The influence of molecular weight on the melt rheology of polypropylene

Melt viscosity and melt elasticity data were obtained over a broad range of temperatures and shear rates on a series of four polypropylenes of different molecular weight but approximately the same molecular weight distribution. The superposition technique was used with both temperature and molecular weight to shift flow curves for all four materials at three temperatures each along the shear rate axis to generate a master flow curve at a given temperature and molecular weight. For polypropylenes of this type, and molecular weight distribution shift, factors which can be used to extend the useful range of experimentally obtained flow data were determined. The dependency of apparent viscosity on weight average molecular weight at shear stresses as high as 10⁶ dynes/cm² is shown. The dependency of melt elasticity on molecular weight and temperature is discussed.     

Polarization-optical investigation of normal and shear stresses in flow of polymers

A method has been suggested for calculating the first difference of normal stresses characterizing the flow of polymers at high shear stresses. The calculations are based on the results of rheooptical measurements in a slit of rectangular cross section. It has been found, for several samples of high molecular weight polybutadienes and polyisoprenes, that the flow behavior of the representatives of the given polymer homologous series having different molecular weights is characterized by a general relationship between the first normal stress differences and the shear stresses in those cases where the polymers are characterized by narrow molecular weight distributions. It has also been established that the first normal stress difference sharply increases in the region of shear stresses which immediately precedes the spurt—a jumpwise increase of the flow rate at a certain critical value of shear stress; while for polymers of wide molecular weight distribution the increase of the normal stress difference in the region of high values of shear stresses is retarded. Equilibrium swell of the extrudate has been measured and the first normal stress difference determined by the rheo-optical method has been found to agree satisfactorily with the values calculated from the swelling ratios according to theoretical models.     

Crystallization of polyethylene oxide under shear

A concentric cyclinder dilatometer was designed and built to study the influence of shear on the crystallization kinetics of polymers. This instrument allows crystallization to be followed at both constant temperature and shear rate. Several samples of polyethylene oxide (Carbowax 4000, Carbowax 20-M, and WSR-205) were used. A low molecular weight fraction of the Carbowax 20-M, as well as the unfractionated material, was crystallized under shear. The WSR-205 was studied only in a mixture with Carbowax 4000. It was shown that the kinetics of crystallization of uncrosslinked melts of polyethylene oxide are altered by shear. The induction times for the appearance of crystallinity are shorter in the sheared systems than in the quiescent melts. The Avrami exponents are also higher for crystallization in sheared melts than in quiescent systems and increase with decreasing supercooling. The high values of the Avrami exponent are attributed to the disruption of crystalline aggregates into particles larger than the critical sized nucleus. These particles will persist in the melt and continue to grow spontaneously. A continuous infusion of growing particles into the melt occurs. At constant temperature and shear rate, the induction time of the crystallization curve is influenced by polymer molecular weight. In moderate to high molecular weight samples, the effect of shear becomes saturated at very low shear rates. Decreasing the molecular weight separates the crystallization curves. The curves from the higher shear rates appear at the shorter induction times. However, decreasing the molecular weight below that at the critical entanglement molecular weight allows the nucleation rate, strongly dependent upon the supercooling, to influence the relative positions of the sheared crystallization curves.     

Viscoelastic parameters of characterized branched polyethylenes

Certain steady state viscoelastic parameters, including melt viscosities, normal stress coefficients, and shear compliances, are determined for a series of well-characterized low, density polyethylene samples, and the results are analyzed. The effects of shear rate, temperature, molecular weight, molecular weight distribution, and the degree of long chain branching are demonstrated. The agreement observed between steady state shear compliance values derived from normal stresses and those obtained from die swell measurements is significant.     

A study of low shear viscosity of polymer melts

An inexpensive, accurate falling coaxial cylinder viscometer is described. Viscosities can be measured at shear stresses at least as low as 10³ dynes per cm² and flow curves can be obtained with shear thinning fluids. Data for a polystyrene and a polyethylene polymer coincide with those from other techniques and with corresponding literature values. The lower Newtonian viscosities pf both polymers were experimentally accessible, and it is shown that estimation of η_o by extrapolation from viscosities in the non-Newtonian region may be subject to errors of uncertain magnitude. Shear history of the sample affects the Newtonian and low shear viscosities of high molecular weight polymer melts.     

Rheological characterisation of hydroxyapatite filled polyethylene composites. Part 2 – Isothermal compressibility and wall slip

Abstract

Rheological characterisation of hydroxyapatite–high density polyethylene (HA–HDPE) composites has been performed in terms of isothermal compressibility and wall slip. Addition of HA to the polymer melt decreases the compressibility of the melt. The unfilled HDPE was found to exhibit wall slip at shear stresses as low as 0·10 MPa. The flow curves of the composites showed three distinct regions: a gradient at low shear rates; a plateau region; and a gradient at higher shear rate. An increase in rheometer pressure seems to suppress the slip in composites. The 40 vol.-% HA–HDPE composite exhibited two critical shear stresses, one corresponding to wall slip, which occurs in the lower shear rate region of the flow curve, and the other corresponding to a plateau, which is identified with the stick–slip behaviour of unfilled HDPE reported in the literature. The plateau shear stress increased with filler volume fraction and this effect is attributed to the decreased compressibility of the melt. A good correlation with a negative correlation coefficient was found to exist between compressibility and shear stress in the plateau region. The slip observed in unfilled HDPE and at low shear rates in the 40 vol.-% HA–HDPE systems has been explained in terms of a low molecular weight polymer layer formed at the melt/wall interface. The large interfacial slip observed in the plateau region is attributed to complete disentanglement of adsorbed chains from free chains at the melt/wall interface at and beyond the plateau region.     

Prediction of high density polyethylene processing behavior from rheological measurements

In order to predict the processing behavior of a high density polyethylene resin one must know the resin flow behavior over a wide range of shear rates. Low shear properties are important in applications where melt strength, sagging, etc. are critical. On the other hand, high shear flow properties are a determining factor in applications where melt instability, melt fracture and heat generation are important. The flow behavior of a resin can be established by measuring the zero shear viscosity, η₀, the maximum relaxation time, τ₀, and the shape of the flow curve. We have measured these basic rheological parameters on a large number of high density polyethylene resins. A shear sensitivity parameter which is independent of molecular weight was derived from a correlation between η₀ and τ₀. This parameter, together with η₀, provide the vital information needed in order to predict the processing behavior of the resin. This method is applicable to other polymer systems provided that the rheological parameters η₀ and τ₀ can be experimentally obtained.     

Rheological properties of branched low-density polyethylene

The shear flow properties of six commercially available long-chain branching low-density polyethylene resins were determined, using a cone-and-plate rheometer at low shear rates and a capillary rheometer at high shear rates. Also determined were the elongational viscosities of the resins, using an apparatus developed by Ide and White. Interpretation of the rheological measurements is given with the aid of the molecular parameters, namely, molecular weight and molecular weight distribution.     

Unusual rheological behaviors of linear PE and PE/kaolin composite

The unusual flow behaviors of linear PE melts are caused by high molecular weight, tight entanglements of molecular chains, and strong adsorption of the melt at the capillary wall. Especially, the extreme change of interface adsorption is followed by an unusual flow, and at the molecular level, the dynamic variety of entanglement and disentanglement between the adsorption chain near the wall and the nonadsorption chain is the cause of the extrusion pressure vibration. Ultrahigh molecular weight polyethylene (UHMWPE)/kaolin composites prepared by polymerization filling could be smoothly extruded through the capillary. Also, with increase of the kaolin content, the apparent viscosity of the composite decreased and the processability was improved. Under slip boundary conditions, the real shear rate and shear stress of the melt near the capillary wall were reduced. The viscosity descent (desorption) and the deformation energy decrease of the melt near the wall were the important preconditions to gain a steady flow in a second glossy zone. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 2154–2161, 2001     

Experimental study and CFD modelling of a two-phase slug flow for an airlift tubular membrane

The aim of the present study was to develop a computational fluid dynamics (CFD) model to study the effect of slug flow on the surface shear stress in a vertical tubular membrane. The model was validated using: (1) surface shear stresses, measured using an electrochemical shear probe and (2) gas slug (Taylor bubble) rising velocities, measured using a high speed camera. The length of the gas slugs and, therefore, the duration of a shear event, was observed to vary substantially due to the coalescing of gas slugs as they travelled up the tube. However, the magnitude of the peak surface shear stress during a shear event was not observed to vary significantly. The experimental conditions significantly affected the extent to which the gas slugs coalesced. More coalescing between gas slugs was typically observed for the experiments performed with higher gas flow rates and lower liquid flow rates. Therefore, the results imply that the frequency of shear events decreases at higher gas flow rates and lower liquid flow rates.Shear stress histograms (SSH) were used as a simple approach to compare the different experimental conditions investigated. All conditions resulted in bi-modal distributions: a positive surface shear peak, caused by the liquid slug, and a negative shear peak caused by the gas slugs. At high gas flow rates and at low liquid flow rates, the frequency of the shear stresses in both the negative and positive peaks were more evenly distributed. For all cases, increasing the liquid flow rate and decreasing the gas flow rate tends to result in a predominant positive peak. These results are of importance since conditions that promote evenly distributed positive and negative peaks, are likely to promote better fouling control in membrane system. At high liquid and low gas flow rates, the frequencies obtained numerically and experimentally were found to be similar, deviating by less than approximately 10%. However, at high gas and low liquid flow rates, the differences were slightly higher, exceeding 20%. Under these conditions, the CFD model simulations over predicted the shear stresses induced by gas slugs. Nonetheless, the results indicate that the CFD model was able to accurately simulate shear stresses induced by gas slugs for conditions of high liquid and low gas flow rates.     

Rheology of unsaturated polyester resins. I. Effects of filler and low-profile additive on the rheological behavior of unsaturated polyester resin

Measurements were taken of the bulk rheological properties of concentrated suspensions of particulates in unsaturated polyester resins, using a cone-and-plate rheometer. The particulates used were clay, calcium carbonate, and milled glass fiber. With clay and milled glass fibers, shear-thinning behavior of suspensions was observed at low shear rates or low shear stresses as the concentration of particulates was increased, whereas concentrated suspensions of calcium carbonate exhibited Newtonian behavior over the range of shear stresses or shear rates investigated. The cone-and-plate rheometer was also used for measurements of the bulk rheological properties of various mixtures of polyester resin and low-profile additives. For low-profile additives, solutions, in styrene, of poly(vinyl acetate) (PVAc) and poly(methyl methacrylate) (PMMA) were used. It was found that the bulk viscosities of all mixtures of polyester resin and PVAc solution lie between those of the individual components, whereas the bulk viscosities of some mixtures of polyester resin and PMMA solution go through a minimum and a maximum, depending on the composition of the mixture. While all mixtures of polyester resin and PVAc solution exhibited negligible normal stress, some mixtures of polyester resin and PMMA solution exhibited noticeable normal stresses. It should be mentioned that polyester resin follows Newtonian behavior. It turned out that all mixtures of polyester resin and PVAc solution exhibited clear, homogeneous solutions, whereas mixtures of polyester resin and PMMA solution exhibited optical heterogeneity, i.e., turbidity. When polyethylene powders were used as low-profile additives, suspensions of polyester resin and polyethylene powders exhibited negative values of normal stress as the concentrations of suspension reached a critical value. When both filler and low-profile additive were put together in polyester resin, the rheological behavior became quite complex, indicating that some interactions exist between the filler and the low-profile additive.     

UHMWPE/HDPE/纳米SiO2共混体系的毛细管挤出流变行为

采用毛细管流变仪,研究了超高分子量聚乙烯(UHMWPE)/高密度聚乙烯(HDPE)/纳米二氧化硅(SiO2)共混体系,及其对照组的流变行为和挤出过程中的不稳定流动现象,分析了共混物发生鲨鱼皮畸变和整体破裂的临界剪切应力和临界剪切速率的变化情况。结果表明,经过偶联剂改性的纳米SiO2粒子,在PE基质的共混体系中存在一定的界面黏附作用,降低了纳米共混体系的挤出胀大比,弹性特征减轻。这种界面相互作用限制了纳米共混材料在口模区域的黏性流动以及分子链离开口模后的构象恢复,降低了发生流动不稳定现象的临界剪切速率,发生鲨鱼皮畸变的临界剪切应力增大,整体破裂后,形成交替出现"鲨鱼皮-破裂"的振荡性变化外观。     

Predicting nonlinear viscosity and elasticity from zero-shear parameters in the Pao-Rouse model

When the Rouse distribution of relaxation times is inserted into Pao's constitutive equation as expressed by Huseby and Blyler, a simple two-parameter model results. The parameters can be fitted using the limiting values of viscosity and modulus at low shear rates. The modulus in this case is defined as the ratio of shear stress during steady flow to the recovered shear during creep recovery with the stress removed. The mathematical model, is then used to predict the behavior at high shear rates where flow is pseudoplastic and elasticity is non-Hookean. A sample of polyisobutylene and several high molecular weight poly(dimethylsiloxanes) can be fitted reasonably well. Silicones of lower molecular weight (3.7 and 5.5 × 10⁵) are not correlated successfully, perhaps because not all the “recoverable shear” stored during flow can actually be recovered experimentally. The Rouse distribution can be generalized for added flexibility.     

Melt viscosity of polyethylene: Shear dependence

Apparent viscosities of linear polyethylene melts may be simply related to molecular weight at various shear stresses. One gets constant slopes on a log–log scale with higher critical M?_w at higher shear stresses. The validity of Ferry's equation and the dependence of its coefficients are extensively analyzed.     

Crystallization of polyethylene under shear flow as studied by time resolved depolarized light scattering. Effects of shear rate and shear strain

We have studied structure formation during crystallization of polyethylene (PE) under shear flow using time resolved depolarized light scattering (DPLS) in order to elucidate the formation mechanism of the so-called shish-kebab structure. Two-dimensional (2D) DPLS pattern clearly showed streak-like scattering normal to the flow direction in the early stage during the crystallization after pulse shear, suggesting the formation of the shish-like structure in μm scale. In order to analyze the 2D DPLS pattern we defined measures for the acceleration of the crystallization rate and the degree of anisotropy and found that there are critical shear rates for both of the acceleration and the anisotropy at a given shear strain: the former is much smaller than the latter. We also determined the critical shear rate for the anisotropy as a function of the shear strain. Extrapolating to inverse of the infinite shear strain=0, we found the critical shear rate for the anisotropy at the infinite shear strain to be 1.5 s⁻¹. The results were discussed in relation to a competition between the relaxation rate of polymer chains and the orientation-induced crystallization rate.     

Effects of polymer molecular weight and filler particle size on flow behavior of wood polymer composites

The influence of polymer matrix molecular weight and filler particle size on rheological properties and extrudate distortions of metallocene polyethylene (mPE)/wood flour (WF) composites has been investigated by rotational and capillary rheometers. It was found that at low shear rates smaller filler particles provide higher shear viscosity than the larger sized filler. At high shear rates and WF loadings above 30 wt%, the effect of particle size on the melt flow properties becomes negligible. The relative increase of the storage modulus with decreasing particle size is more pronounced in the case of low molecular weight polymer matrix than that in higher molecular weight polyethylene based composites. The wood filled polyethylenes exhibit extrudate surface defects, which are complex function of the shear rate, polymer matrix molecular weight, and filler particle size. Increasing the shear rate results in pressure oscillations and spurt‐flow. It was also observed that the evolution of the extrudate surface tearing is strongly dependent on the pressure during a single pressure oscillation cycle in the spurt flow regime. POLYM. COMPOS., 2008. © 2008 Society of Plastics Engineers     

Critical regimes of oscillatory deformation of polymeric systems above glass transition and melting temperatures

High molecular weight linear polymers and their concentrated solutions were investigated over a wide range of frequencies and amplitudes of oscillatory deformation. At definite critical deformation and stress amplitudes, the resistance to deformation drops abruptly as a result of the rupture of continuity of polymer specimens in the region of action of the highest shear stresses. The lowest critical values of deformation rate amplitudes are inversely proportional to the initial viscosity and correspond quantitatively to the critical shear rates at which the spurt occurs during the flow of polymeric systems in ducts. The spurt effect is due to the transition of the polymer systems to the forced high-elastic state, in which they behave like quasi-cured polymers whose deformability is always limited. Up to the critical values of the stress amplitudes, narrow-distribution high molecular weight linear flexible-chain polymers behave like Hookean bodies, whereas the broad-distribution polymers show a sharply defined nonlinear behavior which asymptotically passes to a spurt. The amplitude dependence of the dynamic characteristics of the high molecular weight linear polymers, as well as their non-Newtonian behavior, is due to polymolecularity. An increase in deformation amplitudes reduces the frequency at which the spurt, and hence the transition of the polymer systems to the high-elastic state, is observed. Therefore, under conditions of oscillatory deformation the physical state (fluid or high-elastic) is determined not only by the frequency but also by the value of deformation. In the high-elastic state region (estimated at low amplitude deformation), the critical deformation amplitude is frequency independent and has an unambiguous relationship with the molecular mass of the chain (M_e) between the entanglements. For the bulk polymers studied, the spurt in the high-elastic state occurs at stress amplitudes of the order of 10⁵ N/m² irrespective of frequency, molecular mass, or polymolecularity. In concentrated polymer solutions, in the high-elastic state the critical stress amplitudes decrease with reducing polymer content, whereas the critical deformation amplitudes increase.     

Flow behavior of well characterized polyethylene melts

A careful characterization and rheological study of low density polyethylene (LDPE) reveals that long-chain branching (LCB) plays a decisive role. At constant molecular weight (M?_w) higher LCB reduces the Newtonian viscosity η_o and the shear sensitivity, increases the activation energy E_o, and finally delays transition to pseudoplastic flow to higher shear rates and the onset of melt fracture to higher shear stresses (τ_d). The flow parameters η_o, \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma _{cr} $\end{document}_cr, τ_d, and the derived flow relaxation times are uniquely correlatable by means of a modified molecular weight (gM?_w) incorporating the LCB effect. High density polyethylene are less shear sensitive than their low-density counterparts, have a lower activation energy, fracture at higher shear stress levels and cannot be regarded as branchless LDPE's.     

Time-dependent flow of cement pastes

The time-dependent behavior of viscosity of clinker pastes was studied with a coaxial cylinder type viscometer. In order to characterize the flow behavior of cement pastes, the flow curve obtained by the minimum values of shear stresses at different shear rates was proposed. Two types of time dependence were found; the increase in viscosity caused by shearing and the increase in minimum viscosity caused by hydration. The effect of sodium lignosulfonate on the flow behavior was also considered.     

Structural time dependency in the rheological behavior of molten polymers

In order to elucidate the role of reentanglement processes in the rheology of molten polymers, we have used the interrupted shear test and the reduction-;in-;shear-;rate test to study a linear and a branched polyethylene at 170°C. A cone-;plate rheometer was used, and shear rates were thus limited to values below 1 sec^?1. For both polymers, the characteristic time for reentanglement was found to be significantly greater than the time scales associated with the relaxation of shear and normal stresses after cessation of steady shear. This observation has important implications for the modelling of melt flow in plastics processes and the evaluation of constitutive equations.