Viscous properties of biaxial nematic liquid crystals: The method of calculation of the Leslie viscosity coefficients

We present a microscopic approach to the theory of viscosity of biaxial nematic liquid crystals consistent with the existing 2-director continuum Leslie's theory and show the method of obtaining microscopic formulas for viscosity coefficients. The derived formulas are expressed in terms of order parameters, temperature, number density, and diffusion constants. Obtained viscosity coefficients satisfy the four Onsager-Parodi relations. Since no assumptions about diffusion constants are applied and a very general form of an interaction potential is used, presented results are quite general. The approximation concerns shapes of the molecules that are modeled by ellipsoids with three different principal axes. In the limiting case, when appropriate biaxial order parameters vanish and the system becomes uniaxial, we obtain the six Leslie viscosities involving, in general, two diffusion coefficients related to the rotational motion about short and long axes, respectively, and two ellipsoidal axis ratios. When the molecules possess symmetry axes, the formulas for the Leslie coefficients recover known results for uniaxial system.