Sub-Rouse modes

Pa , (2) the sub-Rouse modes from Jsa up to somewhere near Jsr 10 Pa , and (3) the modified Rouse modes from Jsr 10 Pa up to the plateau level. These estimates may vary for polymers with very different chemical structures. 

Sub-Rouse modes are discussed in Reference 196. NMR and dielectric spectroscopy have been employed to study the dynamics of polymeric melts from low to high molecular... 

From the results in Fig. 2.29, the three groups of viscoelastic mechanisms, namely local segmental, sub-Rouse, and Rouse modes, all have different temperature shift factors and the sensitivities of their relaxation times to temperature decrease in that order. The shift factors ar used for time-temperature superposifioning of the creep or stress-relaxation data in temperature regimes I, II, and III are, respectively, that of the local segmental relaxation, that of the sub-Rouse modes, and that of the Rouse modes. Over the entire temperature range aj is not the shift factor of any one of the three mechanisms. 

It has previously been shown for PS, poly (vinyl acetate), and atatic polypropylene that the shift factor of the terminal relaxation or the viscosity aT,n has a weaker temperature dependence than do the softening dispersion ar.s (Fig. 2.11) and the local segmental relaxation ar,a (Figs. 2.19 and 2.20). Therefore, in practice the shift factors ut used to obtain master curves for polymers by time-temperature superposition are actually combinations of the individual shift factors of the several different viscoelastic mechanisms. At low temperatures, aj is principally determined by the shift factor of the local segmental mode aT,a- With increasing temperature, aj is principally determined sequentially by the shift factors of the sub-Rouse modes, r,sR. the Rouse modes, modes in the rubbery plateau, and, finally, the terminal modes, aT,r,- Hence, it is not correct to assume that aj describes the temperature dependence of any or all of the viscoelastic mechanisms in a polymer. 

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