The Microstructural Approach - Polymers

There are a wealth of experiments, papers and texts covering the nonlinear viscoelastic response of polymers. In this book we cannot hope to cover the area in as much detail as the many admirable texts in this field. 

The time ie represents the entanglement formation time at the current shear rate. The second term g is the average number of entanglement sites for a chain of fixed length in steady flow relative to the number in the zero shear rate limit  

This deceptively simple expression is capable of describing the shear thinning response of monodisperse polymers with a high level of precision. In the high shear limit we obtain 

A numerical implementation of this approach can be generalised to include the polydispersity of the polymer. As polydispersity is increased the power law of — 0.8181... reduces. The onset of shear thinning, where Tn y 1 — 1, results in a slightly lower viscosity for polydisperse systems at this rate. So far we have neglected the origin of the characteristic time for the system which we would like to describe in terms of the chemical 

We would expect a difference between the average time and that which determines the onset of shear thinning since the low shear viscosity tends to be dominated by the longest mode of relaxation. 

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