Frequency dependence of intrinsic viscosity of macromolecules with finite internal viscosity

In order to explain the observed nonvanishing limiting value of dynamic intrinsic viscosity of polymer solutions at ω = ∞ one has considered the necklace model with finite resistance to the rate of coil deformation introduced long ago by Cerf for the study of gradient dependence of intrinsic viscosity and streaming birefringence. The calculation need not take into account change of hydrodynamic interaction as a consequence of coil deformation because the experimental data are always either obtained at very low gradient or extrapolated to zero gradient so that in the experiment the macromolecule has the same conformation as in the solution at rest. The model indeed yields a finite η]′_{ω = ∞} in good agreement with experiments on polystyrene in Aroclor. According to the theory η]′_{ω = ∞}/η]₀ decreases with increasing molecular weight as M^?1 and M^?1/2 for the free-draining and impermeable coil, respectively. The absolute limiting value η]_∞′, therefore turns out to be nearly independent of M, at least for small values of internal viscosity. From the observed value η]_∞′/η₀] one can obtain the coefficient of internal viscosity of the macromolecule. The value for polystyrene in Aroclor calculated from dynamic experiments on rather concentrated solutions is close to that derived by Cerf from streaming birefringence observations of polystyrene in a series of solvents of widely differing viscosity.