FRICTION TENSOR OF FLEXIBLE POLYMER-CHAINS IN NEMATIC LIQUID-CRYSTALS

Hydrodynamic properties of a flexible polymer chain in low molecular weight liquid crystals (LC) have been studied. The starting point is the derivation of the hydrodynamic Oseen tensor for anisotropic fluids that satisfy a modified Navier-Stokes equation. The nematics of LC breaks the spatial isotropy and leads to a necessary introduction of the friction tensor SIGMA for polymers. The general expression for SIGMA is obtained as a formal perturbation expansion within the Kirkwood-Riseman theory, and the component corresponding to the polymer diffusive motion along the nematic direction is evaluated explicitly by using the renormalization group method and by considering the smallness of one of the Leslie coefficients of the nematic solvent. The result depends on the LC Miesowicz viscosities in a nontrivial way, yet the molecular weight dependence is still universal.