Tube diameter entanglement molecular

The mathematical treatment that arises from the dynamic dilution hypothesis is remarkably simple - and very effective in the cases of star polymers and of path length fluctuation contributions to constraint release in Hnear polymers. The physics is equally appealing all relaxed segments on a timescale rare treated in just the same way they do not contribute to the entanglement network as far as the unrelaxed material is concerned. If the volume fraction of unrelaxed chain material is 0, then on this timescale the entanglement molecular weight is renormalised to Mg/0 or, equivalently, the tube diameter to However, such a... 

Note that p is independent of molecular weight, since for Gaussian chains M/ [R )q is a constant. At 140°C, the entanglement molecular weight Mg, plateau modulus G, and the tube diameter a (defined below in Section 3.7.1) are related to p by (Fetters et al. 1994)... 

Entanglement molecular mass Mg Tube diameter d, Packing length p... 

Table 10.2 collects various PLA properties obtained using Equations 10.35,10.36. For comparison, values for two other linear polymers are also tabulated poly(ethylene oxide) (PEO) and isotactic polypropylene (i-PP). These polymers are selected because they share some common molecular features with PLA. It should be noted that a distinction should be made regarding the nature of the oxygen group in the PLA backbone as it is part of a rigid ester linkage. This distinction is evident in the data the tube diameter and the number of backbone bonds between entanglements in PLA is... 

Table 6.3 Parameters of Polystyrene within the Framework of the Reptation Theory [20]. The Entanglement Molecular Weight, M, and the Tube Diameter, dt, of Polystyrene is 13309 g/mol and 76.5 A, Respectively [21]...

The tube model gives a direct indication of why one might expect the strange observations on star melts described above. Because the branch points themselves in a high molecular weight star-polymer melt are extremely dilute, the physics of local entanglements is expected to be identical to the linear case each segment of polymer chain behaves as if it were in a tube of diameter a. However, in... 

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