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

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 equations of 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.

Molecular-statistical theory of ferromagnetic liquid crystal suspensions.

A tensor variant of molecular-statistical theory is developed, within the framework of which it is possible to describe the appearance of spontaneous magnetization of anisotropic ferromagnetic nanoparticles dispersed in a nematic liquid crystal. Along with the tensor order parameters characterizing the orientational ordering of the liquid crystal and dispersed anisometric particles, the vector order parameter determining the magnetization of the ensemble of particles is additionally taken into account. A comparison between the previously known phenomenological theories of ferronematics and the proposed molecular-statistical theory is made. Phase diagrams of the suspension are constructed and the mean-field theory parameters are calculated on the basis of experimental data available in the literature.

Magnetic segregation effect in liquid crystals doped with carbon nanotubes.

We study the orientational transitions in a suspension of carbon nanotubes in a nematic liquid crystal induced by an external magnetic field. The case of a finite orientational anchoring of liquid crystal molecules at the surface of doped carbon nanotubes is considered. It is shown that in a magnetic field the initial homogeneous planar texture of the liquid crystal-carbon nanotubes mixture is disturbed in a threshold manner (Fréedericksz transition). The orientational and concentration distributions of the suspension are studied for different values of the magnetic field strength and segregation intensity of the impurity subsystem. The optical phase lag between ordinary and extraordinary rays of light transmitted through a layer of a liquid crystal composite is calculated. The possibility of changing the nature of the Fréedericksz transition from second order to first order is shown. This tricritical behavior is related to the redistribution of the carbon nanotubes (segregation effect) inside the layer.

Magnetic field induced orientational transitions in liquid crystals doped with carbon nanotubes.

We propose a continuum theory of orientational phase transitions induced by an external magnetic field in a suspension of carbon nanotubes in a nematic liquid crystal. It is shown that in a magnetic field a non-uniform and two different uniform phases are possible in the suspension. The uniform phases of the suspension differ by the type of orientational coupling of nanotubes with the liquid crystal matrix (the planar type when the nanotubes are oriented along the matrix director, and the homeotropic type when the nanotubes are perpendicular to the director). The possibility of a redistribution of the nanotube concentration (segregation effect) is shown. The fields of orientational transitions between uniform and non-uniform phases of the suspension are found analytically. It is shown that, when the nanotubes are weakly coupled to the matrix, the magnetic field induces reentrant transitions (uniform planar phase-non-uniform phase-uniform homeotropic phase-non-uniform phase). These transitions can be of first or of second order depending on the carbon nanotubes segregation intensity.