Landau-de Gennes modeling of confinement effects and cybotactic clusters in bent-core nematic liquid crystals

We study bent-core nematic (BCN) systems in two-dimensional (2D) and three-dimensional (3D) settings, focusing on the role of cybotactic clusters, phase transitions, confinement effects, and applied external fields. We propose a generalized version of Madhusudana's two-state model for BCNs [Phys. Rev. E 96, 022710 (2017)2470-004510.1103/PhysRevE.96.022710] with two order parameters: Q_{g} to describe the ambient ground-state (GS) molecules and Q_{c} to describe the additional ordering induced by the cybotactic clusters. The equilibria are modeled by minimizers of an appropriately defined free energy, with an empirical coupling term between Q_{g} and Q_{c}. We demonstrate two phase transitions in spatially homogeneous 3D BCN systems at fixed temperatures: a first-order nematic-paranematic transition followed by a paranematic-isotropic phase transition driven by the GS-cluster coupling. We also numerically compute and give heuristic insights into solution landscapes of confined BCN systems on 2D square domains, tailored by the GS-cluster coupling, temperature, and external fields. This benchmark example illustrates the potential of this generalized model to capture tunable director profiles, cluster properties, and potential biaxiality induced by antagonistic Q_{g} and Q_{c} profiles.