Frederiks Transition and Display Applications

The first scientists to investigate liquid crystals soon noticed that sample orientation was strongly influenced by the glass slides between which they sandwiched their nematic phases. Simply rubbing the slide in one direction with drawing paper, molecules are anchored to the surface, parallel to the direction of rubbing. We thus obtain a nematic monocrystal. Optically, the texture is uniform. Suitable surface treatments allow perpendicular anchoring of the molecules and a so-called homeotropic texture. 

Let us now apply a magnetic field H (or an electric field E) perpendicular to the director n of a nematic monocrystal (see Fig. 9.6). If the magnetic (electric) susceptibility of the compound is such that molecules seek to align themselves with the field, it is easy to see that the nematic structure will distort under the antagonistic constraints of anchoring and external field. 

Carrying out the experiment under the microscope, we observe that nothing happens for very small values of H. The visual field remains dark when viewed with crossed polarisers. Then at a threshold value Hq, the field of view is suddenly lit up. The sample has been deformed. This is the Frederiks transition., named after the Russian physicist who first observed the phenomenon in the 1930s. The experiment is easy to carry out in the laboratory, with quite rudimentary equipment. For a nematic slab of thickness 25 gm. He is about 0.2 Tesla and Eq about 400 V/cm. 

Let us attempt to explain the observed phenomena for the simplest Frederiks transition, starting from the deformation energy calculated previously in (9.3), and the magnetic energy which accounts for the effects of the field H. The latter is written 

We note immediately that, when H is strictly perpendicular to n, the magnetic field has no effect. Only fluctuations 8n in n allow the field to act upon the orientation of the director. The elastic energy can be simplified by observing that, for each case represented in Fig. 9.6, the deformation is associated with a single Frank-Oseen constant Ki, and that it depends only on z. Hence we can write 

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