Determination of the molecular weight distribution of entangled linear polymers from linear viscoelasticity data

In a companion paper [Macromolecules 35 (2002) 2689], we have addressed the direct problem of predicting the linear viscoelastic response of entangled linear polymers from their molecular weight distribution, using a suitable model inspired by reptation theory. By comparing the theoretical results to experimental data for a variety of samples of different nature (polystyrene, polycarbonate, high-density polyethylene) and distribution (monomodal and multimodal), we found that the time-dependent diffusion reptation model proposed by des Cloizeaux, suitably modified to treat short chains and to include Rouse processes, is capable of quantitative predictions. In the present paper, we use the modified des Cloizeaux model to address the inverse problem of predicting molecular weight distribution from dynamic moduli. A parametric approach is implemented to deal with the ill-posedness of the problem. Results are given for most of the samples studied in [Macromolecules 35 (2002) 2689]. They are in quantitative agreement with size-exclusion chromatography data. In particular, the proposed methodology is able to resolve small amounts of short chains in bimodal blends containing large amounts of long chains. (C) 2002 Elsevier Science B.V. All rights reserved