Evaluation of molecular weight distribution from dynamic moduli
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A method to evaluate molecular weight distribution (MWD) from dynamic moduli is presented here. It relies on the least-square fitting of the dynamic data to a model whose parameters depend on the MWD. In particular, the analytical solution for the relaxation modulus previously obtained from the double reptation model, with the Tuminello step relaxation function and the Generalized Exponential Function (GEX) describing the MWD (Nobile and Cocchini 2000), has been used. A Finite Element Approximation (FEA) has been applied to calculate dynamic moduli from the relaxation modulus as a function of MWD. The sensitiveness of the GEX-double reptation dynamic moduli on the model parameters has also been investigated and the results show that large changes of the Mw/Mn ratio weakly affect the dynamic moduli, while small changes of the Mz/Mw ratio significantly deform the dynamic moduli curves. The use of rheological data to obtain MWD, by the model used in this paper, will, therefore, be able to give rather well defined Mz/Mw ratios, while more uncertainty will be presented in the Mw/Mn results. The so-called GEX-rheological model for the dynamic moduli was applied to fit the experimental data of different polymers in order to obtain the best-fit parameters of the MWD of these polymers, without the need for the inversion of the double reptation integral equation. The stability of the results has been confirmed through the evaluation of the 90% confidence intervals for the first molecular weight averages. Finally, concerning the Mw and Mz values, the predictions obtained from the dynamic moduli measurements differ by less than 10% from those obtained from GPC measurements while, as expected, more uncertainty is present in the Mn predictions.
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