The dynamics of highly entangled polymers

Recent research has addressed the shortcomings of the original Doi-Edwards exposition of reptation theory, firstly for low shear rate linear behaviour and secondly for non-linear behaviour at large shear rates. Doi-Edwards linear reptation theory predicts thatar scales with A as A, whereas there is a large body of experimental evidence that viscosity scales with molecular mass M as M -. Secondly, linear theory predicts that the dynamic loss modulus G2 o)) is proportional to in the intermediate frequency range whereas experiment 

The stress relaxation modulus G t) then has three components  

High-frequency modes due to contour-length fluctuations at the ends of the tubes. 

Lower frequency modes associated with reptation. 

Very high-frequency (short-time) Rouse modes where the tube constraints are not felt. 

Doi and Edwards [32] have extended the work of de Gennes, and have derived mathematical expressions for features such as the stress relaxation that occurs after a large 

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K. E. Evans and S. F. Edwards, Computer Simulation of the Dynamics of Highly Entangled Polymers. Part 2 — Static Properties of the Primitive Chain , J. Chem. Soc., Faraday Trans. 2,11,1981, pp 1913-1927. 

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