Pattern forming instability induced by light in pure and dye-doped nematic liquid crystals

We study theoretically the instabilities induced by a linearly polarized ordinary light wave incident at a small oblique angle on a thin layer of homeotropically oriented nematic liquid crystal with special emphasis on the dye-doped case. The spatially periodic Hopf bifurcation that occurs as the secondary instability after the stationary Freedericksz transition is analyzed.Comment: 8 pages, 7 figures, LaTeX, accepted to Phys. Rev.

Numerical study of surface-induced reorientation and smectic layering in a nematic liquid crystal

Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a smooth behavior of the solutions at "infinity" a boundary energy functional was derived by linearizing the Landau energy around its equilibrium solutions. We find that the intrinsic wave number of the smectic structure, which plays the role of a coupling between nematic and smectic order, strongly influences the director reorientation. Whereas the smectic order is rapidly decaying when moving away from the surface, the uniaxial nematic order parameter shows an oscillatory behavior close to the substrate, accompanied by a non-zero local biaxiality.Comment: LaTeX, 17 pages, with 4 postscript figure

Possible boundary discontinuities of the tilt angle in nematic liquid crystals

The boundary energy term, introduced by Dubois-Violette and Parodi, which depends on the first derivatives of the nematic liquid crystal director, is considered. It is shown that if it is written as a purely surface term, the problem of finding stable director configurations cannot be solved. Further information is required about the interaction forces giving rise to this energy term. On the basis of a simple model for such an interaction, it is shown that its main effect is to give a non negligible variation of the tilt angle in a thin boundary layer, when the easy axis is tilted. It is also shown that all the previously used methods for finding the stable director configurations, when surface energy terms dependent on the director derivatives are present, must be reconsidered.On considère l'énergie de surface de Dubois-Violette et Parodi dépendant des premières dérivées de l'orientation du directeur nématique. On montre qu'en l'écrivant comme un simple terme de surface, on ne peut résoudre le problème de trouver les configurations stables du directeur. D'autres informations sont nécessaires sur les interactions donnant lieu à cette énergie. En modélisant simplement cette interaction, on montre que son effet principal est d'imposer une variation non négligeable de l'orientation du directeur près de la surface, quand l'orientation spontanée est inclinée. Toutes les méthodes utilisées précédemment pour trouver les configurations stables du directeur doivent être reconsidérées lorsque les énergies de surface contiennent des termes en gradient de l'orientation du directeur