Mesoscopic model for the viscosities of nematic liquid crystals

Based on the definition of the mesoscopic concept by Blenk et al. [Physica A 174, 119 (1991); J. Noneq. Therm. 16, 67 (1991); Mel. Cryst. Liq. Cryst; 204, 133 (1991)] an approach to calculate the Leslie viscosity coefficients for nematic liquid crystals is presented. The approach rests upon the meso scopic stress tenser, whose structure is assumed similar to the macroscopic leslie viscous stress. The proposed form is also the main dissipation part of the mesoscopic Navier-Stakes equation. On the, basis of the corresponde nce between microscopic and mesoscopic scales a mean-held mesoscopic potent ial is introduced. It allows us to obtain the stress tenser angular velocit y of the free rotating molecules with the help of the orientational Fokker- Planck equation. The macroscopic stress tenser is calculated as an average of the mesoscopic counterpart. Appropriate relations among mesoscopic visco sities have been found. The mesoscopic analysis results are shown to be con sistent with the diffusional model of Kuzuu-Doi and Osipov-Terentjev with t he exception of the shear viscosity lug. In the nematic phase alpha(4) is s hown to have two contributions: isotropic and nematic. There exists an indi cation that the influence of the isotropic part is dominant over the nemati c part. The so-called microscopic stress tenser used in the microscopic the ories is shown to be the mean-field potential-dependent representation of t he mesoscopic stress tenser. In the limiting case of total alignment the Le slie coefficients are estimated for the diffusional and mesoscopic models. They are compared to the results of the affine transformation model of the perfectly ordered systems. This comparison shows disagreement concerning th e rotational viscosity, whereas the coefficients characteristic for the sym metric part of the viscous stress tenser remain the same. The difference is caused by the hindered diffusion in the affine model case. [S1063-651X(99) 11410-7].