An analytical relation between relaxation time spectrum and molecular weight distribution

In this article it is shown that the relaxation time spectrum 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 time spectrum. In this mixing rule a generalized mixing parameter beta has been introduced. This parameter has been controversially discussed in the literature. The value of beta has been determined theoretically by Doi and Edwards [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] as beta = 1 and Des Cloizeaux [Europhys. Lett. 5, 437-442 (1988); 6, 475 (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 beta on shape and position of peaks in bimodal molecular weight distributions is emphasized. (C) 1999 The Society of Rheology. [S0148-6055(99)02406-2].