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Ferroelectric nematic liquid crystals are formed by achiral molecules with large dipole moments. Their three-dimensional orientational order is described as unidirectionally polar. We demonstrate that the ground state of a flat slab of a ferroelectric nematic unconstrained by externally imposed alignment directions is chiral, with left- and right-handed twists of polarization. Although the helicoidal deformations and defect walls that separate domains of opposite handedness increase the elastic energy, the twists reduce the electrostatic energy and become weaker when the material is doped with ions. This work shows that the polar orientational order of molecules could trigger chirality in soft matter with no chemically induced chiral centers.

 

We explore the structures and confinement-induced edge dislocations in Grandjean-Cano wedge cells filled with the recently discovered chiral ferroelectric nematic (N_F^*) and chiral antiferroelectric smectic-Z 〖(SmZ〗_A^*). The chiral mixture is formed by DIO mesogen doped with a chiral additive. Wedge cells with parallel and antiparallel rubbing at the opposite plates show quantitatively different structures which is attributed to the polar in-plane anchoring of the spontaneous polarization at the rubbed substrates. The helical pitch shows a non-monotonous temperature dependence upon cooling, increasing as the temperature is lowered to the N^*-SmZ_A^* phase transition. The SmZ_A^* formed from an untwisted N^* in the thin portion of the wedge shows a bookshelf (BK) geometry, whereas the twisted N^* transforms into a twisted planar (PA) SmZ_A^* structure. In the N_F^* phase, the untwisted N^* becomes twisted in a wedge with antiparallel assembly of plates and monodomain in wedges with parallel assembly. The twisted regions of N_F^* show only one type of Grandjean zones separated by thick edge dislocations with Burgers vector b=P; the neighboring regions differ by 2π- twist. 

Spontaneous electric polarization of solid ferroelectrics follows aligning directions of crystallographic axes. Domains of differently oriented polarization are separated by domain walls (DWs), which are predominantly flat and run along directions dictated by the bulk translational order and the sample surfaces. Here we explore DWs in a ferroelectric nematic (N_F) liquid crystal, which is a fluid with polar long-range orientational order but no crystallographic axes nor facets. We demonstrate that DWs in the absence of bulk and surface aligning axes are shaped as conic sections. The conics bisect the angle between two neighboring polarization fields to avoid electric charges. The remarkable bisecting properties of conic sections, known for millennia, play a central role as intrinsic features of liquid ferroelectrics. The findings could be helpful in designing patterns of electric polarization and space charge.

 

Abstract Surface interactions are responsible for many properties of condensed matter, ranging from crystal faceting to the kinetics of phase transitions. Usually, these interactions are polar along the normal to the interface and apolar within the interface. Here we demonstrate that polar in-plane surface interactions of a ferroelectric nematic N F produce polar monodomains in micron-thin planar cells and stripes of an alternating electric polarization, separated by $${180}^{{{{{{\rm{o}}}}}}}$$ 180 o domain walls, in thicker slabs. The surface polarity binds together pairs of these walls, yielding a total polarization rotation by $${360}^{{{{{{\rm{o}}}}}}}$$ 360 o . The polar contribution to the total surface anchoring strength is on the order of 10%. The domain walls involve splay, bend, and twist of the polarization. The structure suggests that the splay elastic constant is larger than the bend modulus. The $${360}^{{{{{{\rm{o}}}}}}}$$ 360 o pairs resemble domain walls in cosmology models with biased vacuums and ferromagnets in an external magnetic field.