Symmetries and physical properties of polar columnar phases in materials composed of achiral molecules

– Motivated by puzzling experimental observations made in compounds composed of banana-shaped molecules, we investigate the symmetries and the physical properties of liquid crystalline columnar phases with a macroscopic polarization in achiral materials. This study is driven by two key observations made for the still poorly understood B7 phase: a) freely suspended films decompose spontaneously into strands and b) several of the textures observed for the B7 phase are reminiscent of textures observed for liquid crystalline columnar phases. One of the main results of our analysis is that a chiral phase of C1-symmetry results as soon as the macroscopic polarization includes an angle different from zero or 90◦ with the columnar axes. We argue that a chiral columnar phase composed of achiral molecules, not previously considered for classic columnar phases, is sufficient to account for many of the unusual physical properties of B7. Introduction. – Liquid crystalline phases formed in compounds composed of achiral banana-shaped molecules have recently attracted considerable attention [1–13]. A still puzzling phenomena observed in this field is the phase transition from an optically isotropic liquid phase to the B7 phase [9,14]. Neither the symmetry nor the ground state of B7 are understood. So far large B7 monodomains have not been successfully grown. Presumably it is not a typical smectic phase as it does not form stable freely suspended films. Rather, B7 films break up into strands [14, 15]. X-ray investigations give rise to many diffraction peaks that cannot be indexed by a standard smectic or columnar phase known to form in other lowmolecular-weight liquid crystalline compounds [14]. In the optical microscope, one observes many different patterns on cooling including: spirals of both hands growing into the isotropic phase, myelinic patterns and patterns showing spatial modulations, sometimes regular, in a second direction [9, 14]. Intrigued by the spontaneous break-up of freely suspended films into strands and the observation of textures that closely resemble those observed in discotic liquid crystals [16,17], we study the symmetries and physical properties of columnar phases that possess a macroscopic polarization even when composed of achiral molecules. While this study is a natural complement to our previous work on smectic and nematic phases with a macroscopic polarization in achiral systems [6, 11], it has uncovered a novel columnar structure not previously observed