis based on the diffusion equation is also reported.

PACS
83.80.Xz - Liquid crystals: nematic, cholesteric, smectic, discotic, etc.
61.30.Hn - Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions.

© EPLA 2009