Modeling the Rheology of Commercial Long Chain Branched Polymer Melts
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Modeling the Rheology of Commercial Long Chain Branched Polymer Melts Seung Joon Park and Ronald G. Larson Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA ABSTRACT The predictions of a general “hierarchical model” for the rheology of general mixtures of linear and branched polymers are compared to experimental data for well-defined long-chain branched polymers. For a wide range of branched polymer melts, which include star-linear blends, H-polymers, and comb polymers, the predictions of the model agree well with experimental data. We apply the hierarchical model to metallocene-catalyzed polyethylenes (mPEs), in which the branched structures are generated by a Monte Carlo method based on the known reaction kinetics. The hierarchical model captures the shape of the curves of viscoelastic moduli vs. frequency of mPEs well and predicts accurately the effect of long chain branching on the linear viscoelastic properties. The quantitative agreement of the hierarchical model prediction with experimental data of well-defined long-chain branched polymers and mPEs shows that information on branching structure could be inferred from rheological measurements on combinatorial sets of mixtures of an unknown branched with different combinations of linear polymers.
INTRODUCTION One of the most important practical polymer characterization problems is the characterization of long chain branch (LCB). Given the low levels of branching one would desire to detect (less than one branch per 10,000 backbone carbons), rheological data are a practically promising source of information on branching density, average branch length, and other branching characteristics due to the extreme sensitivity of rheological measurements to longchain branching [1]. However, inferring branching information from rheology has not proved possible so far, due to the ill-posed problem of fitting rheological data with a branching model in which there are too many parameters, including the density of branch points, branch lengths, the locations of the branches along the polymer backbone, and the polydispersity of molecular weight. Larson [2] developed an algorithm that generalizes the Milner-McLeish theories [3,4] to predict the relaxation of general mixtures of the branched polymers. This “hierarchical algorithm” could be used to design a branching structure necessary to achieve a desired target rheological response, through combinatorial computations that span a wide range of branching structures quickly on the computer. However, the hierarchical algorithm needs to be improved for quantitative predictions of well-defined branch structures such as star, H, and comb polymers because these simple branched structures are basic elements for the combinatorial rheology of more general branched polymers. Recently Park et al. [5] have improved the original hierarchical algorithm by inclusion of early time fluctuations and other refinements drawn from the theories of Milner and McLeish. Here we apply the modified hierarchical al
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