A rheology theory and method on polydispersity and polymer long-chain branching (original) (raw)
Model calculations were performed to investigate the sensitivity of zero-shear melt viscosity (h 0 or Eta0) on the molecular weight (MW) polydispersity of linear polymers. Simulated MW distributions (MWD) were generated with the generalized exponential (GEX) distribution function for various levels of polydispersity M w /M n and M z /M w . For linear entangled polymeric chains in the melt, the linear viscoelastic properties were predicted by using the double reptation blending rule and the so-called BSW relaxation time spectrum, named after the authors: Baumgaertel, Schausberger and Winter [Baumgaertel M, Schausberger A, Winter HH. Rheol Acta 1990;29:400e8]. Published rheological parameters appropriate for polyethylene were used in the calculations. It was found that Eta0 depended mostly on M w , but it also significantly depended on the extent of high-MW polydispersity M z /M w . A revision to the fundamental MW dependency of Eta0 was proposed to compensate for this polydispersity effect. To offset the polymer polydispersity differences, we propose a new MW average (M HV or M x with x ΒΌ 1.5) to replace M w in the historical rheological power-law equation of Eta0 f M w a , where the literature value of exponent ''a'' ranges from 3.2 to 3.6. The use of M HV instead of M w in the power-law equation made the calculated Eta0 independent of the sample high-MW polydispersity. With the removal of the complication from polydispersity effect, the new Eta0 power law can now provide a more robust base for studying polymer long-chain branching (LCB). A new LCB index is thus proposed based on this new melt-viscosity power law. The values of M HV in the new power law can be calculated for polymer samples from the conventional gel permeation chromatographic (GPC) slice data.
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