Dielectric response of a ferroelectric nematic liquid crystalline phase in thin cells

We studied the dielectric properties of a polar nematic phase (NF) sandwiched between two gold or ITO electrodes, serving as a cell surface. In bulk, NF is expected to exhibit a Goldstone mode (phason), because polarisation can uniformly rotate with no energy cost. However, because the coupling between the direction of nematic director and polarisation is finite, and the confinement, even in the absence of the aligning surface layer, induces some energy cost for a reorientation of polarisation, the relaxation frequency of the phason mode is measured in a kHz regime. The phason mode is easily quenched by a bias electric field, which enables fluctuations in the magnitude of polarisation to be followed in both the ferroelectric and paraelectric nematic phases. This amplitude (soft) mode is also influenced by boundary conditions. A theory describing the phase and amplitude fluctuations in the NF phase shows that the free energy of the system and, consequently, the dielectric response are dominated by polarisation-related terms with the flexoelectricity being relevant only at a very weak surface anchoring. Contributions due to the nematic elastic terms are always negligible. The model relates the observed low-frequency mode to the director fluctuations weakly coupled to polarisation fluctuations.