Among the interesting problems concerning viscoelasticity of polymer solutions there are three subjects for the present consideration, the hydrodynamic interaction of polymer segments, the non-Newtonian viscosity and entanglement among the polymer chains.
(1) Hydrodynamic interaction: As the model of polymer chains the nondraining sphere with the same radius as the radius of gyration of a polymer chain itself seems to be inadequate, seeing that nearly the half number of the segments are located outside the supposed sphere. By adopting the concept of shielding length after the Debye-Bueche's paper, we can derive the relation between the geometrical expansion factor α and the expansion factor for the viscosity αη such as αη3≅α2.43, under some conditions. The precise relation has been derived by Kurata-Yamakawa near Θ-temperature. This indicates that the partially draining model will be better for the model of polymer chains, because the experimental results support this relation.
(2) Non-Newtonian viscosity: The experiments show non-Newtonian intrinsic viscosity even at Θ-temperature. Chikahisa applied the equivalent rigid ellipsoid model after Kurata-Stockmayer-Roig's paper to this problem; in this case the non-Newtonian viscosity is due to the orientation of the ellipsoid in a shear field, and may be observed at any temperature. It is pointed out in this review that the conformation change of the chain due to micro-Brownian motion may cause further effect, and it is not easy to show which is dominant for the shear-rate dependence of viscosity.
(3) Entanglement; As soon as the concentration of the polymer solution exceeds the order of one percent, the entanglement of polymer chains becomes appreciable. Up to the concentration of the order of ten percents, perhaps a few chains entangle with each other, and make a cluster in the solution. At higher concentrations, the entanglement results in the network formation throughout the system. These situations are supported by the concentration as well as molecular weight dependences of viscosity, equilibrium compliance, dynamic modulus, Weissenberg effect, and so on.
