Anisotropic diffusion of tagged spheres near the isotropic-nematic phase transition

Molecular dynamics simulations of diffusion of isolated tagged spheres in liquid crystalline molecules have been carried out. While the diffusion is isotropic at density slightly below the isotropic-nematic phase transition, it is found to become strongly anisotropic very close to the I-N transition where the diffusion perpendicular to the direction of the order parameter g(D \perp) decouples from the parallel (D\parallel) component. The diffusion coefficient of the sphere also shows a marked slowing down as the I-N transition approaches, in accordance with the mode coupling theory analysis. The variation of the orientational order parameter with the density shows a sharp transition at a reduced density, \rho*IN where plot of the ratio, D\parallel /D\perp against the reduced density,\rho * clearly shows the emergence of anisotropy. D\perp could be fitted to a form (\rho*c - \rho*)p which is slightly larger than \rho*IN. The diffusion shows a strong non-Stokesian dependence on the radius of the spheres, in agreement with recent experiments