Relaxation Gross’ frequency

Figure 8. Reduced Gross frequency relaxation spectrum for Serles-I and II. The arrows Indicate computed coordinates of the maximum (Hg niax>Hiiax) ...

Substituting Eq 7.42 into the Gross frequency relaxation spectrum, H, results in an expression ... 

Since the Gross frequency relaxation spectrum can be computed from r , i.e., from the loss modulus, G = T co, the agreement between the computed and measured G values provides good means of verifying both the computational and experimental procedures. It has been found that Eqs 7.83 and 7.84 are useful to evaluate the rheological performance of systems that obey the linear viscoelastic principles. 

Figure 7.14. Coordinates of the maximum of the Gross frequency relaxation function, Hq (top) and (bottom), vs., respectively, the polydispersity index, M,/M, and the zero shear viscosity, T , a measure of the molecular weight [Utracki and Schlund, 1987].

Once these parameters are known, the Gross frequency relaxation spectrum can be calculated (see Eqs 7.85-7.87) and as a result all linear viscoelastic functions. 

Substituting Eq. 7.42 into Gross frequency relaxation spectmm, Hq, results in the following expression ... 

Dynamic testing of polymer blends at small amplimde is a relatively simple and reliable procedure. The resulting storage and loss shear moduli, G and G", respectively, should be first corrected for yield stress then the loss data can be fitted to Eq. 7.42 to determine the value of the four parameters, t)o, x, nii, and m2. Once these parameters are known, the Gross frequency relaxation spectrum, and as a result aU linear viscoelastic functirms, can be calculated (see Eqs. 7.85, 7.86, and 7.87). 

Coordinates of the Gross frequency relaxation spectrum maximum (see below). Deviation from the log-additivity, log rjbiend = Z log etc. 

Gross frequency relaxation spectrum, Hq(x), leads to (Utracki and Schlund 1987)... 

The dynamic tests at small amplitude in parallel plates or cone-and-plate geometry are simple and reproducible. From the experimental values of storage and loss shear moduli, G and G", respectively, first the yield stress ought to be extracted and then the characteristic four material parameters in Eq. (2.13), rjo, r, mi, and m2, might be calculated. Next, knowing these parameters one may calculate the Gross frequency relaxation spectrum (see Eqs. (2.31) and (2.32)) and then other linear viscoelastic functions. 

Thus, at low frequencies the Gross susceptibility (280) reduces to the Debye relaxation spectrum. 

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