Modelling of Elongational Flow of HDPE Melts by Hierarchical Multi-Mode Molecular Stress Function Model

The transient elongational data set obtained by filament-stretching rheometry of four commercial high-density polyethylene (HDPE) melts with different molecular characteristics was reported by Morelly and Alvarez [Rheologica Acta 59, 797–807 (2020)]. We use the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model of Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheology 60, 625–636 (2016)] for linear and long-chain branched (LCB) polymer melts to analyze the extensional rheological behavior of the four HDPEs with different polydispersity and long-chain branching content. Model predictions based solely on the linear-viscoelastic spectrum and a single nonlinear parameter, the dilution modulus GD for extensional flows reveals good agreement with elongational stress growth data. The relationship of dilution modulus GD to molecular characteristics (e.g., polydispersity index (PDI), long-chain branching index (LCBI), disengagement time τd) of the high-density polyethylene melts are presented in this paper. A new measure of the maximum strain hardening factor (MSHF) is proposed, which allows separation of the effects of orientation and chain stretching.

Influence of molecular structure on the foamability of polypropylene: Linear and extensional rheological fingerprint

The foaming structure and rheological properties of four different isotactic homo-polypropylenes with various molecular weights and an isotactic long chain branched polypropylene were investigated to find a suitable rheological fingerprint for PP foams. The molecular weight distribution and thermal properties were measured using GPC-MALLS and differential scanning calorimetry, respectively. Small amplitude oscillatory shear data and uniaxial extensional experiments were analyzed using the frameworks of van Gurp-Palmen plot (δ vs. | G*|) and the molecular stress function model, respectively. These analyses were used to find a correlation between the molecular structure, rheological properties and foaming structures of linear and long chain branching polypropylenes. Two linear viscoelastic characteristics, | G*| at δ = 60° and | η*| at ω = 5 rad/s were used as criteria for foamability of these polymers, where decreasing of both parameters by increasing the long chain branching content results in smaller cell size and higher cell density. The molecular stress function model was able to quantify the strain hardening properties of long chain branching blends using small amplitude oscillatory shear data and two nonlinear material parameters, 1 ≤ β ≤ 2.2 and 1 ≤ [Formula: see text] ≤ 600, where the minimum and maximum values of these parameters belong to the linear and long chain branched polypropylene, respectively. Increasing the long chain branched polypropylene content of the PP blends increased strain hardening, and therefore improved the foaming characteristics significantly by suppressing the coalescence of cells. Dilution of linear PP with only 10 wt% of long chain branched polypropylene enhanced the cell density from 5.7 × 106 to 2.7 × 107 cell/cm3 and reduced the average cell diameter from 58 to 26 µm, respectively, while their volume expansion ratio remained in the same range of 2–3. Increasing of long chain branching to 50 and 100 wt% enhanced the V.E.R. to 6.2 and 7.8, respectively.