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     

An empirical model relating the molecular weight distribution of high-density polyethylene to the shear dependence of the steady shear melt viscosity

An empirical model has been developed to relate molecular weight distribution to the shear dependence of the steady shear viscosity in high-density polyethylene melts. It uses a molecular weight, M_c, which partitions molecular weights into two classes; those below M_c contribute to the viscosity as they do at zero shear, and those above M_c contribute to the viscosity as though they were of molecular weight M_c at zero shear. Each individual molecular weight species contributes on the basis of its weight fraction. M_c is proposed to be a unique function of the shear rate. Using this method of treating the molecular weight distribution, and the zero shear relation for relating η0 to molecular weight, the calculated steady shear viscosities at various shear rates for polyethylene samples of widely varying polydispersities agree well with experimental results. The model makes no judgment on the existence or importance of entanglements in non-Newtonian behavior since it has no specific parameters involving an entanglement concept. Use of the model suggests that for the samples studied, only the upper portion of the molecular weight distribution contributes toward the experimentally observed decrease of steady shear viscosity with shear rate for shear rates of up to 10,000 sec^?1. The lower molecular weight species are assumed to behave in a Newtonian manner.     

Polystyrene-equivalent molecular weight versus true molecular weight in size-exclusion chromatography

The evaluation of the size-exclusion chromatography (SEC) concentration elution curves by means of a calibration dependence obtained in a given SEC set for a polymer different from the polymer to be analyzed results in an error in the determination of both molecular weight and molecular-weight distribution (MWD). The problem is analyzed assuming the validity of the universal-calibration concept. The differences between the true and apparent values of molecular weight, MWD and M_w/M_n depend on and are expressed in terms of the parameters of the Mark-Houwink-Kuhn-Sakurada equation, describing the molecular-weight dependence of intrinsic viscosity, for the polymer to be analyzed and the polymer used for calibration. The differences in molecular weight and the M_w/M_n ratio are typically tens of percent and, in extreme cases, can amount up to a factor of three for molecular weight and a factor of two for the M_w/M_n ratio.     

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.     

Shear rheology of diluted solutions of high molecular weight cellulose

A steady-state and dynamical rheological study was performed with dilute solutions (1–4%) of high molecular weight cellulose (M_w = 350,000). The solutions are strongly viscoelastic. The steady-state viscosity and the first normal stress difference have a power law dependence on the shear rate. The power law indices have the same dependence on temperature and concentration. These results as well as the correlation between the steady-state viscosity and the real part of the complex viscosity are in good agreement with the Spriggs model. The 4% concentrated solution shows the beginning of a rubber-like storage modulus plateau, suggesting the existence of an entanglement network.     

Influence of molecular structure on the rheological and processing behavior of polyethylene resins

The rheological and processing behavior (melt fracture performance) of linear lowdensity polyethylenes (LLDPEs) is studied as a function of both the weight average molecular weight (M_w) and its distribution (MWD). A number of LLDPE resins having different molecular characteristics were tested, with essentially one characteristic (M_w or MWD) changing at a time. The first series of resins consisted of nine samples having a wide range of polydispersities (3.3–12.7) and nearly constant M_w and short chain branching. The second series had six resins with varying M_w (51,000–110,000) but fixed MWD (about 4). The influence of M_w and MWD on the viscosity profiles, linear viscoelastic moduli as expressed by means of a discrete spectrum of relaxation times, extrudate swell, and melt fracture behavior for these resins is reported. Correlations between the molecular characteristics of the resins and their rheological and processing behavior are also reported. It is found that for a given molecular weight, the optimum melt fracture performance is obtained at a specific polydispersity value, and it is characterized by a minimum relaxation time for the resin defined in terms of recoverable shear.     

Mechanical degradation of high molecular weight polymers in dilute solution

The mechanical shear degradation of polydisperse polyisobutene and monodisperse polystrene in oils of different viscosities in the concentration range of 0.1% to 1% was studied using a high-shear concentric cylinder viscometer under laminar and uniform well-defined shear field conditions. Molecular weight distributions (MWDs) were measured by gel permeation chromatography (GPC). Degradation of polydisperse polyisobutene solutions narrows the distributions principally through the breaking down of large molecules. Degradation of monodisperse polystyrene broadens the distributions at lower shear stress. At higher shear stresses, the distributions do not broaden as much but are still broader than those of the original polymer. The final M_w/M_n ratios are considerably different from the value of 2 expected for random degradation. Hence, the degradation is likely a nonrandom process. It was found that the extent of degradation has a negative concentration dependence coefficient at relatively high molecular weight and a positive concentration dependence at lower molecular weight. Competing mechanisms of “stretching” and “entanglements” for degradation were postulated to explain the results. The degradation data indicate that the shear stress is the controlling parameter, not the shear rate. The shear degradation is independent of initial molecular weight and viscosity of the solvent.     

Molecular weight characterization of polybutadiene rubber with high molecular weight and broad molecular weight distribution

Following the molecular weight characterization of two polybutadiene samples, it was found that M _w from gel permeation chromatography with universal calibration and light scattering were in agreement, but M _n by gel permeation chromatography was less than M _n from membrane osmometry. A more detailed analysis revealed that the high molecular weight and broad molecular weight distribution of the two samples forced two corrections to the membrane osmometry results for (a) diffusional layer effects caused by high solution viscosities, and (b) solute permeability of the membrane. In the latter effect, the high viscosities of the solutions prevented actual diffusion through the membrane, but “reflection” of these species as defined by the Staverman coefficient prevented an accurate M _n determination. After making these corrections, it was found that M _n from membrane osmometry using a very tight membrane was in very good agreement with M _n from gel permeation chromatography. A method is demonstrated for obtaining M _n from a combination of membrane osmometry and gel permeation chromatography, where membrane osmometry data from membranes of different porosities (after corrections for diffusional layers and membrane reflection) are used to verify the accuracy of the gel permeation chromatography data as representing the true molecular weight distribution, allowing the gel permeation chromatography data to be used to calculate M _n.     

Effects of molecular weight and molecular weight distribution on creep properties of polypropylene homopolymer

The molecular weights of the industrial-grade isotactic polypropylene (i-PP) homopolymers samples were determined by the melt-state rheological method and effects of molecular weight and molecular weight distribution on solid and melt state creep properties were investigated in detail. The melt-state creep test results showed that the creep resistance of the samples increased by M_w due to the increased chain entanglements, while variations in the polydispersity index (PDI) values did not cause a considerable change in the creep strain values. Moreover, the solid-state creep test results showed that creep strain values increased by M_w and PDI due to the decreasing amount of crystalline structure in the polymer. The results also showed that the amount of crystalline segment was more effective than chain entanglements that were caused by long polymer chains on the creep resistance of the polymers. Modeling the solid-state viscoelastic structure of the samples by the Burger model revealed that the weight of the viscous strain in the total creep strain increased with M_w and PDI, which meant that the differences in the creep strain values of the samples would be more pronounced at extended periods of time.     

Influence of molecular weight and molecular weight distribution on the tensile properties of amorphous polymers

Tensile property data for polystyrene samples of varying polydispersity are correlated with various parametric measures of molecular weight. Traditional measures of molecular weight, such as M?_n, M?_w, and M?_z, are shown to be unable to account for the variation of tensile properties with molecular weight. However, a new molecular weight parameter, termed the failure property parameter, is able to provide a single relationship between tensile strength and the parameter for both the broad and narrow distribution polymers. The form of this parameter is consistent with its having origins in the view that it is the entanglement network in an amorphous polymer that provides the observed strength properties. Specifically for polystyrene, the failure property parameter results indicate that material below 60,000 molecular weight does not contribute to polymer strength. Although the results of this investigation are specifically for polystyrene, the arguments used to develop the failure property parameter are not dependent on polymer chemical structure. Consequently, we believe that both the concepts and definition of this new parameter are applicable to all amorphous polymers.     

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.     

Change in the molecular weight distribution of poly(ethylene oxide) caused by the complexation with poly(acrylic acid)

The complexation between poly(ethylene oxide) (PEO) and poly(acrylic acid) (PAA) was made by using double the molar quantity of either polymer component at pH 2 where the resulting complex completely precipitates. After the removal of the precipitate, PEO or PAA remaining in the supernatant was subjected to gel permeation chromatography to investigate the change in the molecular weight distribution (MWD) caused by the complexation. No remarkable difference is observed in the MWD curves for PEO[1] (M_w=1.37 × 10⁴) before and after the complexation with PAA[1] (M_w=1.10 × 10³) and PAA[2] (M_w=4.16 × 10⁵). However, the MWD curves of PEO[2] (M_w=1.26 × 10⁵) and PAA[2] become shortened and shift to the low molecular weight side after the complexation with PAA[1] or [2] and PEO[2], respectively. This tendency is enhanced by increasing the complexation temperature. From these results, it is indicated that the complexation between PEO and PAA deals with an equilibrium reaction, and the equilibrium constant is dependent on the chain length of both polymer components and also on the complexation temperature.     

Number‐average molecular weight of branched polymers from SEC with viscosity detection and universal calibration

BACKGROUND: Number‐average molecular weight, M?_n, is an important characteristic of synthetic polymers. One of the very few promising methods for its determination is size‐exclusion chromatography (SEC) using on‐line viscometric detection and assuming the validity of the universal calibration concept. RESULTS: We have examined the applicability of this approach to the characterization of statistically branched polymers using 22 copolymers of styrene and divinylbenzene as well as 3 homopolymers of divinylbenzene with various degrees of branching. SEC with three on‐line detectors, i.e. concentration, light scattering and viscosity, enables us to evaluate experimental data by various computational procedures yielding M?_n and weight‐average molecular weight, M?_w. Analysis of the results has shown that the universal calibration theorem has limited validity, apparently due to the dependence of the Flory viscosity function on the molecular shape, the molecular weight distribution and the expansion of molecules. CONCLUSION: For complex polymers, the universal calibration, i.e. the dependence of the product of intrinsic viscosity and molecular weight, [η]M, on elution volume, can differ in values of [η]M from those obtained for narrow molecular weight standards by 10–15%. The method studied is helpful for the determination of M?_n of polymers, in particular of those with very broad molecular weight distribution, such as statistically highly branched polymers. Copyright © 2008 Society of Chemical Industry     

Improvement of the mechanical properties of chitosan films by the addition of poly(ethylene oxide)

The mechanical properties of films prepared from mixed acetic acid aqueous solutions of chitosan (M_w = 400,000; M_w/M_n = 3.8) and poly(ethylene oxide) (PEO) (viscosity average molecular weight of 200,000 or 600,000) were determined. A chitosan:PEO weight ratio of 10:2 improved the mechanical properties compared with pure chitosan films. The improvement of the mechanical properties correlated with a small reduction of the correlation length measured by small‐angle neutron scattering (SANS).     

Melt fracture of polystyrene

The results of an experimental study of melt fracture using polystyrene samples of narrow and broad molecular weight distribution are presented. The weight average molecular weight (M?_w) ranged from 9.72 × 10⁴ to 1.80 × 10⁶ and the distribution breadth M?_w/M?_η from 1.06 to 9.21. The critical shear stress varies linearly with 1/M?_w, increases slightly with temperature and is independent of the distribution of molecular weights. This type of behavior is satisfactorily explained in terms of Graessley's entanglement theory.     

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.     

Thermal response of low molecular weight poly-(<Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide) polymers in aqueous solution

Temperature-induced phase transition of three low-molecular-weight samples (M _w  < 1.2 × 10⁴) of poly(N-isopropylacrylamide) was studied with the aid of turbidimetry, dynamic light scattering, and rheology. We have demonstrated that the lower critical solution temperature depends on the length of the chain and the concentration of the polymer in the low molecular weight range. The turbidity results show a transition peak in the turbidity curve at intermediate temperatures. This peak, as well as the cloud point, is shifted toward lower temperatures when the molecular weight and the concentration of the polymer increase. The DLS measurements disclose a fast and a slow relaxation mode, which in both cases are found to be diffusive. The fast mode is linked to the diffusion of small species in the solution, and the slow mode is associated with the formation of large aggregates. The formation of these aggregates is less pronounced in solutions of polymers with low molecular weight and the incipient aggregation is shifted to higher temperatures. The shear viscosity measurements show the formation of weak aggregates, which are easily broken in solutions of short polymers. This effect is less pronounced when the molecular weight of the sample is increased. At certain shear rates, temperature-induced transition peaks of the viscosity are observed.     

Experimental investigation of flow induced molecular weight fractionation during extrusion of HDPE polymer melts

In this work, two different HDPEs with virtually identical number, M_n, and weight, M_w, average molecular weights were investigated from rheological as well as die drool phenomenon point of view. It has been revealed that long-chain branching, low polymer melt elasticity and shear viscosity significantly reduce die drool phenomenon at the die exit region. It has been concluded that die drool phenomenon of HDPE polymer melts can be explained by the flow induced molecular weight fractionation.     

Low molecular weight water‐soluble chitosans: Preparation with the aid of cellulase,characterization, and solubility

Preparation of water‐soluble chitosan (WSC) was made by treating partially N‐deacetylated chitosan with acetic anhydride in aqueous acetic acid. The optimal conditions of preparing WSC were determined on the basis of orthogonal tests. Low molecular weight WSC with broad molecular weight (600–1.5 kDa) were obtained by the depolymerization of WSC using cellulase at optimum condition of pH 4.5 and 60°C. The solubility of WSC in water and aqueous organic solvents was investigated in detail. Weight–average molecular weight (M_w) and molecular weight distribution (M_w/M_n) of samples were measured by gel permeation chromatography. The structure of WSC and its degraded products were characterized by XRD, FTIR, and MALDI‐TOF MS. The decrease of molecular weight led to transformation of crystal structure and the increase of solubility, but the chemical structures of residues were not modified compared to WSC, which was not hydrolyzed. The solubility of the WSC in water and aqueous organic solvents increased with the decrease of molecular weight. The solubility of the WSC with low molecular weight was rather high even in aqueous dimethylacetamide and dimethylsulfoxide. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 1098–1105, 2006     

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.