Influence of Molecular Weight on Flow Properties

It has long been known that a polymer s molecular weight exerts a strong influence on its melt or solution viscosity. Experiments show that 

Equation 15.14 holds quantitatively for just about afl polymer melts. The addition of a low molecular weight solvent, of course, cuts down entanglements and raises M c- Equation 7.13 suggests that entan ents set in when the dimensionless product of intrinsic viscosity and concentration exceeds one, [ 7] c 1. Thus, if you know [ /] for your polymer in the solvent, you can get an idea of the concentration above which (15.14b) ought to hold. In practice, even moderately concentrated (say 25% or more) polymer solutions have viscosities proportional to provided A is in the range of commercial importance. 

Example S. Obtain an approximate equation that relates M c to concentration and the MHS constants (6.16) for polymer solutions. 

Solution. First, we assume that entanglements begin when the Berry number, [j/]c, equals 1. Because aU we re after here is a rough estimate, we can assume that w M (see Chapter 6, Example 4). Thus, 

As the shear rate is increased, the number of entanglements between chains is reduced, and as expected, the dependence of viscosity on molecular weight decreases (Fig. 15.11). 

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