Many-chain effects constraint release

Other computer simulations, such as the Evans Edwards model of a chain in an array of fixed obstacles (described in detail in Section 9.6.2) exhibit fluctuations of the tube length and also find stronger molar mass dependences of relaxation time t and diffusion coefficient 

Constraint release mechanism when chain B reptates away, it releases the constraint on chain A. Later, this constraint is replaced by chain C. which confines chain A in a displaced tube. 

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Constraint release (CR). This takes place if a confining chain moves out of the way of a given chain and thus opens some freedom for lateral motion. This phenomenon is an intrinsic many-body effect and for monodisperse polymer melts becomes significant mainly in the creep regime. 

Hess derived a similar expression from his microscopic model by explicitly considering the effective entanglement as a dynamic effect. Hess included the important many chain cooperative effects of constraint release and tube renewal, which are necessary in order to get quantitative predictions for the stress relaxation functions. Ultimately this does not affect the N dependence of the relaxation time. He found that after an initial fast Rouselike decay up to time r, Tp Hess = / irp Rep- Both models describe essentially the same physical picture. For the generalized Rouse model, Kavassalis and Noolandi found that Tp rm N /p. MD simulation results of Kremer and Grest could not distinguish between the standard reptation and Hess models but could rule out the generalized Rouse model. 

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