Liquid-crystal composites of carbon nanotubes in a magnetic field: Bridging continuum theory and a molecular-statistical approach.

Abstract

We propose an approach combining the continuum theory and molecular-statistical approach for a suspension of carbon nanotubes based on a negative diamagnetic anisotropy liquid crystal. Using the continuum theory, we show that in the case of an infinite sample in suspension it is possible to observe peculiar magnetic Fréedericksz-like transitions between three nematic phases: planar, angular, and homeotropic with different mutual orientations of liquid-crystal and nanotube directors. The transition fields between these phases are found analytically as functions of material parameters of the continuum theory. To account for the effects associated with temperature changes, we propose a molecular-statistical approach that allows obtaining the equationsof orientational state for the orientation angles of the main axes of the nematic order, i.e., the liquid-crystal and carbon-nanotube directors in a similar form as was obtained within the continuum theory. Thus, it is possible to relate the parameters of the continuum theory, such as the surface-energy density of a coupling between molecules and nanotubes, to the parameters of the molecular-statistical model and the order parameters of the liquid crystal and carbon nanotubes. This approach allows determining the temperature dependencies of the threshold fields of transitions between different nematic phases, which is impossible in the framework of the continuum theory. In the framework of the molecular-statistical approach we predict the existence of an additional direct transition between the planar and homeotropic nematic phases of the suspension, which cannot be described based on the continuum theory. As the main results, the magneto-orientational response of the liquid-crystal composite is studied and a possible biaxial orientational ordering of the nanotubes in the magnetic field is shown.