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

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.

Download Full-text

Elongational viscosity scaling of polymer melts with different chemical constituents

Rheologica Acta ◽

10.1007/s00397-021-01261-9 ◽

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.

Download Full-text

Modeling elongational viscosity and brittle fracture of polystyrene solutions

Rheologica Acta ◽

10.1007/s00397-021-01277-1 ◽

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).

Download Full-text

Analytical Expressions for the Relaxation Moduli of Linear Viscoelastic Composites With Periodic Microstructure

Journal of Applied Mechanics ◽

10.1115/1.2897015 ◽

1995 ◽

Vol 62 (3) ◽

pp. 786-793 ◽

Cited By ~ 35

Author(s):

R. Luciano ◽

E. J. Barbero

Keyword(s):

Laplace Transform ◽

Viscoelastic Behavior ◽

Relaxation Functions ◽

Periodic Microstructure ◽

The Matrix ◽

The Laplace Transform ◽

Linear Viscoelastic ◽

The Time Domain ◽

Viscoelastic Composites ◽

Long Fibers

In this paper the viscoelastostatic problem of composite materials with periodic microstructure is studied. The matrix is assumed linear viscoelastic and the fibers elastic. The correspondence principle in viscoelasticity is applied and the problem in the Laplace domain is solved by using the Fourier series technique and assuming the Laplace transform of the homogenization eigenstrain piecewise constant in the space. Formulas for the Laplace transform of the relaxation functions of the composite are obtained in terms of the properties of the matrix and the fibers and in function of nine triple series which take into account the geometry of the inclusions. The inversion to the time domain of the relaxation and the creep functions of composites reinforced by long fibers is carried out analytically when the four-parameter model is used to represent the viscoelastic behavior of the matrix. Finally, comparisons with experimental results are presented.

Download Full-text

Effect of high molar mass species on linear viscoelastic properties of polyethylene melts

European Polymer Journal ◽

10.1016/j.eurpolymj.2013.06.015 ◽

2013 ◽

Vol 49 (9) ◽

pp. 2748-2758 ◽

Cited By ~ 6

Author(s):

Jon Otegui ◽

Javier Ramos ◽

Juan F. Vega ◽

Javier Martínez-Salazar

Keyword(s):

Viscoelastic Properties ◽

Molar Mass ◽

High Molar Mass ◽

Polyethylene Melts ◽

Linear Viscoelastic

Download Full-text

The Apparent Viscoelastic Behavior of Articular Cartilage—The Contributions From the Intrinsic Matrix Viscoelasticity and Interstitial Fluid Flows

Journal of Biomechanical Engineering ◽

10.1115/1.3138591 ◽

1986 ◽

Vol 108 (2) ◽

pp. 123-130 ◽

Cited By ~ 254

Author(s):

A. F. Mak

Keyword(s):

Articular Cartilage ◽

Interstitial Fluid ◽

Viscoelastic Model ◽

Viscoelastic Behavior ◽

Fluid Flows ◽

Confined Compression ◽

Interstitial Fluid Flow ◽

The Matrix ◽

Linear Viscoelastic ◽

Interstitial Fluid Flows

Articular cartilage was modeled rheologically as a biphasic poroviscoelastic material. A specific integral-type linear viscoelastic model was used to describe the constitutive relation of the collagen-proteoglycan matrix in shear. For bulk deformation, the matrix was assumed either to be linearly elastic, or viscoelastic with an identical reduced relaxation spectrum as in shear. The interstitial fluid was considered to be incompressible and inviscid. The creep and the rate-controlled stressrelaxation experiments on articular cartilage under confined compression were analyzed using this model. Using the material data available in the literature, it was concluded that both the interstitial fluid flow and the intrinsic matrix viscoelasticity contribute significantly to the apparent viscoelastic behavior of this tissue under confined compression.

Download Full-text

Paper Chemistry: Interactions of thermo mechanical pulp fractions with high molar mass cationic polyacrylamides: Part 2. Flocculation

Nordic Pulp & Paper Research Journal ◽

10.3183/npprj-2010-25-03-p310-318 ◽

2010 ◽

Vol 25 (3) ◽

pp. 310-318 ◽

Cited By ~ 2

Author(s):

Tero Taipale ◽

Janne Laine ◽

Susanna Holappa ◽

Jonni Ahlgren ◽

Juan Cecchini

Keyword(s):

Molar Mass ◽

High Molar Mass ◽

Mechanical Pulp ◽

Paper Chemistry

Download Full-text

Highly Efficient MOF Catalyst Systems for CO2 Conversion to Bis-Cyclic Carbonates as Building Blocks for NIPHUs (Non-Isocyanate Polyhydroxyurethanes) Synthesis

Catalysts ◽

10.3390/catal11050628 ◽

2021 ◽

Vol 11 (5) ◽

pp. 628

Author(s):

Adolfo Benedito ◽

Eider Acarreta ◽

Enrique Giménez

Keyword(s):

Molar Mass ◽

Cycloaddition Reaction ◽

Building Blocks ◽

Catalyst System ◽

Cyclic Carbonate ◽

Ammonium Bromide ◽

Cyclic Carbonates ◽

High Molar Mass ◽

Highly Efficient ◽

Free Process

The present paper describes a greener sustainable route toward the synthesis of NIPHUs. We report a highly efficient solvent-free process to produce [4,4′-bi(1,3-dioxolane)]-2,2′-dione (BDC), involving CO2, as renewable feedstock, and bis-epoxide (1,3-butadiendiepoxide) using only metal–organic frameworks (MOFs) as catalysts and cetyltrimethyl-ammonium bromide (CTAB) as a co-catalyst. This synthetic procedure is evaluated in the context of reducing global emissions of waste CO2 and converting CO2 into useful chemical feedstocks. The reaction was carried out in a pressurized reactor at pressures of 30 bars and controlled temperatures of around 120–130 °C. This study examines how reaction parameters such as catalyst used, temperature, or reaction time can influence the molar mass, yield, or reactivity of BDC. High BDC reactivity is essential for producing high molar mass linear non-isocyanate polyhydroxyurethane (NIPHU) via melt-phase polyaddition with aliphatic diamines. The optimized Al-OH-fumarate catalyst system described in this paper exhibited a 78% GC-MS conversion for the desired cyclic carbonates, in the absence of a solvent and a 50 wt % chemically fixed CO2. The cycloaddition reaction could also be carried out in the absence of CTAB, although lower cyclic carbonate yields were observed.

Download Full-text