Viscosity of Concentrated Solutions and Melts

The models discussed in Section 13.2.3 for dilute polymer solutions all predict [ /] to be independent of concentration that is, they predict linear dependence of viscosity on concentration. When the concentration of polymer in solution is higher than the overlap concentration (c /[ ] the random coils get 

While accounting for the concentration effects by analyzing a single chain placed in an effective medium made up of the other chains, the dependence expressed 

The transition from the Zimm regime [Eq. (17), [f]] N ] at dilute concentrations to Rouse-like behavior [Eq. (16), [rf N] at the intermediate concentrations is related to the hydrodynamic screening at high concentrations the hydrodynamic interactions between segments become negligible because the local velocity around the beads falls quickly. 

At even higher molecular weights and concentrations, the viscosity in concentrated solutions and melts goes from a linear to a 3.4 power dependence on M [Eq. (20) Eigure 13.21]. 

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