The Frederiks Transition in a Smectic

Depending on the arrangement of the smectic layers and the director of the liquid crystal relative to the limiting surfaces, four different configurations 

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). 

Let us identify the three main values of the diamagnetic susceptibility i (i = 1,2,3), where 63 corresponds to the direction along the director, 1 corresponds to the direction perpendicular to the director in the x, -plane, and 62 corresponds to the direction perpendicular to the preceding two (in Fig. 6.31 the directions of the fields Ei, E2, and E3 correspond to these three values specified for Si). 

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 

El L Lo, lying in the x, 2 -plane, induces the same distortion when 62 61. Now the threshold for the reorientation of the director around the z-axis Eo)i is proportional to 62 — Finally, when E2 y the 

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