Storage modulus, definition

Eqs. (1.16) are, of course, very well-known. G is known as the storage modulus in shear. It describes that part of the shear stress, which is in phase with the deformation. G" is the loss modulus in shear. It describes that part of shear stress which is 90 degrees out of phase. 6 is the loss angle. These definitions will be used occasionally in this review. 

Stiffness, 83, 225, 228, 269, 281 Storage modulus, 618, 631 Straight-sided specimens, 323 Strain and stress, basic definitions and... 

The curves in Fig. 5.21(a) show that in samples with crystallinity less that 2%-3% the storage moduli // do not differ from that of fully glassy PET. In these, the moduh drop quite precipitously near 70 °C down to very low levels typical of uncross-linked linear-chain polymers of around 1.0 MPa. Samples with crystallinities above 16% show more gradual drops in //, which are also moved out to the temperatures of their initial crystalhzation treatments, beyond which the drops become much steeper. Clearly, while there is a definite decrease in storage modulus down to levels of around 100 MPa, this decrease is pushed far out to temperatures reaching 240 °C by the reinforcing effect of the crystalline fraction. 

The quantities E and G refer to quasi-static measurements. When cyclic motions of stress and strain are involved, it is more convenient to use dynamical mechanical moduli. The complex Young s modulus is then defined as = " + iE", where E is the storage modulus and " the loss modulus. The storage modulus is a measure of the energy stored elastically during deformation the loss modulus is a measure of the energy converted to heat. Similar definitions hold for G, J, and other mechanical properties. 

The reader should note that some authors introduce the storage modulus differently — by burying the Goo term into the definition of G — in which case, Eq. 50 assumes the form... 

Figure 4 Comparison of the storage modulus and tack of a PSA as a function of temperature. The frequency of measurement is 1 Hz. When the modulus of the adhesive goes below 3x10 dyn cm , the tack starts to reach a maximum. This is the definition of the Dahlquist criterion for tack.

In the theories for dilute solutions of flexible molecules based on the bead-spring model, the contribution of the solute to the storage shear modulus, loss modulus, or relaxation modulus is given by a series of terms the magnitude of each of which is proportional to nkT, i.e., to cRTjM, as in equation 18 of Chapter 9 alternatively, the definition of [C ]y as the zero-concentration limit of G M/cRT (equations 1 and 6 of Chapter 9) implies that all contributions are proportional to nkT. Each contribution is associated with a relaxation time which is proportional to [ri Ti)sM/RT-, the proportionality constant (= for r i) depends on which theory applies (Rouse, Zimm, etc.) but is independent of temperature, as is evident, for example, in equation 27 of Chapter 9. Thus the temperature dependence of viscoelastic properties enters in four variables [r ], t/j, T explicitly, and c (which decreases slightly with increasing temperature because of thermal expansion). 

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