Orientational Transitions in Magnetically Compensated Liquid-Crystal Suspensions of Ferromagnetic Carbon Nanotubes

Abstract

Purpose of research is to study the influence of ferromagnetic carbon nanotubes on orientational transitions in magnetically compensated liquid-crystal suspensions.Methods. The problem was solved in the framework of the continuum theory. By minimizing the Helmholtz free energy functional, a system of Lagrange-Euler equations is obtained that determines the equilibrium dependences of the orientation angles of liquid crystal and impurity ferromagnetic carbon nanotubes directors, as well as the concentration distributions of the dispersed phase of the suspension as a function of the transverse coordinate, material parameters, and magnetic field strength.Results. It is shown that in the presence of an external magnetic field, a liquid-crystal suspension of ferromagnetic carbon nanotubes can be in a non-uniform phase (angular phase) and two uniform phases (planar and homeotropic phases). Expressions for the threshold fields of transitions between coexisting orientational phases are obtained analytically as functions of the material parameters of the composite. Diagrams of the orientational phases of the suspension are plotted.Conclusion. As a result of the research, it was shown that the addition of low concentrations of ferromagnetic carbon nanotubes can significantly reduce the threshold of the magnetic Fréedericksz transition compared to a pure liquid crystal, which is important for various technical applications. The obtained analytical formulas for the threshold fields of transitions between different orientational phases can be used to determine the anchoring energy and material parameters of suspensions of ferromagnetic carbon nanotubes in a liquid crystal.