Polymer molecular weight,zero shear viscosity,steady state compliance and binary blending law

Viscoelastic properties of binary blends of polystyrenes with a narrow distribution of low and high molecular weights (M₂ > M₁ > M_c) were examined. By combining the theoretical work of Montfort et al., Kurata, and Schausberger, a binary blending law was developed and was used to calculate the zero shear viscosity and steady state compliance of the blend of two monodisperse polymers. The blending law was also used to calculate the molecular weight distribution of a polydisperse polymer. The calculated results were compared with those obtained from viscoelastic ] and GPC measurements, with good agreement.     

A model relating the elastic properties of high-density polyethylene melts to the molecular weight distribution

An earlier model relating the variation of the steady-shear melt viscosity of high-density polyethylene to the molecular weight distribution is applied toward predicting the steady-shear elastic compliance, the first normal stress difference, and relaxation spectrum as a function of shear rate from the molecular weight distribution. The model envisions the cutting off of longer relaxation times as the shear rate is raised such that at any shear rate ${\rm \dot \gamma }$ the molecular weights and their corresponding maximum relaxation times τ_m are partitioned into two classes; the relaxation times are partitioned into operative and inoperative states, depending on whether they are less than or greater than τ_c, the maximum relaxation time allowed at ${\rm \dot \gamma }$. Equations relating molecular weight and relaxation time to the steady-shear elastic compliance and viscosity are assumed valid at nonzero shear rates, except for the partitioning effect of shear rate. The shear rate dependence of the first normal stress difference and the steady-shear viscosity for polyethylene melts is successfully predicted over the range covered by the cone-and-plate viscometer. The assumed proportionality constant between τ_c and 1/${\rm \dot \gamma }$ was determined to be 1.7. Using this relation, the maximum relaxation time at 190°C for a polyethylene molecule of molecular weight M is given by τ_m = 1.4 × 10^?19 (M)^3.33. Reasonable agreement has been obtained between the experimentally determined relaxation spectrum of a polyethylene melt and that predicted from the molecular weight distribution. The agreement is best at the longest relaxation times.     

Effect of molecular weight and molecular weight distribution on the rheological properties of aqueous poly(ethylene oxide) solution

The effect of the molecular weight and the molecular weight distribution on the rheological properties of aqueous poly(ethylene oxide) (PEO) solutions has been investigated with four PEO samples differing in their M_w, M_w/M_n and purity. The main result of this study is that the steady shear viscosity as well as the complex dynamic viscosity of the samples with broad molecular weight distribution greatly differed from the viscosities of the samples having a narrow molecular weight distribution. Furthermore, the samples with broad molecular weight distribution showed a distinct molecular weight dependent non-Newtonian behavior at increasing shear rates and frequencies. This behavior was not observed for the sample with a narrow molecular weight distribution. Both effects are mainly attributed to the influence of the high molecular weight fraction in the PEO samples of broad molecular weight distribution. The often reported degradation of PEO solutions was not observed within the time scale of our experiment.     

The effect of shear rate on the molecular weight determination of acrylamide polymers from intrinsic viscosity measurements

The rheological response of dilute solutions of high molecular weight polyacrylamides at low shear rates has been measured using a capillary viscometer that provided for a fivefold variation in shear rate at each concentration. The non-Newtonian effects were found to be significant for polyacrylamides with number-average molecular weights exceeding 10⁶. The molecular weight average–intrinsic viscosity relationship most widely used in the literature, [η] = 6.80 × 10^?4M , was found to be valid when [η] was measured at high shear rates where the polymer solutions approached Newtonian behavior. A new relationship was developed relating M _n to the intrinsic viscosity extrapolated to zero shear rate.     

Detection of low levels of long‐chain branching in polydisperse polyethylene materials

Creep experiments have been applied to probe the zero‐shear viscosity, η₀, of polyethylene chains directly and precisely in a constant‐stress rheometer at 190°C. Such experiments, when combined with precise measurements of the weight‐average molecular weight, M_w, calibrated relative to linear chains of high‐density polyethylene, are shown to provide a very sensitive approach to detect low levels (0.005 branches per 1000 carbons) of long‐chain branching (LCB). This detection limit is shown to be insensitive to whether the molecular weight distribution (MWD) breadth, M_w/M_n, rises from about two to ten. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Viscosity and molecular weight distribution of ultrahigh molecular weight polyethylene using a high temperature low shear rate rotational viscometer

To obtain accurate measurements of the limiting viscosity number (LVN) or the intrinsic viscosity [η] of solutions of ultrahigh molecular weight polyethylene (UHMWPE), a low shear floating-rotor viscometer of the Zimm-Crothers type was constructed to measure viscosities at elevated temperatures (135°C) and near zero shear rate. The zero shear rate measurements for UHMWPE whole polymer and UHMWPE fractionated by hydrodynamic crystallization were compared with viscosity measurements at moderate and high shear rates (up to 2000 _s^?1) carried out in a capillary viscometer. The limiting viscosity number of UHMWPE decreases, as expected, with shear rate. The higher shear rate data could not be extrapolated to yield the correct zero-shear rate viscosities. Fractionation of UHMWPE gave 10 fractions ranging in LVN from 9 to 50 dL/g. A tentative integral molecular weight distribution for the whole polymer was calculated on the basis of the Mark-Houwink equation, but because it had been previously established only for lower molecular weight polyethylenes, it may not be accurate. A correlation was found between the LVNs for the fractions in the two types of viscometers.     

A model for the zero shear viscosity

An empirical equation for the number of entanglements per molecule has been proposed, which applies over all the molecular weight range. On this ground a simple equation for the zero shear viscosity of monodisperse polymer melts, η₀, has been worked out that appears able to properly take into account the sharp transition of viscosity between the monomeric and the entanglement regimes. The molecular parameters appearing in the new viscosity equation are: the monomeric molecular weight m₀, the monomeric friction factor ζ₀, the molecular weight M, the average molecular weight between entanglements M_e, and the entanglement friction factor ζ_e^3.4. This last parameter was evaluated for a number of monodisperse polymers.     

Rheology of polymeric solutions I. Zero shear conditions

Based on kinetic considerations, the following equation, connecting the zero‐shear viscosity of polymeric solutions with temperature and the molecular weight and concentration of the polymer was derived: RTln η_R = KBφMⁿ /(1 + BφMⁿ), where η_R is relative viscosity (i.e., the ratio of the solution viscosity to the solvent viscosity); K represents a change in enthalpy of viscous flow from a pure solvent to a pure polymer at the same temperature or from a polymer of low molecular weight (M) to one of higher molecular weight, and has the dimensions of energy (e.g., J/mol) because the ratio BφMⁿ/(1 + BφMⁿ) is dimensionless; φ is the volume or molar fraction of a polymer in solution (concentration units can be used in dilute solutions); B is a constant related to the stiffness of the chains of the polymer in a given solvent; and at BφMⁿ >> 1, ln η_R = K/RT. The equation describes published data on the zero‐shear viscosity of four polar and nonpolar polymers in nine solvents with R² > 0.98. This approach allows the use of solutions of moderate concentrations for the characterization of polymers and opens a way for a single‐point degree of polymerization (DP) determination of polymers at moderate concentrations if constants K, B, and n of the equation are known. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2064–2073, 2002     

A phenomenological master curve for viscosity—structure data for two phase polymer systems in simple shear flow

A master curve hypothesis is established based on a mass balance and an assumption of continuous stress through interfaces for well dispersed two phase systems with “defined” zero shear viscosity. The master curve, which is in reasonable accordance with experimental data is represented in a double logarithmic plot of log (η_T/_T,0) against log \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{\eta _{T,0} M_C H\rho}}{{c^2 RT}}\dot \gamma _T} \right) $\end{document}. M_c is the molecular weight between entanglements, H = M?_w/M?_n, ρ is the density, c is the polymer concentration, all defined for the continuous phase. η_T and η_T,0 are the viscosity and zero shear viscosity of the blend, η_T is the apparent shear rate, R the gas constant, and T is absolute temperature.     

Effect of morphology on shear viscosity for binary blends of polycarbonate and polystyrene

The structure and rheological properties of binary blends of polycarbonate (PC) and polystyrene (PS) were investigated using various PS samples with different molecular weights, namely PS1k (M_w = 1,000), PS53k (M_w = 53,000), and PS240k (M_w = 240,000). The blends with PS53k and PS240k show phase-separated structures, whereas the blend with PS1k is miscible. The shear viscosity decreases greatly on addition of PS53k and PS240k, especially at high shear rates, which would be a great advantage at processing operations. Because the nonlinear response occurs in the small strain region for multilayered films of PC and PS240k, the origin of the significant viscosity drop for the phase-separated system is interfacial slippage at the phase boundary.     

The relation between melt flow properties and molecular weight of polyethylene

The non-Newtonian behavior of commercial linear polyethylene samples and their fractions were studied at 190°C. The viscosity η versus shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} curves of whole polymers could be superimposed onto a single master curve despite the variations of their molecular weights and molecular weight distributions. For fractions, however, the same master curve was inapplicable, and the sensitivity of the viscosity to shear rate was found to be greater than those of the whole polymers. The zero-shear viscosities η₀ of fractions were related to the 3.42 power of the weight-average molecular weight M_u as follows: For whole polymers, the zero-shear viscosities were found to be considerably higher at the same M_w and markedly lower at the same z-average molecular weight M_z than those of the fractions. Thus, it was concluded that η₀ corresponds to an average of molecular weight between M_w and M_z. It was found that the molecular relaxation time τ is proportional to M_z^5.3 for whole polymers and to η₀M_w for fractions. Using these relations it was possible to relate the flow ratio, the ratio of flow rates at two different shear stresses, with the molecular weight distribution.     

Thermal and rheological properties of polyethylene blends with bimodal molecular weight distribution

Polyethylene blends with bimodal molecular weight distribution were prepared by blending a high molecular weight polyethylene and a low molecular weight polyethylene in different ratios in xylene solution. The blends and their components were characterized by the high temperature gel permeation chromatograph (GPC), different scanning calorimetry (DSC), and small amplitude oscillatory shear experiments. The results showed that the dependence of zero‐shear viscosity (η₀) on molecular weight followed a power law equation with an exponent of 3.3. The correlations between characteristic frequency (ω₀) and polydispersity index, and between dynamic cross‐point (G_x) and polydispersity index were established. The complex viscosity (η^*) at different frequencies followed the log‐additivity rule, and the Han‐plots were independent of component and temperature, which indicated that the HMW/LMW blends were miscible in the melt state. Moreover, the thermal properties were very similar to a single component system, suggesting that the blends were miscible in the crystalline state. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Simplified theory for linear rheology of monodisperse linear polymers

A new version of the tube theory based on the de Gennes–Doi–Edwards reptation concept (reported in Likhtman and McLeish's work published in 2002) is evaluated, modified to allow for simplified computations, and used to study the relationship between zero‐shear viscosity and molecular weight for monodisperse entangled linear homopolymers. The Likhtman–McLeish model combines self‐consistent theories for contour length fluctuations and constraint release with reptation theory for monodisperse linear polymers. Because of the nature of the Rubinstein and Colby approach used for the treatment of constraint release, the related term is probabilistic and requires stochastic simulations for the calculation of the relaxation modulus G(t). This makes the Likhtman–McLeish model computationally difficult to use. In this work we solve this problem by generating an approximate closed‐form solution for the stochastic term. Then analytical integration of the relaxation modulus function G(t) provides an expression for the zero‐shear viscosity (η₀). Results of the computations of the zero‐shear viscosity and of the slope of η₀ versus molecular weight are compared with available experimental data for monodisperse entangled linear polystyrene and polyethylene (hydrogenated polybutadiene). The model is a major improvement over previous theoretical models, even if there is still some disagreement between the predictions and experimental data of the slope of η₀ versus molecular weight. The possibility of inferring monomer chemistry–dependent parameters from the zero‐shear viscosity remains a difficult task because of the introduction of a constraint‐release parameter. Nevertheless, the model is a useful tool for the prediction of linear viscoelasticity data. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 569–586, 2004     

The reactive modification of polyethylene. I: The effect of low initiator concentrations on molecular properties

Commercial samples of high density, linear low density, and low density polyethylene were modified by injection of low concentrations of free radical initiator during extrusion. Molecular properties monitored included molecular weight distribution, degree of unsaturation, and branching. When the polyethylene teed to this reactive extrusion process had similar values of M_w, but varying polydispersity, degree of branching and degree of unsaturation, the magnitude of the change in molecular weight distribution was found to be in the following order: HDPE 1 > LDPE2 > LLDPE. In general, terminal vinyls enhanced molecular weight increase, and branching promoted degradation. However, for a second high density polyethylene sample with M_w = 154,000 (rather than the previous sample's M_w of 85,600), the change in molecular weight distribution was small and located at the lower molecular weight end. This work provided data for the kinetic model development detailed in Part II.     

Concentrated solution and melt rheology of poly(vinylidene fluoride)

The concentrated solution and melt rheology of poly(vinylidene fluoride) [PVDF] were studied by using a falling needle solution viscometer, a Brookfield viscometer, and a Kayeness capillary rheometer. It was found that the concentrated solution (15 wt% in N-dimethyl acetamide) rheology exhibited a different behavior for various grades of PVDF produced by different types of polymerization. While Newtonian behavior was found in one type of PVDF, shear thinning was found in another type. The power law model was used to describe the general solution behavior of these materials. Zero shear rate viscosity correlated well with the molecular weight (M_w) of the material. Melt viscosity of PVDF exhibited continuous shear thinning behavior throughout the whole range of shear rates. The data were best fitted by a second-degree polynomial curve. Correlations were established between the molecular weight, molecular weight distribution, and the parameters of the polynomial curve. These correlations are useful for the prediction of various grades of PVDF designated for specific engineering applications. The correlations obtained from solution provided better and more accurate correlations to M_w parameters than those of melt rheology.     

Spray applications: Part III. Assessment of viscosities at high shear rates and dynamic uniaxial extensional viscosities on fan nozzle air sprayability

The relationship between rheological parameters and the atomization and sprayability of a fluid can be quantified through examination of blends of structurally different water-soluble polymers (W-SPs). This was done previously for roll coatings by blending two high-molecular weight W-SPs: one with segmental rigidity, hydroxyethyl cellulose (HEC), that has a greater impact with increasing concentration on shear viscosities than on extensional viscosities and one with segmental flexibility, poly(oxyethylene) (POE), that exhibits a counter effect. Within these blends the molecular weight of the HEC is varied to increase the viscosities at high shear rates. By blending these two types of W-SPs, two sets of HEC and POE blends (high M _v HEC/high M _v POE and low M _v HEC/high M _v POE) were prepared exhibiting the same low shear rate viscosity but different viscosities at high shear rates (HSVs). Within each blend set, three ratios of HEC:POE were formulated to have essentially identical shear viscosity profiles, surface tensions, and storage (elastic) moduli (G′), but differences in dynamic uniaxial extensional viscosity (DUEV). This allowed the role of HSVs and DUEVs to be separated in their influence on atomization and sprayability. Within a set, variations in the HEC:POE ratio highlight the dominance of DUEVs as the controlling parameter in the sprayability of a formulation. Presented in part at the 2006 FutureCoat! conference, sponsored by the Federation of Societies for Coatings Technology, in New Orleans, LA, on November 1–3, 2006.     

Rheological properties of polypropylenes with different molecular weight distribution characteristics

Relationships between the rheological properties and the molecular weight distribution of two polypropylene series with different molecular weight distribution characteristics were studied. The end correction coefficient in capillary flow is determined by the molecular weight M_w and the molecular weight distribution M_w/M_n, and is higher as both characteristic values are larger. The die swell ratio at a constant shear rate depends on M_w, M_w/M_n, and M_z/M_w, and is higher as the three characteristic values are larger. The critical shear rate at which a melt fracture begins to occurs depends on the molecular weight M_w and the molecular weight distribution M_z/M_w, and is proportional to M_z/M_w² in a log–log plot. The critical shear stress does not depend on the molecular weight, and is higher as M_z/M_w is higher. The zero‐shear viscosity is determined by a molecular weight of slightly higher order than M_w, and the characteristic relaxation time is determined by M_z. The storage modulus at a constant loss modulus scarcely depends on the molecular weight, and is higher as the molecular weight distribution M_w/M_n is higher. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2128–2141, 2002     

Characterization of branched polyethylene fractions from the elution column

Fractions from several elution column runs on samples of up to 6 g. of a well-characterized high-pressure polyethylene were analyzed by absolute molecular weight methods and several other techniques. The M_n and M_w integral distribution curves are free from any reversal, as was the viscosity distribution curve. Fractions with M_w as high as 8 × 10⁶ were recovered, more than 20 times higher than the original sample's M_w. The polydispersity of the fractions increases from M_w/M_n = 1.5 or less in the low molecular weight fractions to a nearly constant value of 4.5–5.0 in fractions above 60% cumulative sample weight. Nonetheless, refractionation on the elution column shows that the fractions are narrowly distributed in terms of solubility, while GPC analysis reveals that the fractions have an extremely narrow size distribution. It is concluded from the combined results that long-chain branching plays an important role in determining the equilibrium solubility and, further, that long-chain branching increases the polymer solubility. Sample calculations are provided, which illustrate the effect of fraction polydispersity on calculated original sample molecular weights and the fit of the fractionation results to several model distribution functions.     

Non‐newtonian rheological behavior of semi‐dilute ultra‐high molecular weight polyethylene solution in gel‐spinning process. 1: Concentration effect on the fundamental rheological properties

The rheological properties of a semi‐dilute ultra‐high molecular weight polyethylene (UHMw‐PE)/paraffin wax solution were investigated by mainly focusing on the influence of its concentration on the shear flow viscosity. It was found that the UHMw‐PE solution exhibits a shear‐thinning behavior at a very wide shear rate range from 10^?4 to higher than 10³ sec^?1. Furthermore, this typical non‐Newtonian behavior was more obvious with a concentration increase. From the concentration dependence of the zero‐shear creep compliance or other rheological factor, it was found that the extremely large M_e value of the system gives rise to various kinds of non‐Newtonian behaviors, especially those highly elastic in nature. Finally, the origin of the abnormal stress fluctuation during the steady shear measurement was found to be related to the shear‐induced structural development of the solution.     

Apparent and Real Distribution in GPC (Experiments with PMMA Samples)

Abstract

Molecular weight distribution curves obtained by GPC are broadened if concentration and flow rate are fixed in the usual range. Therefore, the apparent nonuniformity U _app of the samples is larger than the real non-uniformity U = (M_w/M_n) ?1. For a number of fractionated and unfractionated samples of polymethyl methacrylate we determined M _n and M _w by osmotic, light-scattering, and viscosity measurements. Thus, the real value of U can be compared to U _app obtained by GPC at different concentrations and flow rates, υ. The excess nonuniformity U _exc is evaluated as function of concentration c, polydispersity, molecular weight, and flow rate. For c = 0 and υ = 0, U _exc is not far from zero. For standard conditions one certain value of the excess standard deviation of the elution volume allow calculation of U _exc for narrow and broader distributions and the obtaining of nearly correct values for the real nonuniformity U.