Entanglement distance constant

Me molecular mass of these entanglement strands) and the volume spanned by the entanglement distance is approximately a constant... 

The beads represent entanglement sites which are distributed uniformly along the chain contour the frictional coefficients increase rapidly with distance from the chain ends. The spring constant also depends on contour position, being governed by the mean equilibrium distance of that position from the center of gravity. The resulting spectrum is narrower than the Rouse spectrum, and for E > 1 ... 

Validity of Eqs 7.81 and 7.82 was examined for mixtures of entangled, nearly monodispersed blends of poly(ethylene-a/r-propylene) with head-to-head PP [Gell et al., 1997]. The viscoelastic properties compared at constant distance from the glass transition temperature of each system were found to obey the time-temperature superposition principle. The data agreed better with the predictions of Eq 7.82 than Eq 7.81. However, for blends of linear and branched PE the relations 7.82 were found valid only when MW and rheological properties of the two components were similar [Groves et al., 1996]. 

Stress relaxations at constant strain in entangled systems occur as the strained chains tend to recover equilibrium conformations by Brownian motion. Therefore it is reasonable to expect that has something to do with the rate at which the slowest mode of chain motion leading to steady self-diffusion takes place. An adequate measure of this rate is the average time tq in which the chain self-diffuses a distance equal to its radius of gyration. Thus, we have... 

How could we transfer these results to our entangled molecules It is initially tempting simply to introduce into equation (24) the macroscopic diffusion coefficients defined by (21) and (22). The constant k should then be proportional to iV . We can, however, show that this idea is wrong. The reaction occurs at spatial distances between reagents of the order of b, which are smaller than the statistical size Rq of the chains an analysis solely based on macroscopic concepts is not sufficient. 

In the uncorrelated drag model of Graessley, entanglement loci are assigned friction coefficients which increase rapidly with distance from the chain ends, and their motions are associated also with spring constants which are governed by the mean equilibrium distance from the center of mass. The result is a much sharper relaxation spectrum in the terminal zone it predicts, for M > Me and M > M c respectively,... 

Equations 6.6 and 6.7 show that in both unentangled and entangled regimes, when the reaction is diffusion controlled, the interfacial rate constant is insensitive to interfacial structure (e.g. interfacial thickness) and dynamics. This is because the rate limiting step is the slow diffusive transport of a reactive chain to within a critical distance of the interface. In the entangled regime, this critical distance is comparable to the radius of gyration of the chain, Rg. Sub-diffusive transport is assumed to be very rapid. 

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