Reduced variables shift factor Relaxation

The inclusion of values in Table 1 l-III derived from dynamic bulk viscoelastic measurements implies the concept that the relaxation times describing time-de-pendent volume changes also depend on the fractional free volume—consistent with the picture of the glass transition outlined in Section C. In fact, the measurements of dynamic storage and loss bulk compliance of poly(vinyl acetate) shown in Fig. 2-9 are reduced from data at different temperatures and pressures using shift factors calculated from free volume parameters obtained from shear measurements, so it may be concluded that the local molecular motions needed to accomplish volume collapse depend on the magnitude of the free volume in the same manner as the motions which accomplish shear displacements. Moreover, it was pointed out in connection with Fig. 11 -7 that the isothermal contraction following a quench to a temperature near or below Tg has a temperature dependence which can be described by reduced variables with shift factors ay identical with those for shear viscoelastic behavior. These features will be discussed more fully in Chapter 18. 

An example of nonlinear stress relaxation is shown in Fig. 16-17, where the ratio of time-dependent tensile stress to tensile strain is plotted logarithmically against time for different strains for cellulose monofilaments. (In this case the structure is no doubt preoriented.) The differences can be interpreted as due to a decrease in relaxation times with increasing stress, and the curves can be combined approximately into a composite curve by plotting with reduced variables, with a shift factor Os which decreases very rapidly with increasing strain. It is doubtful, how-ever, 2 whether the latter can be entirely related to fractional free volume in crystalline polymers as it is for amorphous polymers (Section Cl of Chapter 15). 

In most the cases, r(T) is a monotonous function, moreover, it is reducing with temperature increase. Keeping in mind that other variables in the expression (35) can be assumed as temperature-independent at least at low temperatures, one can see that the relaxation attenuation has maximum at a certain temperature T = Tm-Similar to the resonant attenuation, its position is shifted due to the the factor /T with respect to T = T which is defined in this case with the condition... 

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