scholarly journals Modeling elongational viscosity and brittle fracture of polystyrene solutions

2021 ◽  
Author(s):  
Manfred H. Wagner ◽  
Esmaeil Narimissa ◽  
Leslie Poh ◽  
Taisir Shahid
Keyword(s):  
Brittle Fracture ◽  
Molar Mass ◽  
Covalent Bond ◽  
Weight Fraction ◽  
Elongational Viscosity ◽  
Polymer Chains ◽  
Viscosity Data ◽  
Filament Stretching ◽  
Polymer Liquids ◽  
Linear Viscoelastic

AbstractElongational 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).

scholarly journals Elongational viscosity scaling of polymer melts with different chemical constituents

2021 ◽  
Vol 60 (4) ◽  
pp. 163-174
Author(s):  
Esmaeil Narimissa ◽  
Leslie Poh ◽  
Manfred H. Wagner
Keyword(s):  
Power Law ◽  
Molar Mass ◽  
Polymer Melts ◽  
Chemical Constituents ◽  
Elongational Flow ◽  
Weissenberg Number ◽  
Elongational Viscosity ◽  
Viscosity Data ◽  
Strain And Strain Rate ◽  
Linear Viscoelastic

AbstractMorelly 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.

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

2021 ◽  
Author(s):  
Manfred H. Wagner ◽  
Esmaeil Narimissa ◽  
Taisir Shahid
Keyword(s):  
Molar Mass ◽  
Mass Matrix ◽  
Viscoelastic Behavior ◽  
Elongational Viscosity ◽  
Viscosity Data ◽  
High Molar Mass ◽  
The Matrix ◽  
Linear Viscoelastic ◽  
Interchain Pressure ◽  
Long Chains

AbstractElongational 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.

scholarly journals Molar mass characterization of hydrophilic copolymers, 2 Size exclusion chromatography of cationic (meth)acrylate copolymers

e-Polymers ◽  
2005 ◽  
Vol 5 (1) ◽  
Author(s):  
Martina Adler ◽  
Harald Pasch ◽  
Christian Meier ◽  
Raimund Senger ◽  
Hans-Günter Koban ◽  
...  
Keyword(s):  
Stationary Phase ◽  
Size Exclusion Chromatography ◽  
Molar Mass ◽  
Extended Period ◽  
Size Exclusion ◽  
Viscosity Data ◽  
Exclusion Chromatography ◽  
Reproducible Method ◽  
Novel Method ◽  
Sec System

AbstractA robust and reproducible method for the molar mass analysis of cationic copolymers based on dimethylaminoethyl methacrylate or trimethylammonioethyl methacrylate and different (meth)acrylates has been developed. Size exclusion chromatography (SEC) using a novel polyester-based packing as the stationary phase and dimethylacetamide (DMAC) as the mobile phase yields highly accurate results for copolymers with an amino comonomer content up to 50 wt.-%. To suppress the different polar and ionic interactions between sample molecules, stationary phase and eluent, DMAC was modified with LiBr and tris(hydroxymethylamino) methane (TRIS). Calibrating the SEC system with poly(methyl methacrylate) of narrow polydispersity, molar masses were obtained that are in good agreement with viscosity data. Reproducibility and robustness of the novel method were proven by running samples for an extended period of two weeks.

Measurement and Evaluation of Bitumen/Toluene-Mixture Properties at Temperatures Up to 190?°C and Pressures Up to 10 MPa

SPE Journal ◽  
2016 ◽  
Vol 21 (05) ◽  
pp. 1705-1720 ◽  
Author(s):  
Hossein Nourozieh ◽  
Mohammad Kariznovi ◽  
Jalal Abedi
Keyword(s):  
Excess Volume ◽  
Weight Fraction ◽  
Viscosity Reduction ◽  
Viscosity Data ◽  
Pipeline Transportation ◽  
Density Data ◽  
Mixture Density ◽  
Oil Processing ◽  
Measurement And Evaluation ◽  
Volume Method

Summary The viscosity of bitumen and heavy oil is extremely high at both reservoir and surface conditions, on the order of 1 million cp. Therefore, viscosity reduction is necessary for production from the reservoir, pipeline transportation, and oil processing. The aim of this study is to evaluate the effect of different parameters (temperature, pressure, and solvent-weight fraction) on the density and viscosity of bitumen-containing mixtures. Thus, the density and viscosity of mixtures are measured for a sample of Athabasca bitumen diluted with different fractions of toluene at pressures from 0.1 to 10 MPa and at temperatures from 22 to 190 °C. The mixture densities show a linear decrease with temperature, pressure, and solvent concentration. The viscosity of the mixtures indicates a curvilinear trend with respect to the solvent-weight fraction and temperature. The effect of pressure on the mixture viscosity is more pronounced at lower-solvent-weight fractions. The mixture-density data are evaluated with two different methods: no volume change upon mixing and excess volume. The excess-volume method predicts the mixture-density data with an overall average absolute relative deviation (AARD) of 0.34%. The viscosity data for mixtures are compared with different models: Arrhenius (1987), Cragoe (1933), Shu (1984), Lobe (1973), double-log (Yarranton et al. 2013), Lederer (1933), power-law (Kendall and Monroe 1917), and Bij (Yarranton et al. 2013). The Bij model (Yarranton et al. 2013) produces the most-reliable results for mixture viscosities, with 5.5% AARD.

scholarly journals A Novel Viscosity-Temperature Model of Glass-Forming Liquids by Modifying the Eyring Viscosity Equation

2020 ◽  
Vol 10 (2) ◽  
pp. 428 ◽  
Author(s):  
Chunyu Chen ◽  
Huidan Zeng ◽  
Yifan Deng ◽  
Jingtao Yan ◽  
Yejia Jiang ◽  
...  
Keyword(s):  
Mathematical Expression ◽  
Impact Factors ◽  
Viscosity Data ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Regression Methods ◽  
Glass Forming ◽  
Viscosity Models ◽  
Polymer Liquids ◽  
Dependent Viscosity

Many models have been created and attempted to describe the temperature-dependent viscosity of glass-forming liquids, which is the foundational feature to lay out the mechanism of obtaining desired glass properties. Most viscosity models were generated along with several impact factors. The complex compositions of commercial glasses raise challenges to settle these parameters. Usually, this issue will lead to unsatisfactory predicted results when fitted to a real viscosity profile. In fact, the introduction of the reliable viscosity-temperature data to viscosity equations is an effective approach to obtain the accurate parameters. In this paper, the Eyring viscosity equation, which is widely adopted for molecular and polymer liquids, was applied in this case to calculate the viscosity of glass materials. On the basis of the linear variation of molar volume with temperature during glass cooling, a modified temperature-dependent Eyring viscosity equation was derived with a distinguished mathematical expression. By means of combining high-temperature viscosity data and the glass transition temperature (Tg), nonlinear regression analysis was employed to obtain the accurate parameters of the equation. In addition, we have demonstrated that the different regression methods exert a great effect on the final prediction results. The viscosity of a series of glasses across a wide temperature range was accurately predicted via the optimal regression method, which was further used to verify the reliability of the modified Eyring equation.

Isothermal crystallization of high density polyethylene with monomodal and bimodal molar mass distribution

e-Polymers ◽  
2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Yujing Tang ◽  
Zhiyong Jiang ◽  
Jens Rieger ◽  
Hans-Friedrich Enderle ◽  
Dieter Lilge ◽  
...  
Keyword(s):  
Mass Distribution ◽  
Isothermal Crystallization ◽  
High Density Polyethylene ◽  
Molar Mass ◽  
High Density ◽  
Polymer Chains ◽  
Molar Mass Distribution ◽  
Scanning Calorimetry ◽  
Polymeric Chains ◽  
Crystallization Tendency

AbstractThe isothermal crystallization behavior of two different high density polyethylene grades with monomodal and bimodal molar mass distribution was investigated by means of differential scanning calorimetry. The results indicate that extensive cocrystallization between linear short chains and long chains with short branches in bimodal polyethylene grade occurred. In contrast, polymer chains of different lengths in monomodal polyethylene exhibit different tendency to crystallize. This finding was explained qualitatively based on a general discussion of the effect of molar mass and branch content/length on crystallization tendency of polymeric chains.

Elongational Viscosity Measurements Using a Semi-Hyperbolic Die

2006 ◽  
Vol 16 (6) ◽  
pp. 312-320 ◽  
Author(s):  
D. G. Baird ◽  
J. Huang
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Extensional Flow ◽  
Elongational Viscosity ◽  
Extensional Viscosity ◽  
Viscosity Data ◽  
Low Density ◽  
Lubrication Approximation ◽  
Type Device ◽  
Shear Effects

Abstract The lubricated semi-hyperbolic die has been proposed as a technique for generating uni-axial extensional flow and, hence, as a device for measuring elongational viscosity. Two methods for extracting extensional viscosity data for polymer melts in laminar flow from this device have been proposed and are evaluated here. Following the approach proposed by Collier and coworkers, values of the transient extensional viscosity, ηe+, obtained from a non-lubricated semi-hyperbolic (SHPB) die for several polyethylene (PE) melts were found to be considerably higher than values obtained by means of the Münstedt-type device. Furthermore, the values of ηe+ obtained from the SHPB die were considerably higher than the strain averaged values of ηe+ which Everage and Ballman proposed would be obtained from a lubricated SHPB. The pressure drop across a SHPB die was estimated assuming resistance was all due to wall shear (using the lubrication approximation) for two PE resins. In the case of low density PE (LDPE) the values agreed to within 20% of the measured values suggesting that shear effects at the die wall were dominating the pressure drop and not extensional stresses. An analysis was carried out which showed that in the presence of lubrication the conditions for which the values of ηe+ obtained from the SHPB would be relatively accurate (Hencky strains > 5.0).

Influence of Energy Input on Suspension Properties

2010 ◽  
Vol 62 ◽  
pp. 141-146 ◽  
Author(s):  
Anja Meyer ◽  
Kerstin Lenzner ◽  
Annegret Potthoff
Keyword(s):  
Energy Input ◽  
Molar Mass ◽  
Mechanical Energy ◽  
Particle Surface ◽  
Significant Loss ◽  
Polymer Chains ◽  
Background Solution ◽  
Electrosteric Stabilization ◽  
Before And After ◽  
Nanoscale Range

Electrosteric stabilization of a commercially available boehmite powder in water was investigated to perform milling experiments and reduce the particle size to the nanoscale range. The effect of three sodium polyacrylate dispersants (Na-PA) with different molar masses (2,100, 8,000, 15,000 g/mol) on the suspension properties before and after milling experiments was assessed by electroacoustic measurements in comparison with rheological tests. A significant loss of the stabilizing effect of the sodium polyacrylates due to the application of mechanical energy was detectable. Measurements of the adsorbed amount of the dispersants after milling via detection of the COD in the background solution show a considerable desorption from the particle surface. Accessorily performed analyses of the molar mass of the polymers yielded a destruction of the polymer chains due to the mechanical energy.

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