Theory of translational diffusion in nematic liquid crystals

The theory of translational diffusion in nematic liquid crystals is developed from the standpoint of hydrodynamics and molecular-hydrodynamic interactions. The anisotropy of the diffusivity is obtained and related to the orientational order parameter, viscosity coefficients, and the detailed molecular geometry. Liquid-crystal hydrodynamics, Riemannian geometry, and molecular chain space are utilized in the theoretical development. The results for the diffusivity parallel and perpendicular to the director in p-azoxyanisole (PAA) at 125^∘{}C are D^∥=4.3×10^-6 and D^⊥=3.1×10^-6 cm²/sec, respectively, giving an anisotropy ratio D^∥D^⊥=1.4. In addition, the temperature dependence of D^⊥ is obtained, using available viscosity data. D^⊥ (D^∥) shows an increase (decrease)---corresponding to the decrease in order parameter---as the isotropic transition temperature is approached.