Smectics Frederiks transitions

FIGURE 6.31. The Frederiks transition in a smectic C. Three principal directions of the field are shown, for which simple finite orientational deformations can occur (El, E2, E3). 

When the field is oriented along the director, a Frederiks transition is possible when 2 > 3- The director should rotate around the z-axls not changing its angle ft, so that in its final position, i.e., in the strong field limit, its projection onto the smectic planes, coincides with the y-axis. The corresponding threshold field (Eo)3 is proportional to ( 2 A field... 

The Frederiks transition in smectics C has been investigated by a variational approach to the solution of the Euler-Lagrange equation [115]. Only changes in the azimuthal angle of the director were considered and the interlayer spacing and the tilt angle were assumed to be invariant. The Frederiks transition was shown to occur in a stepwise manner from one stable configuration of the azimuth of the director to the other. 

Measurements have been made of the Frederiks transition in various smectic C liquid crystals [158-161], using the conventional sandwich cells and optically transparent electrodes. The director was oriented uniaxially by rubbing the electrodes, and the smectic layers were tilted with respect to the cell plane (a bookshelf geometry). Due to positive dielectric anisotropy, an electric field applied along the cell normal z direction) (Fig. 22) induces director rotation around the normal to the smectic layers. 

Figure 22. Geometry of the Frederiks transition for a planar-oriented smectic C liquid crystal.

Frederiks transition in the hexagonal smectic I phase (and also in the smectic C phase with a weak hexagonal order [163]) has... 

It is also possible to use turbidity measurements to evaluate elastic constants (Fig. 5, though elastic constants measured in this way for alkylcyanobiphenyls (nCBs) [25] and mixtures [26] are consistently higher than those determined by Frederiks transition studies. Hakemi [27] measured j, 22 and 33 for 8CB (octylcyano biphenyl) close to the nematic-smectic A phase transition and deduced a value of the critical exponent from the divergence of 22 and 33. 

T. Carlsson, I.W. Stewart and F.M. Leslie, Theoretical studies of smectic C liquid crystals confined in a wedge Stability considerations and Frederiks transitions, Liq. Cryst, 9, 661-678 (1991). 

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