A rheology theory and method on polydispersity and polymer long-chain branching

Model calculations were performed to investigate the sensitivity of zero-shear melt viscosity (η0 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 Mw/Mn and Mz/Mw. 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;29:400-8]. Published rheological parameters appropriate for polyethylene were used in the calculations. It was found that Eta0 depended mostly on Mw, but it also significantly depended on the extent of high-MW polydispersity Mz/Mw. 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 (MHV or Mx with x = 1.5) to replace Mw in the historical rheological power-law equation of Eta0 ∝ Mwa, where the literature value of exponent “a” ranges from 3.2 to 3.6. The use of MHV instead of Mw 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 MHV in the new power law can be calculated for polymer samples from the conventional gel permeation chromatographic (GPC) slice data.