Colloidal nanoparticles in liquid crystals: bulk properties, biaxiality and untwisting in cholesterics

Abstract We study the effects of colloidal nanoparticles (NPs) in liquid crystal samples in the dilute limit, in a Landau–de Gennes theoretical framework. The effects of the suspended NPs are captured by a homogenized energy, as outlined in Canevari & Zarnescu (2020a, Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation. Math. Models Methods Appl. Sci., 30:309–342). For spatially homogeneous samples, we explicitly compute the critical points and minimizers of the modified Landau–de Gennes energy and show that the presence of NP eliminates the first-order isotropic-nematic phase transition, stabilizes elusive biaxial phases over some temperature ranges and that the symmetry of the NP boundary conditions or surface treatments dictates the bulk equilibrium phase at high temperatures. We also numerically demonstrate structural transitions from twisted helical director profiles to untwisted director profiles in cholesteric-filled channel geometries, driven by the collective effects of the NPs and increasing temperature. These transitions are reversible upon lowering the temperature in sufficiently large domains, where thermal hysteresis can also be observed. This behaviour opens interesting avenues for tuning the optical properties of confined, nano-doped cholesteric systems.