Polymer chains global relaxation times

While all relaxation times depend on temperature and pressure, only the global motions (viscosity, terminal relaxation time, steady-state recoverable compliance) are functions of Af , (and to a lesser extent MWD). The glass transition temperature of rubbers is independent of molecular weight because chain ends for high polymers are too sparse to affect this bulk property (Figure 3.14 Bogoslovov et al., 2010). The behavior can be described by the empirical Fox-Hory equation (Fox and Flory, 1954) ... 

In the Rouse-Zimm bead spring model of polymer solution dynamics, the long-range global motions are associated with a broad spectrum of relaxation times given by equation (10) and where tj is the relaxation time of the h such normal mode of the chain... 

Polymers, with M smaller than a certain critical value, exhibit negligible chain entanglement and self-diffusion is controlled by the monomeric friction coefficient. Rouse s theory is more applicable to this case it predicts correctly that the relaxation times associated with global rearrangements should be proportional to M. 

Figure 7.4 A long polymer chain entangled with both long and short chains. At times greater than the reptation time of the short chain, .e., f > r,js Z5, the short polymer releases a constraint by reptation, and the long chain can then relax its configuration /oco//y. Global relaxation can only occur at f > Zl, when the entangling long chains have also relaxed.

We need to know the characteristic time beyond which we will cease to observe the global chain dynamics but only the center of mass motion. In answering such a question we need the relaxation time for a polymer chain which has been disturbed from its equilibrium configuration, and the mean square displacement of a labeled monomer as a function of time. 

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