On the theory of the dynamical properties of nematics

The Leslie–Ericksen coefficients of a thermotropic nematic are determined by using an approximate solution of the Fokker–Planck equation for the one-particle distribution function over orientations of the nematic molecules. The results show that the well-known Doi–Edwards theory of the dynamical properties of nematics leads to a qualitatively wrong result for the Leslie angle. The “isotropic medium - nematic” (I–N) transition induced by the shear flow is considered. When the temperature decreases, the I–N transition in the shear flowing system takes place at the temperature T1 higher than the temperature Tc of the equilibrium transition in the motionless system. The interface boundary in this case is parallel to the plane formed by the flow velocity and its gradient. When the shear flowing nematic phase is heated, the N–I transition occurs at another temperature T2, and the following inequalities T1>T2>Tc hold. In this case the boundary between the isotropic and nematic phases is perpendicular to the flow velocity. Thus, unlike the equilibrium phase transition, a temperature hysteresis of the phase transition is expected.