Modulus storage

Figure 3.16 Some experimental dynamic components, (a) Storage and loss compliance of crystalline polytetrafluoroethylene measured at different frequencies. [Data from E. R. Fitzgerald, J. Chem. Phys. 27 1 180 (1957).] (b) Storage modulus and loss tangent of poly(methyl acrylate) and poly(methyl methacrylate) measured at different temperatures. (Reprinted with permission from J. Heijboer in D. J. Meier (Ed.), Molecular Basis of Transitions and Relaxations, Gordon and Breach, New York, 1978.)...

The storage modulus rather than compliance is plotted. This is a trivial difference, but note that the modulus is measured at a single frequency, 1 Hz. 

Fig. 18. Resolution of the complex modulus G into two vectors, G the storage modulus, and G the loss modulus the phase angle is 5.

Fig. 21. Dynamic viscoelastic properties of a low density polyethylene (LDPE) at 150°C complex dynamic viscosity Tj, storage modulus G and loss modulus G" vs angular velocity, CO. To convert Pa-s to P, multiply by 10 to convert Pa to dyn/cm, multiply by 10.

Class and Chu [34] have studied the tackification of natural rubber and SBR over a wide range of resin concentrations for several tackifiers. From their graphical data it can be estimated that 1 1 tackification (by weight) with a poly(/-butyl styrene) resin, MW 850 and Tg = 59°C, gives a PSA with Tg about — 13°C, and storage modulus, G about 8.8 x 10 Pa, well within the PSA window. 

Fig. 15. Effect of tackifying resin on storage modulus of addition-cured silicone PSA.

This presentation format leads to the terminology EI = real modulus or storage modulus 2 = imaginary modulus or loss modulus. 

As one example, in thin films of Na or K salts of PS-based ionomers cast from a nonpolar solvent, THF, shear deformation is only present when the ion content is near to or above the critical ion content of about 6 mol% and the TEM scan of Fig. 3, for a sample of 8.2 mol% demonstrates this but, for a THF-cast sample of a divalent Ca-salt of an SPS ionomer, having only an ion content of 4.1 mol%, both shear deformation zones and crazes are developed upon tensile straining in contrast to only crazing for the monovalent K-salt. This is evident from the TEM scans of Fig. 5. For the Ca-salt, one sees both an unfibrillated shear deformation zone, and, within this zone, a typical fibrillated craze. The Ca-salt also develops a much more extended rubbery plateau region than Na or K salts in storage modulus versus temperature curves and this is another indication that a stronger and more stable ionic network is present when divalent ions replace monovalent ones. Still another indication that the presence of divalent counterions can enhance mechanical properties comes from... 

Figure 15 Storage modulus, (E ), loss tangent (tanS), and loss modulus, (E ), as a function of temperature for P7MB and P8MB at 3 Hz.

Figure 17 Variation of the storage modulus (E ) and loss tangent (tan5) at 3 Hz, for two PDEB specimens freshly quenched, and O aged for 14 months.

In conclusion, the different thermal histories imposed to PTEB have a minor effect on the /3 and y relaxations, while the a. transition is greatly dependent on the annealing of the samples, being considerably more intense and narrower for the specimen freshly quenched from the melt, which exhibits only a liquid crystalline order. The increase of the storage modulus produced by the aging process confirms the dynamic mechanical results obtained for PDEB [24], a polyester of the same series, as well as the micro-hardness increase [22] (a direct consequence of the modulus rise) with the aging time. 

Figure 1 Plots of dynamic storage modulus against temperature at 3.5 Hz [33]. EPO (-), EPl (— —), EP2...

Figure 6 Typical plots from dynamic mechanical thermal analysis showing storage modulus and tan6 variation with temperature [27]. SO (---), S2 (--).

The variation in room temperature storage modulus on filler incorporation is shown in Fig. 7. The results could be fitted into the following equation [27] ... 

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