Generalization of Double-Reptation

Another method that makes use of the double reptation model and the assumption of a Gex MWD is that of Guzman et al. [37]. They also accoimt for the effect of unentangled chains. Their method avoids the use of a regularization technique to infer G t) from dynamic data, and their analysis leads to an estimate of the reliability of the prediction. 

Anderssen and Mead [38] considered a generalized mixing rule that includes both the Doi-Edwards relaxation modulus and that of double-reptation as special cases. 

Obviously = 1 gives the Doi-Edwards function, and j8 = 2 gives double reptation. Anderssen and Mead reported that the scaling of rheological properties with respect to molecular weight averages, e.g., tJq = M , is not sensitive to the value of j8. 

Maier et al. [39] took j8 to be a material-dependent parameter and determined its value for several polymers by fitting data for binary blends of samples having different molecular weight distributions. They assumed a single-exponential form for F tM) and found j8 = 3.3 for PMMA and j8 = 3.8 for polystyrene. The terminal relaxation time was assumed to be proportional to M , where a 3. As we have seen, this can be interpreted as a very crude way of accounting for tube length fluctuations. 

Two procedures based on Eq. 8.39 have been proposed to infer the molecular weight distribution from the relaxation modulus. Maier et al. [39] used Tikhonov regularization to invert the integral, whereas Thimm et aZ. [36 ] used an analytical relation between the relaxation function, H t) and the molecular weight distribution. 

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P exponent in generalization of double reptation mixing rule Eq. 8.39... 

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