Polymer dynamics local segmental relaxation time

In this equation, Gq is the high frequency limiting vzdue of the modulus (the unrelaxed modulus), %ww is the relaxation time, and P a shape parameter. The KWW function has been found to describe various processes. Most importantly for polymers, the local segmental relaxation dynamics conform closely to form of equation 1. 

While all relaxation times depend on temperature and pressure, only the global motions (viscosity, terminal relaxation time, steady state recoverable compliance) are functions of Mw (and to a lesser extent MWD). An example of the various dynamics of 1,4-polyisoprene are illustrated in Fig. 10. At frequencies beyond the local segmental relaxation, or at temperatures below Tg, secondary relaxation processes can be observed, especially in dielectric spectra. In polymers, many of these secondary processes involve motion of pendant groups. However, the slowest secondary relaxation, referred to as the Johari-Goldstein process, involves all atoms in the repeat unit (or the entire molecule for low M materials). This Johari-Goldstein relaxation serves as the precursor to the prominent glass transition. 

Segmental motions of P(3HB) and P(3HB-co-27%3HV) in chloroform-d solution have been studied by measuring NMR relaxation times and NOE factors as a function of temperature [72, 73]. Analysis of the relaxation data on the basis of the Dejean-Laupretre-Monnerie (DLM) model, which describes the dynamics of polymer chains [74], indicates that the local dynamics of a comonomer unit, e.g., 3HB, are independent of the presence of a nearby 3HV unit and vice versa that segmental motion of the P(3HB-co-27%3HV) copolymer described by cooperative conformational transitions [73] is similar to that for the P(3HB) homopolymer [72]. These motional characteristics of the P(3HB-co-3HV) copolymer chain are consistent with the conformational characteristics derived by the analysis of spin coupling as shown in Section 21.2.2.3 [63] and are consistent with the occurence of cocrystallization in this copolymer system. 

Temperature dependence of dielectrically determined relaxation times "c of monomeric segments of poly(2-chlorostyrene) (P2CS) and poly(vinyl methyl ether) (PVME) in P2CS/PVME miscible blends with various P2CS volume fractions ( )p2cs as indicated. (Data taken, with permission, from Urakawa, O., Y. Fuse, H. Hori, Q. Tran-Cong, and O. Yano. 2001. A dielectric study on the local dynamics of miscible polymer blends Poly(2-chlorostyrene)/poly(vinyl methyl ether). Polymer 42 765-773.)... 

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