Corresponding state relations for the Newtonian viscosity of polymer solutions. II. Further systems and concentrated solutions

In earlier work we have indicated a superposition principle for moderately concentrated mixtures (c ? 2/[η]) in good and poor solvents. By an examination of data on a number of vinyl polymers and cellulose derivatives in good as well as poor solvents, the validity of this principle is extended to concentrated solutions (c ? 50%). The characteristic concentration factor γ is proportional to M over the whole concentration range, with 0.47 ≤ a₁ ≤ 1.10 being larger for good than for poor solvents, the result obtained earlier. Significant deviations from this relationship are noted in good solvents for those low molecular weights at which deviations from the usual intrinsic viscosity relationship occur. This may be related to the expansion factor of the polymer coil. On the basis of these results, the concentration and molecular weight dependence of the viscosity in the concentrated solution can be related to each other in terms of the parameter a₁ and thus to thermodynamic characteristics. In this manner a bridge between the relatively dilute and concentrated regions is established. Currently used semiempirical expressions are analyzed in terms of these results. For the polystyrene–cyclohexane systems and θ ? 9 ≦ T ≦ θ + 3, γ can be identified with the critical concentration for phase separation. Provided an “entanglement” concentration c_e exists, in the neighbourhood of which the concentration dependence of the viscosity changes reapidly, γ can alternatively be shown to be proportional to c_e, or c_e ∝ M. The temperature reduction scheme suggested earlier remains to be investigated.