Entangled segments

The other important physical assumption is that the friction is local (hydro-dynamic interactions are screened in the melt [2]) so that D -(N /N)D with the diffusion constant in the melt of an unentangled chain of segments. Now the characteristic relaxation (Rouse) time of an entanglement segment % is just a /D. so that... 

For times less than the Rouse time of an entanglement segment, Tg and short distances, the chain behaves as if it were free since no section has moved far enough to be strongly affected by the tube constraint. The characteristic decay-rate of the scattering function at wavevector k is dominated by the Rouse-time of chain segments whose size is the order of k % k. A detailed calculation gives for t % [2]... 

Afterwards, based on the hypothesis that the elasticity development in plasticized PVC was due to the enhancement of micro-Brownian motions of the polymer, Doolittle, Stickney and Cheyney and Alfrey et developed the Gel Theory. They considered that the mechanical properties of a polymer were due to the elastic resistance of entangled segments of the macromolecules structured as a three-dimensional network. The plasticizer molecules which are dissolved into the polymer matrix break some points of attachment between macromolecules leading to an easier glide. Moreover,... 

The rapid motion of the entanglement segments at the chain (and tube) ends allows these to have their equilibrated configuration ... 

K. Osaki and M. Kurata, Stress Relaxation of a Polymer Solution in Double-Step Shear Deformations A Separate Evaluation of the Stress Components due to Entangled Segments of Different Orientations Polym. ScL, Polym. Phys. Ed. 20, 623-632... 

E-network model is based on that the entangled polymer chain may be decomposed into three and four-body constituent chains by entanglements as shown in Fig. la. The constituent chain by entanglement with different sizes is shown in Fig. 2a. They can be divided into the terminal or tail and loop forms which are located at the end and middle of polymer chain, respectively. The entangled segments with different lengths are tail and loop segments which are located at the end and middle of polymer chains, respectively. 

Eniture efforts will address other systems such as entangled (linear and branched) polymers where, inspired by the corresponding GENERIC formalism, one should resort to a description in terms of the orientational distribution function of an entanglement segment along the primitive path of the chain. 

The tube comprises N/Ne entanglement segments, where Ng is the average degree of polymerisation between entanglements, such that the mean-squared end-to-end distance is given by. 

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