Global relaxation time

In Figures 24.7 through 24.9 are shown the volume dependences of the local and global relaxation times for 1,4-polyisoprene [90], polypropylene glycol [91], and polyoxybutylene [76]. For either mode, volume does not uniquely dehne the relaxation times, as the curves for different... 

Where p defines the shape of the hole energy spectrum. The relaxation time x in Equation 3 is treated as a function of temperature, nonequilibrium glassy state (5), crosslink density and applied stresses instead of as an experimental constant in the Kohlrausch-Williams-Watts function. The macroscopic (global) relaxation time x is related to that of the local state (A) by x = x = i a which results in (11)... 

In the case of crosslinked polymers, the global relaxation time X has to be generalized by including a shift factor for the crosslink density (av)... 

H( P) as a function of the nondimensional relaxation time, 7 = u/x, the ratio of local to global relaxation times, and p. When Equations 3 and 5 are used simultaneously in analyzing experimental data, we have found that p= 1/2 for most amorphous polymers which will also be assumed for lightly crosslinking systems. 

The relaxation phenomenon which has been discussed so far is within the linear viscoelastic range. Under large deformation, the global relaxation time has to include the contribution from the external work Aw done on the lattice site and takes the form (20)... 

The yield occurs when the product of the applied strain rate (e) and the global relaxation time reaches the order of unity, i.e., ex 1. Thus, we obtain... 

To is a terminal relaxation time describing chain motions. Other global relaxation times can be defined experimentally, for example as the inverse of the frequency of the maximum in the terminal dispersion in the loss modulus, Tmax from the time for equilibration following cessation of nonlinear shear flow, XR rj, measured by recovery of the overshoot in the transient viscosity the corresponding time for recovery of the overshoot in the second normal... 

Fig. 19. Temperature dependence of the shift factors of the viscosity (T), terminal dispersion ( ), and softening dispersion (0) of app from Ref. 73. The temperature dependence of the local segmental relaxation time determined by dynamic light scattering ( ) (30) and by dynamic mechanical relaxation (o) (74). The two solid lines are separate fits to the terminal shift factor and local segmental relaxation by the Vogel-Fulcher-Tammann-Hesse equation. The uppermost dashed line is the global relaxation time tr, deduced from nmr relaxation data (75). The dashed curve in the middle is tr after a vertical shift indicated by the arrow to line up with the shift factor of viscosity (73). The lowest dashed curve is the local segmental relaxation time tgeg deduced from nmr relaxation data (75).

By means of mechanical, mechano-optical, or (under certain favorable circumstances) dielectric, measurements, we can assign to a chain (in dilute solution) a global relaxation time Ti. A suggestive description of Ti makes use of the dumbbell model of Kuhn and Peterlin, according to which one describes the chain by its elongation r only. For small values of r, Peterlin wrote down a force balance of the form... 

At this junction it is common to discuss various short time expansions and/or long time situations, i.e. to consider partitions of relevant time scales. We will principally mention two interdependent scales, i.e. a global relaxation time - ei and a local collision time Tc. For instance, during Tc the amplitude

[Pg.8]

---