Melts and Highly Concentrated Solutions

If the logarithmus of the viscosity of concentrated polymer solutions is plotted against the logarithmus of the concentration, a curve is obtained 

The concept of entanglements or close packing leads one to expect a dependence of the critical concentration on the molar mass of the polymer. Actually, a proportionality between Ccrit and M is experimentally observed. Theoretical considerations suggest a value for the exponent a of unity for entanglements and 0.5 for close packing of coil-like macromolecules. 

Theoretically, the viscosity of rod-shaped macromolecules for a shear gradient of zero should be proportional to both the volume fraction / and the molar mass M of the polymer  

A critical molar mass is analogously found for melts. Below the critical molar mass, the melt viscosity at zero shear gradient is directly proportional to the molar mass  

In contrast, the viscosity above the critical molar mass is given by (see Fig. 7-8)  

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This distinctive t]0 vs M behavior in melts and highly concentrated solutions is one of the features attributed to chain entanglement. The intensitivity of Mc to temperature, the simplicity and insensitivity to solvent power of the con-... 

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