PHYSICAL REVIEW E 88, 024501 (2013) Lehmann effects and rotato-electricity in liquid crystalline systems made of achiral molecules Helmut R. Brand 1,2 * , Harald Pleiner 2 , and Daniel Svenˇ sek 3 1 Theoretische Physik III, Universit¨ at Bayreuth, 95440 Bayreuth, Germany 2 Max-Planck-Institute for Polymer Research, POBox 3148, 55021 Mainz, Germany 3 Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1111 Ljubljana, Slovenia (Received 5 June 2013; published 19 August 2013) We discuss Lehmann effects and rotato-electricity for liquid crystalline phases made of achiral molecules. We point out that for static and dynamic Lehmann effects to exist, it is not necessary to have chiral molecules provided the overall structure has macroscopic chirality. This question is of direct relevance for liquid crystalline phases formed by bent-core molecules provided they have a sufficiently low symmetry. This includes systems which break parity symmetry and have overall C2 or C1 symmetry. We point out that for liquid crystalline gels and elastomers one should be able to observe rotato-electricity for systems with macroscopic chirality. Rotatoelectricity is associated with the relative rotations between two subsystems, namely between the network and the director, in an external electric field. Candidates include gels and even monolayers prepared from bent-core molecules with sufficiently low symmetry. DOI: 10.1103/PhysRevE.88.024501 PACS numbers: 05.70.Ln, 61.30.Gd, 61.30.Dk, 82.70.Gg I. INTRODUCTION The first scientist to observe experimentally the cou- pling between an external force and the orientation of the director field in a cholesteric liquid crystal was Lehmann [1]. He observed the rotation of the director in a cholesteric droplet in an external temperature gradient. Several decades later Leslie [2] (compare also the text- books by de Gennes [3] and Chandrasekhar [4]) described Lehmann effects in a continuum theory for cholesteric liquid crystals assuming a helical structure and a purely dynamic coupling. After Lehmann’s pioneering paper it took almost nine decades before an experiment of a similar nature was performed [5, 6] for cholesteric droplets in an external electric field in the two phase region near the isotropic - cholesteric phase transition. Stimulated by the exper- imental work described by Madhusudana and Pratibha [5], Lehmann-type effects were reexamined using the hy- drodynamic approach [7]. It turns out that in general Lehmann effects in external fields have a static as well as a dissipative dynamic contribution [7]. In addition it was pointed out, that Lehmann-type effects are not con- fined to cholesteric liquid crystals, but can also arise for chiral smectic liquid crystals such as smectic C * ,I * and F * [7]. It was also suggested already in [7] to use freely suspended smectic C * films to observe Lehmann-type ef- fects. Indeed, only recently have Lehmann-type effects been reported experimentally for freely suspended smec- * corresponding author: brand@uni-bayreuth.de tic C * with a layer thickness of about 3,..., 15 layers in a concentration gradient by Tabe’s group [8]. In these experiments phase winding patterns of Lehmann-type due to concentration gradients have been documented in detail [8]. The observation of these patterns comple- ments nicely the studies on pattern formation in freely suspended smectic C and smectic C * films due to a me- chanical torque [9] and due to rotating electric fields [10– 12]. Inspired by biophysical work on synthetic molecular motors [13–15], Tabe and Yokoyama [16] did the next decisive experimental step by studying Lehmann-type effects in Langmuir monolayers and the associated pat- tern formation due to a concentration gradient near an air-liquid interface. They demonstrated experimentally that effectively one layer of a chiral smectic C * phase was enough to generate Lehmann-type effects [16], which were also shown to be absent when nonchiral molecules of the same type were used. These experimental results are put on a firm basis from a modeling point of view [17] by introducing the concept of macroscopic chirality. The latter means the existence of a pseudoscalar quantity, q 0 , that changes sign under spatial inversion and that allows the discrimination of the inverted state from the original one. The existence of q 0 is not necessarily based on the presence of chiral molecules, and macroscopic chirality can occur in systems made of achiral molecules, if the symmetry of the phase is low enough. In the realm of biophysical applications we also sug- gested that inverse Lehmann-type effects can be used as a microscopic pump [18]. Stimulated by recent progress on liquid crystalline phases formed by banana-shaped or bent-core molecules