Dynamics of orientation fluctuations. Order parameter of a nematic liquid crystal

A dynamical approach to the theory of nematic liquid crystals is developed on the basis of the Maier–Saupe model. The relative mean square orientation displacements of the particles from the equilibrium position (the local fluctuations) are calculated as functions of the temperature up to the instability point of the system. It is shown that at sufficiently low temperatures there is a linear growth of the fluctuations, this acquiring a strongly anomalous nature in the neighborhood of the phase transition from the nematic liquid crystal to an isotropic liquid. The temperature dependences of the specific heat and the order parameter are discussed. The results are compared with experimental data and theoretical calculations.