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Evalutation of MWD from dynamic moduli: predictions from the double reptation model
Autori: M.R. Nobile, F. Cocchini Presentato al:Southern Europe Conference on Rheology Anno: 1999 Volume: 2 Issue: Unico Casa Editrice: SIR-Cuen Napoli Lingua: English
Abstract
The rheology of polymer melts is highly sensitive to their molecular weight distribution (MWD). Different mixing rules have been proposed in literature to describe the behavior of polydisperse systems. The concept of double reptation proposed by Tsenoglou (Tsenoglou, 1991) and Des Cloiseaux (1988) has been used to calculate the dynamic moduli from known MWDs by Wasserman and Graesslay (1992). Indeed, in this paper the inverse problem of obtaining the MWD from the linear viscoelastic behavior of entangled polymer melts has been analyzed. In literature it has been emphasized that the solution of the inverse problem can be ill-posed; i.e. the solution might be extremely sensitive to small changes in the input (Mead, 1994, Nobile et al. 1996). To escape from the ill-poseness we have incorporated some prior knowledge of the nature of the solution into the functional equation correlating the MWD to the dynamic moduli, i.e. an a priori analytical MWD function is assigned. The General Exponential Function (GEX) is chosen among the different functions that describe the MWD of polymers since it is capable of accurately reproducing the MWD of a wide class of unimodal polymers. The best-fit parameters of this rheological model directly give the MWD of the polymers. To test the predictions of the model the Tuminello step function is used as the stress relaxation function for the monodisperse melt. The zero shear rate viscosity and the steady state compliance have been analytically computed and estimated as a function of the different moments of the GEX distribution. The predictions have been satisfactorily compared with experimental results reported in literature.
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