An analytical relation between relaxation time spectrum and molecular weight distribution

In this article it is shown that the relaxation time spectrum can be analyt ically related to the molecular weight distribution regarding a recently de rived generalized mixing rule. This analytical relation greatly reduces the computational effort to determine the molecular weight distribution from t he relaxation time spectrum. In this mixing rule a generalized mixing param eter beta has been introduced. This parameter has been controversially disc ussed in the literature. The value of beta has been determined theoreticall y by Doi and Edwards [The Theory of Polymer Dynamics (Clarendon, Oxford, 19 86)] as beta = 1 and Des Cloizeaux [Europhys. Lett. 5, 437-442 (1988); 6, 4 75 (1988)] and Tsenoglou [Polym. Prepr. (Am. Chem. Sec. Div. Polym. Chem.) 28, 185-186 (1987)] (beta = 2) and experimentally by Maier et al. [J. Rheol . 42, 1153-1173 (1998)] (beta = 3.84). In this article the influence of bet a on shape and position of peaks in bimodal molecular weight distributions is emphasized. (C) 1999 The Society of Rheology. [S0148-6055(99)02406-2].