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Landau-de Gennes Modelling 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 generalised version of Madhusudana's two-state model for BCNs in [Madhusudhana NV, Physical Review E, 96(2), 022710] with two order parameters: $\mathbf{Q}_g$ to describe the ambient ground-state (GS) molecules and $\mathbf{Q}_c$ to describe the additional ordering induced by the cybotactic clusters. The equilibria are modelled by minimisers of an appropriately defined free energy, with an empirical coupling term between $\mathbf{Q}_g$ and $\mathbf{Q}_c$. 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 generalised model to capture tunable director profiles, cluster properties and potential biaxiality induced by antagonistic $\mathbf{Q}_g$ and $\mathbf{Q}_c$-profiles.