Abstract
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.