Storage relaxation modulus

Double logarithmic plots of the storage relaxation modulus versus frequency for a viscoelastic material are shown in Figure 8.12 (9). By taking into account Eq. (6.3), the correspondence between the results at tempera-... 

Figure 8.12 Logarithmic plots showing storage relaxation modulus of polyisobutylene in the frequency domain. The isotherms coresponding to the terminal region are not drawn. (From Ref. 9.)...

Figure 8.19 Influence of molecular weight on the plateau length of narrow distribution polystyrene. The curves represent the storage relaxation modulus in the frequency domain reduced to 160°C. Viscosity-average molecular weights from left to right, xlO" 58, 51, 35, 27.5, 21.5, 16.7, 11.3, 5.9, and 4.7. (From Ref. 25.)...

Following the same procedure, the components of the complex relaxation modulus can be expressed in terms of the relaxation spectrum. Thus, by substituting the difference Git) — Gg given in Eq. (9.5) into Eq. (6.3), we obtain the following expression for the storage relaxation modulus ... 

The storage relaxation modulus for liquids is also given by Eq. (9.8) with Ge = 0. Proceeding in the same way for the loss modulus, one obtains... 

Figure 9.3 Double logarithmic plots of the storage compliance function ( ) and the reciprocal of the storage relaxation modulus (O ) for a 40% solution of polystyrene in tri-m-tolyl phosphate.

Figure 9.5 Plots of the kernels of the relaxation modulus and the storage relaxation modulus versus — logr/x and log cox, respectively.

Because the relaxation spectra are similar for transient and dynamic relaxation viscoelastic functions, H t) can also be obtained from the storage relaxation modulus. The plot of the kernel of the integral of Eq. (9.8), x /(l + (o x ), versus logcax is a sigmoidal curve that intercepts the ordinate axis at 0.5 and reaches the value of 1 in the limit cox oo (see Fig. 9.5). The kernel can be approximated by the step function... 

Therefore the storage relaxation modulus can be written approximately as... 

Figure 12t3 Illustrative curves showing the temperature dependence of both the storage relaxation modulus G and the logarithmic decrement A in the glassy state and glass-rubber transition. (From Ref. 47.)...

Figure 12.10 Temperature dependence of the tensile storage relaxation modulus for poly(vinyl chloride) at frequencies of (O) 0.1 Hz, ( ) 0.3 Hz, ( ) 1 Hz, ( ) 3 Hz, and (A) 10 Hz.

Figure 12.33 Storage relaxation modulus and logarithmic decrement for poly-oxymethylene specimens of two crystallinities (O) 76% and ( ) 54%. Squares refer to the values of G and A of a specimen measured immediately after storage at room temperature ( ). (From Ref. 43.)...

The parameter iVi is also related to the storage relaxation modulus. Actually, from Eqs. (6.52) and (13.25),... 

Accordingly, the value of Ni at very low shear rates is twice that of the storage relaxation modulus at very low frequencies. The second normal stress difference, 2 = 7111—5133, is negative and smaller in magnitude than the first normal stress difference. The ratio —Ni/Nx lies in the interval 0.1A).3. 

Figure 17.8 Variation of the storage relaxation modulus, E, with temperature measured during a cooling experiment. Ep represents the actual value of the storage relaxation modulus in absence of contraction forces which increase the longitudinal tension.

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