Lehmann Rotation

The first recorded example of thermomechanical coupling, as explained in the Les- 

A chiral nematic film is assumed to be a semi-inifinite planar sample with its helix axis in the z direction bound by planes at z=0 and z=d. The director n is described as in Eq. (1) with 0=0, i.e., [cosd(z, 0, sin 6 z, t), 0]. The boundary conditions are that there are (1) no external body forces, (2) no heat sources within the liquid crystal, and (3) that the velocity vector is zero, i.e., fi=Gi=dij=Wij=0 and that T=T(z)-Conservation of angular momentum [Eq. (83)] then gives 

The energy balance per unit volume (Eq. 91) then gives 

If we assume the polar field comes from the temperature gradient between z=d and z=0, i.e., T] - To d that the director is unbound at the surfaces (i.e., weak anchoring), then the surface torques or couple stresses Zii- ijk i ik zero, which leads to 

If the material constants are assumed to be, in a first approximation, independent of 

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Fig. 4.4.3. Photographs demonstrating the Lehmann rotation effect in cholesteric drops under the action of a DC electric field, (fl)-(c) taken about 30 s apart, illustrate a clockwise rotation of the structure, and (d)- f) an anticlockwise rotation when the voltage is reversed. The material used was a binary nematogenic mixture of alkoxyphenyl-trows-alkylcyclohexyl carboxylates (supplied by Merck) to which was added 5 wt % of cholesteryl chloride. (After reference 60).

Figure 8.11 Illustration of Mauguin twisted nematic cell, reported in 1911. Substrates are thin mica plates, which are uniaxial with their optic axis parallel to plane of plates. Apparently, uniaxial crystal stmcture of mica produces strong azimuthal anchoring of nematic LCs of Lehmann, such that director is parallel (or perpendicular) to optic axis of mica sheets at both surfaces. Mauguin showed that method of Poincard could be used to explain optics of system if it was assumed that LC sample created layer of material with uniformly rotating optic axis in twisted cells.

Figure 0.2 Direct overtone spectroscopy of C2H2 using Fourier transform spectroscopy. Here, at high resolution, the entire band of rotational transitions, which accompany a given vibrational transition, can be resolved. Here the band, in the visible range, corresponding to the direct excitation of v = 5 of the v3 stretch mode is shown. (Adapted from Herman et al., 1991. See also Scherer, Lehmann, and Klemperer, 1983, and Figure 8.4.)...

Zeeman quantum beat spectroscopy was used by Gouedard and Lehmann (1979, 1981) to measure the effect of various lu perturbing states on the gj-values [Eq. (6.5.21)] of more than 150 rotational levels of the Se2 B 0+ state (see Section 6.5.2 and Fig. 6.16). In that experiment, the excitation polarization was perpendicular to the applied magnetic field so that quantum beats were observed between nominal B-state components differing in M by 2. The frequencies of these beats increase linearly from 0 MHz at 0 G until the AM — 2 splitting falls... 

Fig. 4.4.1. Lehmann s diagrams depicting the rotation phenomenon in open cholesteric droplets heated from below. (After Lehmann. )...

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. 

Thus the director rotates about Oz with an angular velocity [Pg.263]

Dickinson, M. 2001. Solving the mysteries of insect flight. Scientific American 284(6) 49-57. Dickinson, M.H., F.-O. Lehmann, and S.P. Sane. 1999. Wing rotation and the aerodynamic basis of insect flight. Science 284(5422) 1954-1960. 

Lehmann has drawn attention to the fact that oils of recent distillation have frequently had a lower specific gravity and optical rotation than usual, and also showed a marked decrease of solubility in 90 per cent, alcohol. The amount of oil obtainable from the herb is also decidedly smaller, seldom being above 2 per cent. Two of the typically abnormal oils showed the following constants —... 

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