A molecular-statistical model of liquid crystalline suspensions of ferromagnetic carbon nanotubes

One of the primary tools for describing temperature phase transitions in nematic liquid crystals is the Maier-Saupe theory, which is based on the mean-field or self-consistent field method. Despite its long history, this theory remains relevant and forms the foundation of the statistical thermodynamics of liquid crystals. A significant advantage of the Maier-Saupe theory is that it belongs to the class of exactly solvable models in statistical physics and allows for the calculation of temperature-dependent order parameters that align with experimental data. However, even in the simplest case of a uniaxial nematic liquid crystal, the self-consistency equation derived within the Maier-Saupe theory is nonlinear and integral, this necessitating numerical solutions. This model can be significantly simplified by employing the spherical approximation, a well-known method in the theory of magnetism. The key feature of this approach is that the integrals appearing in the self-consistency equation are reduced to Poisson integrals, which can be evaluated exactly, and the equation itself takes on a simple algebraic form. The present study uses the spherical approximation to consider a modification of the Maier-Saupe theory for the case of a colloidal suspension of ferromagnetic carbon nanotubes in a nematic liquid crystal. The method for deriving the orientational state equations for the suspension is described in detail. The advantages and features of the proposed approach are discussed, and a comparison is made with previously presented methods where the spherical approximation was used to describe liquid crystals and suspensions based on them.