Transient Network Models for Viscoelastic Properties in the Terminal Zone

Transient Network Models for Viscoelastic Properties in the Terminal Zone 

The strands are classifled in the most general case by Lodge according to length (subscript e) and complexity of their junctions with the network (subscript k). Then, if Vue is the moles of strands with given values of e and k per unit volume at any instant, and r e is the probability that any one such strand will leave the network in unit time, the linear viscoelastic properties are given by 

For a polymer solution, i/o in equation 61 should strictly be replaced by i/o Vs-but it is probable that in any solution concentrated enough to have a transient network t/i would be negligible. 

Comparison of the forms of equations 58 to 61 with equations 21 to 23 of Chapter 9 and equations 23 and 24 of Chapter 3 shows that the time and frequency dependence correspond to a generalized Maxwell model as in the Rouse theory and its various modifications, but here the spring constants (or discrete contributions to the relaxation spectrum) are not necessarily all equal they are proportional to the concentrations of the various types of strands, v e. The molecular weight does not enter explicitly, but it may be expected that the higher the molecular weight the greater the concentrations of strands which find it difficult to leave the network and hence have large values of the time parameter 

Without knowledge of the relations between v g and r g, it is impossible to formulate the viscoelastic properties more specifically. The fact that Jg is independent of M for high uniform molecular weight suggests that there is a rather narrow distribution of r e s in this case. 

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