Elongational viscosity and brittle fracture of bidisperse blends of a high and several low molar mass polystyrenes

Elongational viscosity data of four well-characterized blends consisting of 10% mass fraction of monodisperse polystyrene PS-820k (molar mass of 820 kg/mol) and 90% matrix polystyrenes with a molar mass of 8.8, 23, 34, and 73 kg/mol, respectively, as reported by Shahid et al. Macromolecules 52: 2521–2530, 2019 are analyzed by the extended interchain pressure (EIP) model including the effects of finite chain extensibility and filament rupture. Except for the linear-viscoelastic contribution of the matrix, the elongational viscosity of the blends is mainly determined by the high molar mass component PS-820k at elongation rates when no stretching of the lower molar mass matrix chains is expected. The stretching of the long chains is shown to be widely independent of the molar mass of the matrix reaching from non-entangled oligomeric styrene (8.8 kg/mol) to well-entangled polystyrene (73kg/mol). Quantitative agreement between data and model can be obtained when taking the interaction of the long chains of PS-820k with the shorter matrix chains of PS-23k, PS-34k, and PS-73k into account. The interaction of long and short chains leads to additional entanglements along the long chains of PS-820k, which slow down relaxation of the long chains, as clearly seen in the linear-viscoelastic behavior. According to the EIP model, an increased number of entanglements also lead to enhanced interchain pressure, which limits maximal stretch. The reduced maximal stretch of the long chains due to entanglements of long chains with shorter matrix chains is quantified by introducing an effective polymer fraction of the long chains, which increases with the increasing length of the matrix chains resulting in the excellent agreement of experimental data and model predictions.

Modeling elongational viscosity and brittle fracture of polystyrene solutions

Elongational viscosity data of well-characterized solutions of 3–50% weight fraction of monodisperse polystyrene PS-820k (molar mass of 820,000 g/mol) dissolved in oligomeric styrene OS8.8 (molar mass of 8800 g/mol) as reported by André et al. (Macromolecules 54:2797–2810, 2021) are analyzed by the Extended Interchain Pressure (EIP) model including the effects of finite chain extensibility. Excellent agreement between experimental data and model predictions is obtained, based exclusively on the linear-viscoelastic characterization of the polymer solutions. The data were obtained by a filament stretching rheometer, and at high strain rates and lower polymer concentrations, the stretched filaments fail by rupture before reaching the steady-state elongational viscosity. Filament rupture is predicted by a criterion for brittle fracture of entangled polymer liquids, which assumes that fracture is caused by scission of primary C-C bonds of polymer chains when the strain energy reaches the bond-dissociation energy of the covalent bond (Wagner et al., J. Rheology 65:311–324, 2021).

Elongational viscosity scaling of polymer melts with different chemical constituents

Morelly et al. (Macromolecules 52:915-922, 2019) reported transient and steady-state elongational viscosity data of monodisperse linear polymer melts obtained by filament-stretching rheometry with locally controlled strain and strain rate and found different power law scaling of the elongational viscosities of polystyrene, poly(tert-butylstyrene) and poly(methyl-methacrylate). Very good agreement is achieved between data and predictions of the extended interchain pressure (EIP) model (Narimissa et al. J. Rheol. 64, 95-110 (2020)), based solely on linear viscoelastic characterization and the Rouse time τR of the melts. The analysis reveals that both the normalized elongational viscosity and the normalized elongational stress are dependent on the number of entanglements (Z) and the ratio of entanglement molar mass Mem to critical molar mass Mcm of the melts in the linear viscoelastic regime through $$ {\eta}_E^0/\left({G}_N{\tau}_R\right)\propto {\left({M}_{\mathrm{em}}/{M}_{\mathrm{cm}}\right)}^{2.4}{Z}^{1.4} $$ η E 0 / G N τ R ∝ M em / M cm 2.4 Z 1.4 and $$ {\sigma}_E^0/{G}_N\propto {\left({M}_{\mathrm{em}}/{M}_{\mathrm{cm}}\right)}^{2.4}{Z}^{1.4} Wi $$ σ E 0 / G N ∝ M em / M cm 2.4 Z 1.4 W i , while in the limit of fast elongational flow with high Weissenberg number $$ Wi={\tau}_R\dot{\varepsilon} $$ Wi = τ R ε ̇ , both viscosity and stress become independent of Z and Mem/Mcm, and approach a scaling which depends only on Wi, i.e. ηE/(GNτR) ∝ Wi−1/2 and σE/GN ∝ Wi1/2. When expressed by an effective power law, the broad transition from the linear viscoelastic to the high Wi regime leads to chemistry-dependent scaling at intermediate Wi depending on the number of entanglements and the ratio between entanglement molar mass and critical molar mass.

Comparing the elasticity of the melt and electrical conductivity of the solid of PP-HDPE copolymer CNT composites obtained by direct compounding versus dilution of a PP masterbatch

Composites of multiwall carbon nanotubes (CNT) at 1, 2, and 3 wt.% on a polypropylene–polyethylene random copolymer matrix were prepared by melt compounding CNT powder and by dilution of a commercial polypropylene masterbatch (PMB). While the shear viscosity shows similar behavior for both dilution modes, the differences in their elastic properties clearly show the effect of the addition method and the presence of the PMB. This also indicates the relevance of having a difficult to mix masterbatch to enhance the elongational viscosity of the composites for free wall applications such as fiber spinning and blown film. On the other hand, the 2 and 3 wt.% CNT composites from both addition modes have similar electrical conductive behavior, with values near the semiconductors’ range. TEM and SEM images show different states of dispersion for each source of CNT. The immiscibility observed in those images is the simplest explanation for the differences in the molten composites’ elastic properties due to direct CNT addition versus CNT addition by dilution of a PMB.

Influence of Tack Speed on The Rheological Properties of Mortar in Fresh State

In the present work, the squeeze flow techniques were used to investigate the influence of tack speed to the rheological properties of mortar in fresh sate, including yield stress and extensional viscosity.Tested samples were prepared under similar conditions of room temperature and atmospheric pressure. Compositions of mortars were tested at two different squeezing rates (20 and 200 mm/s) 15 min after mixing. Results indicate that mortar’s yield stress increases with the increasing of the pulling speed. This increase is evident at low tensile speeds. At high speed of tack, this increase is not obvious, especially in case of high squeeze speed of 200 mm/s. It can be concluded that the optima speed for removing the mortar and the upper surface is lower than 20 mm/s. The extensional viscosity of fresh mortars significantly decrease as the tack speed increases. Elongational viscosity values decreased as a result of gap increasing. The increase of the gap during tack experiment stimulates different units (grains getting far apart to each other) causing the observed decrease of the mortars' elongational viscosity

Influence of Squeezing Rate on Yield Stress and Viscosity of Fresh Mortar

In the present work, squeeze flow techniques were used to investigate the influence of squeezing rates on the yield stress of mortars in fresh state. The tested samples were prepared under similar conditions of room temperature and atmospheric pressure. The fresh mortars were tested at three squeezing rates (20 and 200mm/s) 15 minutes after mixing. The results show that the material’s yield stress increases with the increasing of the squeeze velocity. This increase is evident at low tensile speeds and is not obvious at high tack velocity. Elongational viscosity values increased as a result of the gap reduction for all the tested samples. However, when the squeeze speed was high, the strain rate increased because of the high displacement rates, a significant reduction in the mortar’s elongational viscosity was observed compared with those obtained when the squeeze speed was low. Despite that this behavior is associated with fluid-solid phase separation, which occurs for low displacement rates, these viscosity values actually represent the behavior of the material in practical situations when submitted to different velocities. The increase in the displacement rate of one order of magnitude caused a reduction in the viscosity of one order of magnitude.