Viscosity in semidilute solutions

While the regions are thermod5mamically and hydrodynamically screened, the actual chains connect regions and influence the viscosity. It has been proposed that the viscosity in the semidilute regime can be described as  

This scaling relation requires that the solution still be quite dilute so that the solvent viscosity remains the dominant local variable and that the chains have not overlapped enough to display evidence of entanglements. 

At the Flory temperature, the radius of gyration is proportional to M and is independent of concentration. The hydrodynamic radius is proportional to the screening length times the number of subregions per molecule, mlUg. The viscosity under these conditions is predicted to scale as  

Under good solvent conditions, both the radius of gyration and the hydro-dynamic radius are functions of concentration. Application of Equations 6.10 and 6.11 leads to a prediction  

Because the chains are shrinking as the concentration is increased, the viscosity increases less strongly with c. 

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Concentration dependence of viscosity in semidilute solutions of polystyrene at 35 °C. (a) Solutions in the good solvent toluene have (pj(p reduce data for different molar masses to a universal curve, using data from M. Adam and... 

The success of the deGermes theory suggests that the viscosity in semidilute solutions can also be explained in terms of the universal length and the actual radius of gyration of the macromolecules. This theory is presented in Section 6.4. 

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