In 1900, Otto Lehmann observed the continuous rotation of cholesteric drops when subjected to a temperature gradient. This thermomechanical phenomenon was predicted 68 years later by Leslie from symmetry arguments but was never reobserved to our knowledge. In this Letter, we present an experiment allowing quantitative analysis of the Lehmann effect at the cholesteric-isotropic transition temperature. More precisely, we measure the angular velocity of cholesteric drops as a function of their size and the temperature gradient and we show that applying an electric field can stop the drop rotation. From these observations and a theoretical model we estimate the Lehmann coefficient $\nu$.

The thermomechanical Lehmann coefficient ν is directly measured as a function of temperature in a compensated cholesteric liquid crystal. The method consists of observing the continuous rotation of the director in samples treated for planar sliding anchoring when a temperature gradient is applied perpendicularly to the director. The main result is that there is no relationship between the Lehmann coefficient and the equilibrium twist q. In particular, we confirm that ν does not vanish at the compensation temperature at which q=0, in agreement with previous static measurements of Éber and Jánossy (Mol. Cryst. Liq. Cryst., 72 (1982) 233) and of ourselves (Europhys. Lett., 80 (2007) 26001). In addition, the sign of the Lehmann coefficient is determined by observing between crossed polarizers the sense of rotation of the extinction branches of the disclination lines.

Suspended droplets of cholesteric (chiral nematic) liquid crystals spontaneously rotate in the presence of a heat flux due to a temperature gradient, a phenomenon known as the Lehmann effect. So far, it is not clear whether this effect is due to the chirality of the phase and the molecules or only to the chirality of the director field. Here, we report the continuous rotation in a temperature gradient of nematic droplets of a lyotropic chromonic liquid crystal featuring a twisted bipolar configuration. The achiral nature of the molecular components leads to a random handedness of the spontaneous twist, resulting in the coexistence of droplets rotating in the two senses, with speeds proportional to the temperature gradient and inversely proportional to the droplet radius. This result shows that a macroscopic twist of the director field is sufficient to induce a rotation of the droplets, and that the phase and the molecules do not need to be chiral. This suggests that one can also explain the Lehmann rotation in cholesteric liquid crystals without introducing the Leslie thermomechanical coupling—only present in chiral mesophases. An explanation based on the Akopyan and Zeldovich theory of thermomechanical effects in nematics is proposed and discussed.

We propose a surface treatment allowing one to obtain a sliding planar anchoring of nematic (or cholesteric) liquid crystals. It consists of depositing a thin layer of the polymercaptan hardener of an epoxy resin on an isotropic substrate (bare or ITO-coated glass plates). Microscopic observations of defect annihilations and capacitance measurements show that the molecules align parallel to the surface and slide viscously on it when they change orientation, which implies a zero (or extremely small) azimuthal anchoring energy. In contrast, the zenithal anchoring energy $W_{\theta }$ is found to be larger than $3\times {10}^{-5}\mathrm{J}∕{\mathrm{m}}^2$. We also measured the liquid crystal rotational surface viscosity ${\gamma }_S$ by a thermo-optical method using the large temperature variation of the pitch of a compensated cholesteric mixture. We found that the sliding length ${\gamma }_S∕{\gamma }_1$ (where ${\gamma }_1$ is the bulk rotational viscosity) is very large in comparison with the length of a liquid crystal molecule. This result is explained by a simple model which takes into account the diffusion of the liquid crystal within the polymer layer.