An analytical relation between relaxation time spectrum and molecular weight distribution

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Abstract
In this article it is shown that the relaxation timespectrum can be analytically related to the molecular weight distribution regarding a recently derived generalized mixing rule. This analytical relation greatly reduces the computational effort to determine the molecular weight distribution from the relaxation timespectrum. In this mixing rule a generalized mixing parameter β has been introduced. This parameter has been controversially discussed in the literature. The value of β has been determined theoretically by [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] as β=1 and [Europhys. Lett. 5, 437–442 (1988); 6, 475 (1988)] and [Polym. Prepr. (Am. Chem. Soc. Div. Polym. Chem.) 28, 185–186 (1987)] (β=2) and experimentally by [J. Rheol. 42, 1153–1173 (1998)] (β=3.84). In this article the influence of β on shape and position of peaks in bimodal molecular weight distributions is emphasized.