Lehmann effect in nematic and cholesteric liquid crystals: a review

The Lehmann effect is the continuous rotation of cholesteric droplets subjected to a temperature gradient. Discovered by Otto Lehmann in 1900, this effect was re-observed recently by several authors not only in cholesterics but also in nematics when the director field is twisted inside the droplets. In most experiments, the droplets coexist with their isotropic liquid, but the Lehmann effect can also be observed when the droplets are dispersed in an isotropic liquid in which the LC is partly miscible. After a brief history on the Lehmann effect and its first explanation by Leslie in 1968, we will review the main experimental results obtained on this subject from 2008. In particular, the role of the temperature gradient, of the size of the droplets, of the textures and their orientation with respect to the temperature gradient, of the confinement effects, of the impurities and of the concentration of chiral molecules will be described. A special emphasis will also be placed on the research of hydrodynamic effects to answer the fundamental question of whether it is just the texture or the droplet itself that rotates. We will then review the different models proposed in the literature to explain the Lehmann effect. Among them are two thermomechanical models directly based on the Leslie explanation (named TM1 and TM2 models), a thermomechanical model of rotating texture ‘surfing’ on a heat wave (TM3 model), a model of melting-growth (MG model) that only applies when the droplets coexist with their own isotropic liquid, and a pure hydrodynamic model (H model) based on the existence of Marangoni flows – currently, only evidenced in emulsified cholesterics. The strengths and weaknesses of each model will be discussed in relation with the experimental results.