The Williamson empirical equation which fits polystyrene melt viscosity data is derived by considering the melt as a system of elastic springs which are entangling and disentangling. The theory allows one to trace changes in the number of extensible elements and the relaxation time for the rupture of intermolecular links. For uniform molecular weight samples, the number of extensible elements per molecule is proportional to the molecular weight. Widening the molecular weight distribution lowers the number of extensible elements per cc. The thermal relaxation time increase rapidly with increasing molecular weight. The effect of fillers on the number of extensible elements and the relaxation time is complex.
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T. Gillespie (1965) studied this question.
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