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.     

Molecular weight distribution of commercial emulsion grade PVC

At first glance the molecular weight distributions (MWDs) of suspension and emulsion grade PVC are very similar. However, studying the MWDs for both polymerization technologies in more detail reveals systematic differences that can be explained by the differences in the polymerization processes. The MWD of continuous emulsion PVC is broader than that of batch emulsion PVC, which, in turn, is broader than that of suspension PVC. When correlating molecular weight data to K values, it has to be considered that K values from resins including polymerization additives are different from the K value of the pure polymer. The knowledge of the differences in MWD may be helpful for estimating differences in other properties of the products.     

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.     

Calibration of GPC with polydisperse standards

An iteration method has been developed to prepare a calibration curve for gel permeation chromatography (GPC). It requires a number of samples of the same polymer which may have broad molecular weight distributions (MWD) of which two molecular weight averages must be known previously. The method has been applied to dextran standards with known M _w and M _n. Modifications involving the use of branched polymers are discussed.     

Molecular weight distribution of PVC blends from resins with different K values

The molecular weight distribution (MWD) of blends of commercial suspension grade PVC resins with different molecular weights (MW) or K values is calculated. If the K‐value difference is not too high, the polydispersity of the blend is only slightly increased as compared to those of the components. It is not possible to get bimodal MWDs by blending. Additionally, a model calculation of mean molecular weights has been performed for temperature‐programmed polymerization. On the basis of the most realistic model, which takes into account the increasing polymerization reaction rate with increasing temperature and increasing conversion, it can be predicted that a linear temperature program will give a product corresponding to an isothermal resin polymerized at a temperature near the high end of the temperature program and showing only a slightly increased polydispersity.     

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     

Molecular aggregation in poly(vinyl chloride)

Molecular weight distributions and molecular aggregation for poly(vinyl chloride) (PVC) polymerized in bulk at ?10, ?30, and ?50°C have been measured using gel permeation chromatography. The aggregate content in PVC polymerized at ?50°C was found to be 87 wt-%. These spherical aggregates of mean diameter of 5000 A are formed preferentially from PVC chains having high molecular weights and long syndiotactic sequence lengths. A temperature of 200°C was used to disintegrate these aggregates into single PVC molecules. In disagreement with measurements of M _n and M _w published in the literature, our measured values do not reach a minimum but rather increase continuously with decreasing temperature of polymerization. This disagreement is most probably due to the phenomenon of molecular aggregation in PVC.     

Linear viscoelastic relaxation modulus of polydisperse poly(dimethylsiloxane) melts containing unentangled chains

This work analyzes the relationship between the shear relaxation modulus of entangled, linear and flexible homopolymer blends and its molecular weight distribution (MWD) when a fraction of the sample contains chains with molecular weight M lower than the effective critical molecular weight between entanglements Mc_eff. This effective critical parameter is defined in terms of the critical molecular weight between entanglements M_c of the bulk polymer that forms the physical network and the effective mass fraction Wc_eff of the unentangled chains. In the terminal zone of the linear viscoelastic response, the double reptation mixing rule for blended entangled chains and a modified law for the relaxation time of chains in a polydisperse matrix are considered, where the effect of chains with M<Mc_eff is included. Although chain reptation with contour length fluctuations and tube constraint release are still the relevant mechanisms of chain relaxation in the terminal zone when the polydispersity is high, it is found that the presence of a fraction of molecules with M<Mc_eff modifies substantially the tube constrain release mode of chain relaxation. In this sense, a modified relaxation law for polymer chains in a polydisperse entangled melt that includes the effect of the MWD of unentangled chains is proposed. This law is validated with rheometric data of linear viscoelasticity for well-characterized polydimethylsiloxane (PDMS) blends and their MWD obtained from size exclusion chromatography. The short time response of PDMS, which involves the glassy modes of relaxation, is modeled by considering Rouse diffusion between entanglement points of chains with M>Mc_eff. This mechanism is independent from the MWD. The unentangled chains with M<Mc_eff occluded in the polymer network also follow Rouse modes of relaxation although they exhibit dependence on the MWD.     

Heterogeneity of active sites of Ziegler‐Natta catalysts: The effect of catalyst composition on the MWD of polyethylene

Experimental data on the molecular weight distribution (MWD) of polyethylene (PE) produced over a broad number of Ziegler‐Natta catalysts differing in composition and preparation procedure are presented. These catalysts include nonsupported TiCl₃ catalyst, four types of supported titanium‐magnesium catalysts (TMC) differing in the content of titanium and the presence of various modifiers in the composition of the support, and a supported catalyst containing VCl₄ as an active component instead of TiCl₄. The studied catalysts produce PE with different molecular weights within a broad range of polydispersity (M_w/M_n = 2.8–16) under the same polymerization conditions. The heterogeneity of active sites of these catalysts was studied by deconvolution of experimental MWD curves into Flory components assuming a correlation between the number of Flory components and the number of active site types. Five Flory components were found for PE produced over nonsupported TiCl₃ catalysts (M_w/M_n = 6.8), and three–four Flory components were found for PE produced over TMC of different composition. A minimal number of Flory components (three) was found for PE samples (M_w/M_n values from 2.8 to 3.3) produced over TMC with a very low titanium content (0.07 wt %) and TMC modified with dibutylphtalate. It was shown that five Flory components are sufficient to fit the experimental MWD curve for bimodal PE (M_w/M_n = 16) produced over VMC. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

A rheology theory and method on polydispersity and polymer long-chain branching

Model calculations were performed to investigate the sensitivity of zero-shear melt viscosity (η₀ or Eta0) on the molecular weight (MW) polydispersity of linear polymers. Simulated MW distributions (MWD) were generated with the generalized exponential (GEX) distribution function for various levels of polydispersity M_w/M_n and M_z/M_w. For linear entangled polymeric chains in the melt, the linear viscoelastic properties were predicted by using the double reptation blending rule and the so-called BSW relaxation time spectrum, named after the authors: Baumgaertel, Schausberger and Winter [Baumgaertel M, Schausberger A, Winter HH. Rheol Acta 1990;29:400-8]. Published rheological parameters appropriate for polyethylene were used in the calculations. It was found that Eta0 depended mostly on M_w, but it also significantly depended on the extent of high-MW polydispersity M_z/M_w. A revision to the fundamental MW dependency of Eta0 was proposed to compensate for this polydispersity effect. To offset the polymer polydispersity differences, we propose a new MW average (M_HV or M_x with x = 1.5) to replace M_w in the historical rheological power-law equation of Eta0 ∝ M_w^a, where the literature value of exponent “a” ranges from 3.2 to 3.6. The use of M_HV instead of M_w in the power-law equation made the calculated Eta0 independent of the sample high-MW polydispersity. With the removal of the complication from polydispersity effect, the new Eta0 power law can now provide a more robust base for studying polymer long-chain branching (LCB). A new LCB index is thus proposed based on this new melt-viscosity power law. The values of M_HV in the new power law can be calculated for polymer samples from the conventional gel permeation chromatographic (GPC) slice data.     

Molecular Weight Polydispersity Effects on Diffusion at Polymer/Polymer Interfaces

The effect of molecular weight distribution (MWD) on diffusion at symmetric polymer/polymer interfaces is investigated by rheological tools. A new model allowing the determination of a self‐diffusion coefficient of polydisperse polymer systems is presented. The model is based on the double reptation theory and Doi and Edwards' molecular dynamics applied to A/A polymers brought into intimate contact in the molten state. The material parameters for the model are obtained from linear oscillatory shear experiments, in which the dynamic shear modulus is measured in parallel plate geometry under a small amplitude of deformation as a function of time and frequency for a sandwich‐like assembly. The experiments were conducted on polystyrene (PS) blends with constant weight average molecular weight (M_w) but with variable number average molecular weights (M_n). The measured self‐diffusion coefficients showed that the presence of short molecules in the blend increases the mean value of the self‐diffusion coefficient and the magnitude of such increase can be quantitatively evaluated by the proposed model.     

Microporous membranes of polyoxymethylene from a melt‐extrusion process: (I) effects of resin variables and extrusion conditions

A two‐part study utilizing polyoxymethylene (POM) was undertaken to investigate a three stage process (melt extrusion/annealing/uniaxial stretching) (MEAUS) employed to produce microporous films. In this first part, three POM resins (D, E, and F) were melt extruded into tubular films (blowup ratio; BUR = 1), where resin D has a higher weight average molecular weight (M_w) than resin E, but both possess similar and relatively narrow molecular‐weight distributions (MWD). In contrast, resin F is characterized by a distinctly broader MWD while its M_w is slightly higher than resin D. Specific attention was focused upon the morphological and crystal orientation results as a function MWD and M_w. A stacked lamellar morphology was obtained in each case from the melt extrusion; however, the type of stacked lamellar morphology, planar or twisted, and the orientation state was found to depend upon both the resin characteristics and the melt‐extrusion conditions. Atomic force microscopy and wide‐angle X‐ray scattering were the main techniques utilized to study the melt‐extruded films while dynamic melt rheometry in conjunction with the Carreau‐Yasuda model aided in differentiating the melt‐flow behavior of the three resins. Small‐angle light scattering (SALS) was also employed to characterize the morphological state. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 2944–2963, 2001     

Synthesis of a cis-rich,living poly[(o-methylphenyl)acetylene] by use of the MoOCl4-n-Bu4Sn-EtOH catalyst

Summary Polymerization of (o-methylphenyl)acetylene (o-MePA) by MoOCl₄-n-Bu₄Sn-EtOH catalyst in toluene at 0°C provided a cis-rich living polymer; cis 77%, M _w/M _n=1.21. The polymerization at -30°C gave results similar to those for 0°C, whereas the polymer obtained at 30°C exhibited a broader molecular weight distribution (MWD) and a lower cis content. Among several organotin compounds, only n-Bu₄Sn was effective for the living polymerization of o-MePA. The bulkier the alkyl group of alcohols as the third catalyst component, the broader the MWD of the polymer, while the geometrical structure was not affected by the alcohols.     

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.     

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.     

Preparation of monodisperse polymer samples by solubility difference method

An attempt was made to prepare the polymer fractions having extremely sharp molecular weight distribution (MWD), by using a successive solutional fractionation (SSF) method, in which a polymer-lean phase was separated as a fraction from a polymer-rich phase. For this purpose a large-scale preparative SSF apparatus was constructed. Atactic polystyrene (PS) high-density polyethylene (PE), and cellulose di- and tri-acetates (CDA and CTA) were fractionated by SSF. The fractions isolated from a quasi-binary mixture (polymer/solvent system) have the same MWD as that predicted by the computer simulation technique. Even under the conventional fractionation conditions (initial polymer volume fraction v^o_p = ～ 0.01, total number of fractions n_t = 10 ～ 20) the fractions with the ratio of the weight to number-average molecular weight M_w/M_n less than 1.1 for PS, 1.2 for PE, 1.3 for CDA and 1.4 for CTA were obtained, with exception of a few initial fractions. The advantage of the SSF method was clarified over the conventional preparative methods such as gel permeation chromatography and the column fractionation method.     

Statistics of star-shaped molecules III. Stars with branched nuclei

Number and weight average molecular weights and scattering behaviour of star molecules with extended branched nuclei are calculated by application of cascade theory. The nuclei considered arise from random polycondensation of monomers of the A₃ or of the A—B/C type. Nuclei of the first type are characterised by very large molecular polydispersities (M_w/M_n α M_w), while nuclei of the second type have less broad molecular weight distributions (M_w/M_n α M_n). The rays of the stars are assumed to be either monodisperse or to obey the Schulz—Flory “most probable” length distribution. Analytic expressions are given for M_w, M_n, 〈S²〉_z and the particle scattering factor P_z(h) which was averaged over the ensemble. The results are compared with stars of spherical and uniform nuclei whose molecular weights and mean square radii of gyration equal M_wN and 〈S²〉_zN from the other two types of nuclei. In the limit of very large ray lengths the scattering behaviour is determined solely by the number of branches z. At shorter chain length of the rays structure and polydispersity of the nuclei have marked influence. This influence is still easily noticed from the angular dependence of scattered light at chain lengths where no differences in the 〈S²〉_z versus M_w plot are detectable. The mean square radius of gyration depends only weakly on the number of rays and eventually becomes independent of it if z 15. In that limit 〈S²〉_z depends virtually on the length of the rays alone and its distribution. Stars whose rays have a most probable length distribution exhibit 〈S²〉_z values twice as large as stars with monodisperse rays. A procedure is suggested and discussed for the determination of the number and length of the rays if the scattering behaviour of the isolated nucleus and the isolated linear chains is known.     

Effect of molecular weight distribution on viscosity of polymeric fluids

Bueche's theory is modified to account for the effect of polydispersity on viscosity of polymeric fluids. Results indicate that the ratio of weight-average to number-average molecular weight, 〈M_w/M_n〉, though a common measure of polydispersity, is insufficient to account completely for the effect of polydispersity on viscosity.