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 Madhusudana (2017) with two order parameters: 𝐐g to describe the ambient ground-state (GS) molecules and 𝐐c 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 𝐐g and 𝐐c. 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 𝐐g and 𝐐c-profiles.