A generalized relation between MWD and relaxation time spectrum

An inversion procedure for converting linear viscoelastic properties of polymer melts into molecular weight distribution (MWD) described by the generalized exponential function (GEX) has been implemented and applied in a previous work (Cocchini F, Nobile MR. Rheol Acta 42:232–242, 2003). It is based on the elegant relationship between the relaxation spectrum and the MWD function proposed by Thimm W, Friedrich C, Marth M. J Rheol 43:1663–1672 (1999). In the present paper, such a methodology has been generalized to properly account for sharp MWDs, in particular, nearly monodisperse or blends of nearly monodisperse polymer samples. The generalized relationship has been verified and calibrated using the BSW kernel (Baumgaertel M, Schausberger A, Winter HH. Rheol Acta 29:400–408, 1990) to describe the rheological behavior of some Polystyrene samples from the literature, in terms of the known MWD. Then, it has been successfully applied to the inversion problem for a wider set of samples, with both broad and sharp distributions. The Rouse contribution at high frequencies and the accelerating effect on the relaxation times due to polydispersion have been also addressed.