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Modeling elongational viscosity of blends of linear and long-chain branched polypropylenes
Authors:Manfred H Wagner  Saeid Kheirandish  Jens Stange  Helmut Münstedt
Institution:1. Technische Universit?t Berlin Polymertechnik/Polymerphysik Fasanenstrasse 90, D-10623, Berlin, Germany
2. Universit?t Erlangen-Nürnberg, Lehrstuhl für Polymerwerkstoffe, Martensstrasse 7, D-91058, Erlangen, Germany
Abstract:To enhance the melt strength of a conventional linear polypropylene (L-PP), blends with a long-chain branched polypropylene (LCB-PP) were produced by adding 2, 5, 10, 25, 50, and 75 wt% of LCB-PP to L-PP and mixing in a twin screw extruder. It was found that, already, an addition of 10% or less of LCB-PP to L-PP leads to significant strain hardening. Elongational viscosity data of L-PP and LCB-PP and those of their blends were analyzed by the use of the molecular stress function (MSF) theory. While L-PP is characterized by the MSF parameter, β=1 (typical for linear melts), and shows very little chain stretch ($$f^{2}_{{\max }} = 1.5$$), melt elongational behavior of LCB-PP is characterized by the MSF parameters, β=2 (typical of LCB melts), and $$f^{2}_{{\max }} = 225$$ (which corresponds to a maximum stretch of molecular chains by a factor of 15). By extruding LCB-PP, a refining effect is observed similar to the refining effects seen in low density polyethylene (LDPE), which reduces the steady-state elongational viscosity and reduces $$f^{2}_{{\max }}$$ to 121. A second-order mixing rule for the fractional relaxation moduli, g i , was found to show good agreement with the linear-viscoelastic data of the blends. To simulate the elongational viscosities of the L-PP/LCB-PP blends, a similar second-order mixing rule was used for the MSF parameter, β, while a first-order mixing rule was found to be appropriate for $$f^{2}_{{\max }}$$. This allows for a quantitative prediction of the time-dependent elongational viscosities of all L-PP/LCB-PP blends on the basis of the linear and nonlinear parameters of the mixing components L-PP and LCB-PP only. Comparison between the steady-state elongational viscosities as obtained from creep experiments shows good agreement with predictions.
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