| Basing on the definition of the mesoscopic concept by Blenk and others in 1991 an approach to calculate the Leslie viscosity coefficients for nematic liquid crystals is presented. The approach rests upon the mesoscopic stress tensor, whose structure is assumed similar to the macroscopic Leslie viscous stress. The proposed form is also the main dissipation part of the mesoscopic Navier Stokes equation. On the basis of the correspondence between micro and meso scale a mean field meso potential is introduced. It allows to obtain the necessary in the stress tensor angular velocity of the free rotating molecules with the help of the orientational Fokker-Planck equation. Macroscopic stress tensor is calculated as an average of the mesoscopic counterpart. Appropriate relations among mesoscopic viscosities have been found. The mesoscopic analysis results are shown to be consistent with the diffusional model of Kuzuu Doi and Osipov Terentjev (KDOT) with exception of the shear viscosity alpha_4. In the nematic phase alpha_4 is shown to consist from two contributions: isotropic and nematic. There exists an indication that the influence of the isotropic part is dominant over the nematic part. The so called microscopic stress tensor used in the microscopic theories is shown to be the mean field potential dependent representation of the mesoscopic stress tensor. In the limiting case of total alignment the Leslie coefficients are estimated for the diffusional and mesoscopic models. They are compared to the results of the AT model of the perfectly ordered systems. This comparison shows disagreement concerning the rotational viscosity, whereas the coefficients characteristic for the symmetric part of the viscous stress tensor remain the same. The difference is caused by the hindered diffusion in the affine model case.
for LaTeX users @article{AChrzanowska1999-60,
author = {A. Chrzanowska and M. Kr\"oger and H. S. Sellers},
title = {Mesosocopic model for the viscosities of nematic liquid crystals},
journal = {Phys. Rev. E},
volume = {60},
pages = {4226-4234},
year = {1999}
}
\bibitem{AChrzanowska1999-60} A. Chrzanowska, M. Kr\"oger, H.S. Sellers,
Mesosocopic model for the viscosities of nematic liquid crystals,
Phys. Rev. E {\bf 60} (1999) 4226-4234.AChrzanowska1999-60
A. Chrzanowska, M. Kr\"oger, H.S. Sellers
Mesosocopic model for the viscosities of nematic liquid crystals
Phys. Rev. E,60,1999,4226-4234 |
mk@mat.ethz.ch
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