Entangled system terminal relaxation time

While the law with index 3.4 for viscosity is valid in the whole region above Mc, the dependence of terminal relaxation time is different for weakly and strongly entangled systems (Ferry 1980) and determines the second critical point M ... 

The difference in the molecular-weight dependence of the terminal relaxation time can be attributed to the change of the mechanisms (diffusive and repta-tion, correspondingly) of conformational relaxation in these systems. Further on in this section, we shall calculate dynamic modulus and discuss characteristic quantities both for weakly and strongly entangled systems. 

Watanabe (1999, p. 1354) has deducted that, according to experimental data for polystyrene/polystyrene blends, when the matrix is a weakly entangled system, terminal time of relaxation depends on the lengths of macromolecules as... 

The Rouse model describes the dynamical properties of melts of macromolecules of a relatively small number of Kuhn segments, Ncritical number Nc is the number of Kuhn segments for the critical molecular mass Me- Flexible polymers have critical Kuhn segment numbers typically in the range Mc=40- 60 [1, 42-44, 52]. On the other hand, chain dynamics in concentrated systems of polymers with N Nc is much slower than expected on the basis of the Rouse model. Alluding to chain entanglements that are considered to become relevant in this case, one speaks of entangled dynamics. For example, experimental terminal relaxation times and center-of-mass self-diffusion coefficients scale as and... 

Highly entangled systems, especially those of narrow molecular weight distribution, are characterized by a set of relaxations at long times (terminal relaxations) which are more or less isolated from the more rapid processes. The modulus associated with the terminal processes is called the plateau modulus G°,. Because t]0 and depend on weighted averages over H(x), their values are controlled almost completely by the terminal processes. These experimental... 

Chompff and Duiser (232) analyzed the viscoelastic properties of an entanglement network somewhat similar to that envisioned by Parry et al. Theirs is the only molecular theory which predicts a spectrum for the plateau as well as the transition and terminal regions. Earlier Duiser and Staverman (233) had examined a system of four identical Rouse chains, each fixed in space at one end and joined together at the other. They showed that the relaxation times of this system are the same as if two of the chains were fixed in space at both ends and the remaining two were joined to form a single chain with fixed ends of twice the original size. 

In thermorheological simple systems, the time-temperature correspondence principle holds. Chapter 8 gives examples of isotherms for compliance functions and relaxation moduli. The shift factors are expressed in terms of terminal viscoelastic parameters, and the temperature dependence of the shift factors is interpreted in terms of the free volume and the WLF equation. The chapter outlines methods for determining the molecular weight between entanglements, and analyzes the influence of diluents and plasticizers on the viscoelastic functions. 

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