Dynamics of chain molecules. I. Solutions to the hydrodynamic equation and intrinsic viscosity

An exact numerical solution to the equation of motion for a flexible macromolecule in solution is given for the bead and spring model incorporating the preaveraged Oseen hydrodynamic interaction. The limits to be imposed on the strength of the interaction are confirmed and discussed. The data obtained for the eigenvalues λK, the eigenvectors QjK, and the quantities μK show that the hydrodynamic interaction affects the relaxation times and the shapes, the mean square length of the modes remaining practically unchanged with respect to the free-draining results. By comparison with the intrinsic viscosity experimental data, the values of r/b (hydrodynamic interaction strength) and b (mean dimension of the subchain) may be obtained. The method has been applied to PS and PDMS. Defined and reasonable values of r/b and b have been obtained. The range of r/b of major interest (0.2–0.3) gives small draining effects over a large molecular weight range; this makes the intrinsic viscosity depend approximately on M0.5, although with a different proportionality constant.