Bulk mesophases modeling of ferroelectric nematic liquid crystals

Ferroelectric nematic liquid crystals (FNLCs) are emerging materials that combine orientational order with spontaneous macroscopic polarization. They exhibit distinctive properties, such as polar domain formation, field-tunable textures, and strong electro-elastic couplings. However, due to the complexity of the underlying mechanisms, the bulk structure of the emergent mesophases is not yet fully understood, and a generalized description of all observed phases is still lacking. Here, we demonstrate the bulk mesophases of FNLCs as stabilized by a combination of flexoelectricity, elasticity, bulk ordering, and polarization-nematic couplings. Specifically, we develop Landau de-Gennes-like free energy framework that predicts and explains the structure of major experimentally observed ferroelectric nematic phases, including ferroelectric nematic, antiferroelectric splay nematic, apolar nematic, and isotropic phase, notably together with the correct phase transition sequences. Additionally, we predict the possible existence of new bend-instability-driven mesophase characterized by periodic splay-bend structure. Finally, we calculate a complete phase diagram of bulk ferroelectric nematics as dependent on the key coupling mechanisms, which could possibly enable the predictive design and applications of these novel emergent ferroelectric nematic materials.