Microscopic description of nematic liquid crystal viscosity

The problem of nematic viscosity is shown to be successfully solved within the framework of a microscopic description. The Kuzuu-Doi approach to hydrodynamics [N. Kuzuu and M. Doi, J. Phys. Soc. Jpn. 52, 3486 (1983)] for a system consisting of anisotropic molecules is reviewed. It has been shown that the incorrect form of the microscopic stress tensor that is used by Doi [M. Doi, J. Polym. Sci. 19, 229 (1981)] does not influence final expressions for the viscosity coefficients due to the fact that the external magnetic field is taken into account. Molecular expressions for the Leslie viscosity coefficients are calculated by use of the theory of Osipov and Terentjev [Z. Naturforsch. Teil A 44, 785 (1989); Phys. Lett. A 134, 301 (1989)]. A systematic solution of the differential kinetic equation is presented. The nonequilibrium distribution function obtained from the kinetic equation allows us to transform Osipov-like expressions for the viscosity coefficients exactly into those obtained by Kuzuu and Doi. The above-mentioned approaches are proved to be equivalent. A realistic mean potential is applied to the expressions obtained for the Leslie coefficients for the case of 4-methoxybenzylidene-4′-n-butylaniline. A comparison of theoretical results and appropriate experimental data is shown to be very good.