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We have evaluated the Green–Kubo relations for the viscosities of a biaxial nematic liquid crystal by performing equilibrium molecular dynamics simulations. The viscosity varies by more than two orders of magnitude depending on the orientation of the directors relative to the streamlines. The molecules consist of nine fused Gay–Berne oblates whose axes of revolution are parallel to each other and perpendicular to the line joining their centers of mass. This gives a biaxial body, the length-to-width-to-breadth ratio of which is equal to 5:1:0.4. The numerical evaluation of the Green–Kubo relations for the viscosities is facilitated by the application of a Gaussian director constraint algorithm that makes it possible to fix the directors in space. This does not only generate an inertial director-based frame but also a new equilibrium ensemble. In this ensemble the Green–Kubo relations for the viscosities are simple linear combinations of time correlation function integrals, whereas they are complicated rational functions in the conventional canonical ensemble. |
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