Isochrones, storage-modulus

Figures 5.21(a) and (b) give the temperature dependencies of the storage modulus fi and loss modulus fi", respectively, of samples with different levels of crystallinity probed in isochronal dynamic experiments at a frequency of 1.0 Hz in a...

Figure 12.52 describes the temperature dependence of dynamic storage modulus G during the isochronal dynamic temperature sweep experiment at an angular frequency (ty) of 0.1 rad/s for PS, PS-t-COONa, (PS-t-COONa)/Cloisite 20A nanocomoposite, and (PS-t-COONa)/Cloisite 30B nanocomposite. The following observations are worth noting in Figure 12.52. Not only is the magnitude of G for PS-t-COONa much larger than that for neat PS, but also the values of G for PS-t-COONa decrease slowly, as compared with the values of G for neat PS, with increasing temperature. We attribute this observation to the formation of ionic clusters in PS-t-COONa. It has been reported...

Fig. 38 Variations of dynamic storage modulus G/ with temperature during the isochronal dynamic temperature sweep experiments at co = O.lrad/s for (open circle) SI-2, open triangle) IS-t-COONa, open square) (IS-t-COONa)/Cloisite SOB nanocomposite, and open inverted triangle) (IS-t-COONa)/Cloisite 20A nanocomposite, (Reprinted from Zha et al. [55], Copyright 2005, with permission from the American Chemical Society)...

Differential scanning calorimetry data (heating rate 1 °Cmin, top) and temperature dependence of the isochronal dynamic storage modulus (morphologies observed by SAXS are indicated. Reprinted with permission from Floudas, G. etal. Europhys. Lett. 2000, 50(2), 182-188. = ... 

The order-disorder transition temperature (ODT) of the block copolymer was determined using a temperature scan under isochronal conditions, which involves measuring the dynamic storage modulus (G ) at a constant frequency (co = 0.2 rad/s) with temperature increasing from 130°C to 240°C in the linear viscoelastic regime. 

Figure 2. Isochronal plot of dynamic storage modulus G as a function of temperature at frequency co = 0.2 rad/s and strain y = 3%.

As shown in Figure 32, around Tg, where the storage modulus E T) shows a pronounced drop, the loss modulus "(T) exhibits a characteristic dispersion peak. The maximum position of the peak for an isochronal loss modulus curve coincides with Tg. In other words, the conversion of the mechanical energy applied to the system into heat is most efficient around the glass-to-rubber transition region. This dispersion peak is so characteristic that it is often used for the detection of Tg of an amorphous polymeric component in a composite material, where the direct measurement of the storage modulus is hampered by the presence of other stiff components in the system. 

FIG. 12-19. Isochronal plots of storage and loss Young s modulus (with a logarithmic scale) at a frequency of 110 Hz against temperature for styrene-butadiene triblock copolymers. Decreasing values of E correspond to decreasing styrene/butadiene ratio (West and Cooper, after Matsuo reproduced by permission of the publishers, IPC Business Press Ltd." )... 

Figure 32 shows the schematic view of a typical isochronal (i.e., fixed deformation frequency) DMA spectra as functions of temperature for an ordinary amorphous polymeric resin, like atactic PMMA or polystyrene. The dynamic storage and loss moduli, E T) and E"(T), measured under a fixed deformation frequency are plotted as functions of temperature T. The dynamic modulus plot is often accompanied with the dissipation factor, tan (5(T). A similar diagram is also obtained for isothermal DMA spectra, where E (o), E (o), and tan (3(co) are plotted as functions of the characteristic experimental time scale, taken as the reciprocal of the deformation frequency co. 

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