Theoretical basis of interpretation

The molecular-level nature of our orientation relaxation data has led us to carry out an interpretation in terms of molecular motions. Therefore we have based our interpretation on the Doi-Edwards model [9]. We briefly recall the main qualitative features of the model and include other processes proposed by 

The first relaxation process (designated A hereafter) corresponds to a Rouse-like relaxation of chain segments between entanglement points. It is assumed that the entanglement points remain fixed during the time-scale of this relaxation and that no diffusion of monomers through the slip-links is allowed in such short times. The associated relaxation time,, is related to a monomeric friction coefficient, to thie number of monomers between 

It has been shown by Doi [11] that on the time scale of Tg contour length fluctuations may induce a rapid relaxation of chain ends, especially for moderately long chains. Indeed, wiggling motions involve forward and backward motions of the chain ends. Thus, chain length fluctuations in oriented materials lead to the creation of isotropic parts of tubes at each end. Their fractional length is roughly equal to 1.3(N e) where N is the number of monomers per chain. An elaborate expression for the relaxation due to this mechanism, based on the Pearson-Helfand picture for star pol5uners [12], has been proposed by Viovy [13]. 

This model involves only one adjustable relaxation time, for instance, since the others are linked by the following scaling laws  

For both linear and star polymers, the above-described theories assume the motion of a single molecule in a frozen system. In polymers melts, it has been shown, essentially from the study of binary blends, that a self-consistent treatment of the relaxation is required. This leads to the concepts of constraint release whereby a loss of segmental orientation is permitted by the motion of surrounding species. Retraction (for linear and star polymers) as well as reptation may induce constraint release [16,17,18]. In the homopol5mier case, the main effect is to decrease the relaxation times by roughly a factor of 1.5 (xb) or 2 (xq). In the case of star polymers, the factor v is also decreased [15]. These effects are extensively discussed in other chapters of this book especially for binary mixtures. In our work, we have assumed that their influence would be of second order compared to the relaxation processes themselves. However, they may contribute to an unexpected relaxation of parts of macromolecules which are assumed not to be reached by relaxation motions (central parts of linear chains or branch point in star polymers). 

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