Dr. Takuya Ohzono and Fukuda found several interesting and novel defect structures in a liquid crystal confined in microgrooves. The orientational order is frustrated because of hybrid boundary conditions; the bottom surface imposes planar anchoring with its preferred direction perpendicular to the grooves, and the LC/air interface imposes normal alignment.
When the LC is nematic, we found a zigzag disclination line together with periodic alignment structures involving twist distortions . We also found a staggered arrangement of focal conic domains when the LC is smectic . Fukuda gave a simple theoretical argument to account for the formation of zigzag disclination line, paying particular attention to why the disclination line deviates from the direction of the grooves .
Their results clearly demonstrate that confined and frustrated liquid crystals can exhibit much more self-organized structures than we already know, and microgrooves can be an arena of such intriguing structures of liquid crystals.
In his seminal work , Berreman showed that a surface with sinusoidal grooves can impose planar anchoring of a nematic liquid crystal. The surface anchoring arises from the distortions of the orientational order induced by sinusoidal grooves and their dependence on the angle between the average director and the groove direction (θ). He also gave an analytic form of the anchoring energy that is proportional to sin2θ (with an assumption of small amplitude of the groove). Fukuda critically reexamined the theory of Berreman and found that his apparently natural assumption made in the treatment of the distortion of the orientational order is in fact invalid . His recalculation of the anchoring energy revealed that its analytic form is much more complicated than that of Berreman and depends on K11, K22, K33, K24 in a nontrivial manner. In some extreme cases, the anchoring energy can be proportional to sin4θ, which marks a sharp contrast to the result of Berreman. Fukuda also extended the reexamined version of the theory to the cases of surfaces with two-dimensional tomographic patterns , and carried out numerical calculations to check if the analytic formula of the anchoring energy is valid [4,5].