The Lehmann rotation phenomenon

An example of this type of thermomechanical coupling appears to have been observed by Lehmann in cholesteric liquid crystals very soon after their discovery. He found that droplets of the material when heated from below seemed to be rotating violently, but from optical studies he concluded that it was not the drops themselves but the structure that was rotating. Fig. 4.4.1 shows a few of the many sketches that he made depicting his observations. Leslie s equations offer a simple explanation of the phenomenon because of the absence of mirror symmetry, an applied field, which is a polar vector, can result in a torque, which is an axial vector. 

Let the cholesteric film be bounded between the planes z = 0 and z = h, and let there be a temperature gradient along the screw axis z. The components of the director in a right-handed cartesian coordinate system are cos0(z, ), sin0(z, ),0. We assume that there are no heat sources within the liquid crystal, no external body forces and that the velocity vector is zero. Hence T = T(z),ff = G, = rfy = Wy = 0. Thus from (4.3.4) 

Thus the director rotates about Oz with an angular velocity w, which explains Lehmann s observations. 

The cholesteric material was then doped with a small quantity of a non-mesomorphic epoxy compound, Lixon, which lowered the cholesteric-isotropic transition temperature and gave rise to a broad two-phase region. Because the glass plates have greater affinity for Lixon than for the liquid crystal compound, the cholesteric drops were surrounded on all sides by the isotropic phase. With thick cells, spherical drops with the characteristic /-line of strength 2 were formed (fig. 4.4.2). In thin cells ( 8 pm thick) flattened drops were obtained in which the central portion 

For a defect-free planar structure, the angular velocity in the presence of an electric field E is in analogy with (4.4.7), 

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