Extended free-energy functionals for achiral and chiral ferroelectric nematic liquid crystals: theory and simulation.

Polar nematic liquid crystals are new classes of condensed-matter states, where the inversion symmetry common to the traditional apolar nematics is broken. Establishing theoretical descriptions for the novel phase states is an urgent task. Here, we develop a Landau-type mean-field theory for both the achiral and chiral ferroelectric nematics. In the polar nematic states, the inversion symmetry breaking adds three new contributions: an additional odd elastic term (corresponding to the flexoelectricity in symmetry) to the standard Oseen-Frank free energy, electrostatic effect and an additional Landau term relating to the gradient of local polarization. The coupling between the scalar order parameter and polarization order should be considered. In the chiral and polar nematic state, we reveal that the competition between the twist elasticity and polarity dictates effective compressive energy arising from the quasi-layer structure. The polarization gradient is an essential term for describing the ferroelectric nature. Besides, we successfully simulate an experimentally reported structural transition in ferroelectric nematic droplets from a concentric-vortex-like to a line-disclination-mediated topology based on the developed theory. The approaches provide theoretical foundations for testing and predicting polar structures in emerging polar liquid crystals.