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.     

A relationship between steady-state shear melt viscosity and molecular weight distribution in polystyrene

A model that relates to the molecular weight distribution (MWD) of high-density polyethylene to the steady-state shear melt viscosity has been applied to polystyrene melts. Relations are developed for predicting the rheological flow curve from the molecular weight distribution. Relationships are also developed to predict the MWD from the flow curve, although practical limitations to this procedure are given. From a consideration of predictions of the model and experimental data, it is concluded that the transition for a given molecular species from Newtonian to non-Newtonian flow is sharp. Additionally, the calculated empirical parameter that partitions the MWD into molecules that act in a Newtonian fashion and those that do not is shown to be equivalent to the largest molecular weight homolog that can still undergo Newtonian flow at a given shear rate for monodisperse fractions. The temperature dependence of the relaxation times is found to be somewhat higher than that predicted by the Rouse theory. An activation energy of 30 kcal/mole for η0 was used to fit the experimental viscosity data adequately at 190° and 225°C. The terminal relaxation spectrum for a narrow-MWD polystyrene standard is calculated and found to agree well for long relaxation times with that reported in the literature.     

An empirical model for the melt viscosity of polymer blends

Summary On the basis of experimental data for blends of polyethylene with different polymers an empirical equation is proposed to describe the dependence of melt viscosity of blends on component viscosities and composition. The model ensures the continuity of viscosity vs. composition curves throughout the whole composition range, the possibility of obtaining extremum values higher or lower than the viscosities of components, allows the calculation of flow curves of blends from the flow curves of components and their volume fractions.     

Molecular weight dependence of melt crystallization behavior and crystal morphology of low molecular weight linear polyethylene fractions

Melt crystallization behavior and corresponding crystal morphology of five low molecular weight (3,900 ≤ MW ≤ 20,800) linear polyethylene (PE) fractions have been investigated. The overall crystallization data indicate that the lower molecular weight (MW) fraction possesses a higher crystallization rate at the same undercooling (ΔT). On the contrary, at the same crystallization temperature (T_c) the rate increases with MW. The Avrami exponent (n) varies from ca. 3 to 4 with decreasing ΔT for the fractions studied, which implies the nucleation process changes from athermal type to thermal type as T_c increases. For the low MW PE’s, the different crystal growth regimes (regime I and II) have been first time identified via linear crystal growth rate (G) measurements. The regime I/II transition temperatures are close to previously reported data, which were obtained through a different method. As reported for intermediate MW PE’s, the transitions occur at an almost constant ΔT of 17.5±1 °C for each fraction studied. Morphological study shows that single crystals could be formed isothermally at low ΔT’s. Typical banded spherulites and axialites, which are MW and ΔT dependent, are also observed. Orthorhombic structure is ascertained to be the dominant crystal structure that exists irrespective of MW and crystal growth regime.     

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.     

The viscosity dependence on concentration,molecular weight and shear rate of xanthan solutions

Summary This paper concerns the viscosity dependence of Xanthan as a function of polymer concentration, shear rate and molecular weight in the ordered conformation. The different samples with various molecular weights are obtained by ultrasonication. A unique curve is obtained for the reduced specific viscosity ( ) as a function of γ · γ _r ⁻¹ for the different molecular weight samples and polymer concentrations below an overlap concentration C [η]₀⩽ 1.5. The master curve giving the relation as a function of C [η]₀ is drawn and compared with that of polystyrene in good solvent. The largest increase of in semidilute solution may be due to larger interchain interactions and to larger stiffness of the Xanthan molecule.     

Correlation between steady state flow curve and molecular weight distribution for polyethylene melts

This article uses Graessley's theory of viscosity to predict the flow curve for several high-density and low-density polyethylene melts using the molecular weight distribution data obtained from the gel permeation chromatograph. The agreement with the experimental flow curve obtained from the Weissenberg rheogoniometer and the Instron rheometer was not quantitative for many high-density polyethylenes studied here. For the low-density polyethylenes, it was shown that the agreement between the theory and the experiment was good even though the molecular weight distribution data were not corrected for long-chain branching. For these samples, the experimental relaxation time τ₀ obtained by superposition of the data with the theoretical master curve was of the order of the Rouse relaxation time τ_R. The systematic increase in the ratio τ_R/τ₀ was ascribed to the increase in the molecular weight or to the increased number of long-chain branches.     

The influence of molecular weight distribution on melt viscosity,melt elasticity,processing behavior and properties of polystyrene

The influence of molecular weight and molecular weight distribution on the melt rheological behavior of two polystrenes of approximately the same weight average molecular weight, but of widely different molecular weight distribution, was determined. Then, using a series of capillaries with different length-to-diameter ratios in an Instron Capillary Rheometer, the entrance correction methods of E. B. Bagley and the relationships of W. Philippoff and F. H. Gaskins, the recoverable shear strain (S_R) in the melt at the capillary wall for these mono- and polydisperse polystyrenes was determined. Shear modulus (G) and normal stress (P_N) were calculated using the relationships: G = τ_RC/S_R and P_N = 2τ_RC S_R, where τ_RC is the corrected shear stress at the capillary wall. These are compared to values obtained using a Weissenberg Rheogonimeter. These two polystyrenes were also injection molded into an ASTM specimen mold over a wide range of stock temperature, using a 12 OZ . in-line reciprocating screw injection press, and evaluated for mechanical property values. The effects of the elasticity parameters (S_R G & P_N) and their magnitude on the rheology, processability and mechanical properties of these polystyrenes are discussed.     

PVC melt rheology III: The effect of order and molecular weight on the shear rate dependence

The effect of polymerization temperature on the melt flow behavior of PVC of varying molecular weights has been studied over a wide shear rate range. For the same molecular weight, higher melt viscosities are observed for polymers prepared at lower temperatures. The shear rate dependence of the viscosity vs molecular weight plot is shown to be nonlinear over the shear rates examined. The inability to achieve a limiting zero-shear viscosity is discussed.     

The dependence of shear and elongational viscosity on the molecular weight of poly(vinylidene fluoride)

The dependence of shear and elongational viscosity on the molecular weight of poly(vinylidene fluoride) has been studied using a capillary rheometer. The elongational viscosity was evaluated based on Cogswell's method with two types of capillaries: capillary length (L)/capillary diameter (D) = 10 mm/1 mm and L/D = 0 mm/1 mm. We used the ratio P₀/P_L that indicates the contribution of elongational flow to the total flow involving both the shear and elongational flows. P_L and P₀ are the pressure losses in the capillary and the converging flows, respectively. P₀/P_L increased with molecular weight and shear rate. This corresponds to decreasing the number of entanglements of molecular chain under a large displacement, especially high shear. Thus, we suggest using P₀/P_L as the parameter of the entanglement interaction on the molecular chain under a large displacement. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 2381–2384, 1999     

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.     

聚丙烯熔体流动指数与分子量及其分布的关系

研究了聚丙烯(PP)的熔体流动指数(MI)与聚合物不同分子量之间的关联性,对于分子量分布较窄的PP,数均分子量(Mn)、重均分子量(Mw)和粘均分子量(Mv)均能较好的关联;反之,MI与Mn关联性下降,而MI与Mn和Mv的关联性仍很好,尤其是MI与Mv的关联性受分子量分布的影响很小;MI与Z均分子量的关联性很差。同时．确定了MI与各种分子量之间的关联式,该式用于本体PP工艺反应器内氢气浓度的计算和MI的预测,与实验测量结果吻合良好。     

Properties of bamboo flour/high-density polyethylene composites reinforced with ultrahigh molecular weight polyethylene

In order to improve the properties of bamboo-plastic composites (BPCs), bamboo flour/high-density polyethylene (HDPE) composites were reinforced with ultrahigh molecular weight polyethylene (UHMWPE). The effects of UHMWPE on properties of composites were studied. The crystallinity of composites decreased slightly. Compared with non-UHMWPE added bamboo powder/HDPE composite, the composite with 6 wt % UHMWPE, showed decrease in water absorption to 0.41%, whereas its tensile strength and flexural strength increased to 34.51 and 25.88 MPa, respectively, a corresponding increase of 34.59 and 12.87%. The temperatures corresponding to initial degradation temperature (T_initial) and maximum degradation temperature (T_max) of the composite increased from 282.7 and 467.4 °C to 288.5 and 474.7 °C respectively. Scanning electron microscopic images showed that UHMWPE was well dispersed and fully extended as long fibers in the composite, forming a “three-dimensional physically cross-linked network structure,” which contributed to the improved properties of the composites. © 2020 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48971.     

Prediction of polyethylene melt rheological properties from molecular weight distribution data obtained by gel permeation chromatography

A method is presented for predicting rheological characteristics, such as shear dependent (non-Newtonian) viscosity and components of linear oscillatory (complex) response functions for polyethylene melts from molecular weight distribution data obtained from gel permeation chromatographic (GPC) analysis. The results are compared with measured values of the rheological functions obtained from a variety of instruments over an extensive range of shear rates-and frequencies. The agreement between predicted and measured rheological functions is quite good for high density resins. However, for a low density resin the agreement is not as good, although still reasonable over a considerable range of conditions. It is concluded that the quality of the GPC data is the key factor in the degree of success of the method.     

Prediction of dynamic and transient rheological properties of polystyrene and high-density polyethylene melts from the molecular weight distribution

A model relating the steady-shear melt viscosity and elasticity to the molecular weight distribution in HDPE and polystyrene melts has been extended to predict the dynamic viscosity, modulus, and loss modulus. Limitations in the model as applied to the dynamic properties are discussed. The model is also applied to the transient response of stress growth during steady shearing. This application is considered useful because it may help describe nonsteady-state flow of polymer melts in short dies and cyclic operations as employed in commercial molding equipment.