Non-Newtonian Viscosities of Polymer Melts

This theory seems not to have been extended to branched polymers in the non-Newtonian range so far as the extended theory does not agree very well with experiment in the Newtonian range, a satisfactory extension to predict the shear-rate dependence of the viscosities of branched polymers is likely to be difficult. The experimental evidence available is discussed in later sections. 

Recent developments in the theory of polymer solutions have been reviewed by Berry and Casassa (32), and by Casassa (71). Casassa, who has contributed very largely to these developments, has adopted a statistical mechanical approach using molecular distribution functions, as first outlined by Zimm (72), rather than using a lattice model like that used by Flory, Huggins, and many later workers. 

The size of molecules in solution, measured by s2 , is important both in its own right and because of the effects of changes in s2 on interactions between molecules in solution. For linear polymers, the expansion factor a of Eq. (3.2) can be expressed as a power series in a dimensionless parameter z which is related to the excluded volume per segment pair, p, and the molecular size  

The excluded volume fi is zero at some temperature 0, near which it is representable by  

It has been generally assumed until recently that the series (6.1) is convergent, at least for sufficiently small z, though it was recognised that convergence was slow except for very small z (32). It has recently been shown that this series is divergent for any non-zero value of z (205) it is suggested that it is nevertheless useful as an asymptotic series, so that the coefficients are of interest. Values have been obtained for the first three coefficients for linear polymers. 

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