Freedericksz Transition Statics

When a nematic liquid crystal is confined, such as when sandwiched between two parallel substrates with alignment layers, in the absence of external fields, the orientation of the liquid crystal director is determined by the anchoring condition. When an external electric field is applied to the liquid crystal, it will reorient because of the dielectric interaction between the liquid crystal and the applied field. If the dielectric anisotropy is positive (Ae 0), the hquid crystal 

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The optical reorientation processes discussed up to now were qualitatively similar to the corresponding low-frequency field effects. As mentioned earlier this is not always the case. A breakdown of the analogy with static fields was first reported by Zolotko et al. who observed in a homeotropic layer a drastic increase of the Freedericksz threshold power for an o-ray as the angle of incidence was increased. Durbin et al. mentioned that in a planar cell Freedericksz transition cannot be induced by a light beam polarized perpendicularly to the director. From a simple analogy one would expect for these cases a threshold not deviating significantly... 

Recently, particular attention has been devoted to the first-order Freedericksz transition (FT), molecular reorientation, and bistability in nematic liquid crystals (NLC s). In the last few years, Ong has shown that all of the electric and magnetic FT s and most of the optical FT s in a nonconducting homogeneous or homeotropic NLC are second-order transitions. However, applying a suitable static field, the second-order optical FT can be converted to first order in all existing NLC s. Similarly, applying a suitable optical field, the second-order electric or magnetic FT can also be converted to first order ... 

Oseen [1] and Frank [2] far before the development of LCD technology. The dynamic continuum theory of nematics, which is frequently called the nematodynamics, was developed by Ericksen [3] and Leslie [4] (hereafter referred to as E-L theory) based on the classical mechanics just in time for the upsurge of LCD technology. In conjunction with the electrodynamics of continuous media, the static and dynamic continuum mechanics of Oseen-Erank and E-L theory provided theoretical tools to analyze quantitatively key phenomena, e.g., Freedericksz transition of various configurations and associated optical switching characteristics. For the details of E-L theory [5-7] and its development [9,10], please refer to the articles cited. 

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