Polarization patterns of ferroelectric nematics not constrained by polar surface interactions

Surface interactions play an important role in aligning liquid crystals. The recently discovered ferroelectric nematic (N_F) shows a uniform monocrystal orientation of spontaneous electric polarization when confined between two plates with unidirectionally treated substrates. We explore N_F structures in which the surface conditions are less restrictive and produce either bidirectional apolar or azimuthally degenerate alignment at the bounding plates. The bidirectional apolar alignment with a prepatterned +1 radial defect is achieved by photoalignment. The radial structure splits into domains of splay and twist deformations, in which the polarization alternates between being inward and outward directed. In the case of azimuthally degenerate confinement at one plate, the texture splits into domains with an alternating sense of twist. Both patterns form to reduce the electrostatic energy associated with the unidirectional orientation of electric polarization. The study demonstrates a dramatic difference between the domain structures in solid ferroelectrics, in which the polarization follows the crystallographic axes, and liquid ferroelectrics, in which the absence of these axes allows the polarization field to deform smoothly in response to the boundary conditions and the electrostatic energy minimization.