Statistical theory of magnetic field induced phase transitions in negative diamagnetic anisotropy liquid crystals doped with carbon nanotubes

Abstract

A statistical mean-field theory is proposed for describing the magneto-orientational ordering of a composite material, namely a liquid crystal suspension of carbon nanotubes. A nematic liquid crystal with negative anisotropy of diamagnetic susceptibility with the molecules, which have long axes tending to be orthogonal to the applied magnetic field, has been considered as a dispersion medium. Since carbon nanotubes possess positive anisotropy of the diamagnetic susceptibility, they tend to align parallelly to the field, causing competition with the ordering of the liquid crystal matrix. Phase transitions induced by temperature and magnetic field have been studied for different values of the coupling energy of carbon nanotubes with a liquid crystal matrix. It is shown that depending on the temperature, magnetic field induces the transition from a highly ordered nematic phase to a weakly ordered paranematic phase with both the positive and the negative value of the order parameter of the liquid crystal, which respectively corresponds to the orientational anisotropy of the “easy-axis” and “easy-plane” types.