Bulk storage compliance

FIG. 18-12. Dynamic bulk storage and loss compliances of poly(vinyl acetate) reduced to I atm and 1000 Hz by equation 6 and plotted against reduced temperature defined by equation 12. Bq and correspond to B, and Bg in the text. (McKinney and Belcher. )... 

FIG. 18-14. Dynamic bulk storage and loss compliances of natural rubber vulcanized by sulfur, reduced to 0°C and 1 atm pressure by equation 6 and plotted against logarithm of reduced frequency, var.p (McKinney, Belcher, and Marvin. )... 

As an example of bulk viscoelastic behavior, data for a poly(vinyl acetate) of moderately high molecular weight are shown in Fig. 2-9. Measurements by McKinney and Belcher of the storage and loss bulk compliance B and B" at various temperatures and pressures are plotted after reduction to a reference temperature and pressure of 50°C and 1 atm respectively (see Chapter 11). The complex bulk compliance is formally analogous to the complex shear compliance, but the two functions present several marked contrasts. 

FIG. 2-9. Storage and loss bulk compliance plotted logarithmically against frequency, for a poly(vinyl acetate) reduced to 50°C and I atm, as described in text. ... 

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. 

The most extensive measurements of dynamic bulk compression have been those of McKinney and Belcher on poly(vinyl acetate), covering ranges of frequency from 50 to 1000 Hz, temperature from 0° to 100°C, and superposed hydrostatic pressure from 1 to about 1000 atm. Both storage and loss bulk compliances, B and B", were obtained. All data were successfully combined by the method of reduced variables taking into account the substantial dependence of both Bg and Bg (the equilibrium and glasslike bulk compliances) on both T and P, as follows ... 

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