Lehmann effect in compensated cholesteric liquid crystals

Abstract

In 1900, Otto Lehmann observed that the texture of a cholesteric droplet heated from below can rotate continuously (Ann. Phys. (Leipzig), 2 (1900) 649). This observation (which has never been reproduced, to our knowledge) was explained in 1968 by Leslie (Proc. R. Soc. London, Ser. A, 307 (1968) 359) from symmetry arguments accounting for the chirality of the material. In 1982, Éber and Jánossy showed experimentally that a similar thermomechanical effect also exists in a compensated cholesteric (in which the helix is completely unwound). This result was immediately questioned by Pleiner and Brand who claimed that only the symmetry of the phase (and not that of the molecule) determines the structure of the macroscopic constitutive equations (Mol. Cryst. Liq. Cryst. Lett., 5 (1987) 61). According to them, the Lehmann effect should necessarily vanish at the compensation temperature. In order to understand the correct interpretation, we conducted very carefully the experiment in two complementary geometries. Our results agree with those of Éber and Jánossy, confirming the predominance of microscopic symmetries over macroscopic ones.

Direct measurement of the thermomechanical Lehmann coefficient in a compensated cholesteric liquid crystal

“…In previous works [7,8], we showed that q changes linearly with temperature around T c within an excellent approximation. This allowed us to write that (7) where dq dT is a constant.…”

“…In our experiment, d =25μm and the maximum temperature gradient used was G ≈ 6 × 10 4 • C/m. Knowing that K 2 ≈ 3 × 10 −12 N [7,8] at T c ,w ee s t i m a t et h a t ξ<3 × 10 −12 kg m K −1 s −2 in our CC-8OCB mixture. This conclusion is not incompatible with a previous estimate of a similar coefficient in the liquid crystal 5CB (pentylcyanobiphenyl) in which ξ ∼ 10 −12 kg m K −1 s −2 [17].…”

“…Recently, we reported the first preliminary observation of the continuous Lehmann rotation of the cholesteric helix under the action of a temperature gradient [7,8]. This experiment was made possible thanks to the development of a new surface treatment allowing for planar and sliding anchoring of the molecules at the glass plates limiting the sample [9].…”

Does the electric Lehmann effect exist in cholesteric liquid crystals?

“…Although this result was conform to theoretical predictions of Pleiner and Brand [19,20], it seemed to contradict previous experiments ofÉber and Jánossy [21], who found that the "classical" thermomechanical Lehmann coefficient was different from 0 at the compensation temperature. Intrigued by these contradictions, we recently redid the experiment ofÉber and Jánossy and confirmed their results [22,23]. Being thus in disagreement with Pleiner and Brand predictions and with Padmini and Madhusudana findings, we felt it was important to also redo and reanalyze the experiment of Padmini and Madhusudana, while extending it to another geometry.…”

“…From these measurements and others described in refs. [22,23], we calculated the dielectric anisotropy ε a = ε − ε ⊥ = 4.8 ± 0.3. We recall that the subscripts and ⊥ refer to the director orientation.…”