Gel permeation chromatography of polyethylene: Effect of long-chain branching

The effect of long-chain branching on the size of low-density polyethylene molecules in solution is demonstrated through solution viscosity and molecular weight measurements on fractionated samples. These well-characterized fractions are analyzed by gel permeation chromatography (GPC), and it is shown that the separation of the polymer molecules by this technique is sensitive to the presence of long-chain branching. By using fractions of branched polyethylene possessing differing degrees of branching, one observes that a single curve is adequate in relating elution volume to molecular weight. This calibration curve is applied in the GPC analysis of a variety of commercial low-density polyethylene resins and it is shown, by comparison with independent osmometric and gradient elution chromatographic data, that realistic values for molecular weight and molecular weight distribution are obtained. The replacement of molecular weight M by the parameter [η]M as a function of elution volume, leads to a single relationship for both linear and branched polyethylenes. This indicates that GPC separation takes place according to the hydrodynamic volumes of the polymer molecules. The comparison of data for polyethylene and polystyrene fractions suggests that this volume dependence of the separation will be observed for other polymer–solvent systems.     

Long-chain branching in low-density polyethylene

A method is given for the analysis of long-chain branching in polymers by using combined GPC and intrinsic viscosity measurements. A computer program was written to evaluate branching indices by a tabular, iterative method. The method was applied to the evaluation of long-chain branching in low-density polyethylene.     

Characterization of low-density polyethylene by gel permeation chromatography—II. Study on the Drott method using fractions

Polyethylenes of different structures were fractionated and the fractions characterized by light scattering, gel permeation chromatography and viscometry. Intrinsic viscosities were measured in solvents of different thermodynamical quality including a θ-solvent (diphenyl at 118° for low-density polyethylene and at 130° for high-density polyethylene and ethylene-butene-1 copolymer). The results were used for examining two aspects of the Drott iterative procedure: (a) the relationship between thermodynamical quality of the solvent and depression in the intrinsic viscosity due to branching; and (b) analytical form of expression relating the so-called g-factor to the number of long-chain branches. The ratio of intrinsic viscosities of branched and linear species at a given weight-average molecular weight has been clearly proved to be solvent independent, and the equation relating the g-factor to the number of branches for polymer monodisperse with respect to molecular weights appears to be a fair representation of long-chain branching in low-density polyethylene. For the polymers examined, the branching frequency λ is not independent of molecular weight.     

Molecular weight and long-chain branching distributions of some polybutadienes and styrene–butadiene rubbers. Determination by GPC and dilute solution viscometry

A method described for the determination of molecular weight and long-chain branching distributions of polymers requires no prior knowledge of the functional relation between branching frequency and molecular weight. It is based on preparative fractionation and viscometric and gel-permeation chromatographic measurements on both fractions and whole polymer. The technique is applied to several polybutadienes and butadiene-styrene copolymers differing widely in method of synthesis and pattern of long-chain branching.     

用GPC-级分特性粘数法表征高顺式-1,4聚丁二烯的长链支化

本文在Ambler方法和kraus方法的基础上,用GPC-级分特性粘数法来测定聚合物的长链支化度,能同时以g_i、λ_i、G_i、m_i、支化重量百分数等支化参数来表征聚合物的支化分布、支化程度和支化含量等;得到了相应的计算gi、λi、[η]_i等有关的计算公式和计算方法;还研制成了以光导纤维为冷光源的高精度光电自动计时毛细管粘度计和60小时内恒温精度优于±5×10~(-4)℃的超级恒温水浴,使计时精度达到≤±4×10~(-3)秒;并以国产和进口的镍系顺丁橡胶为例,讨论了分子量和支化度多分散性之间的某些关系;从而确定了该法比较合理地、全面地相对比较聚合物的长链支化度。     

Morphology and properties of low-density (branched) polyethylene

The different types of morphology that can be developed in a large number of low-density (branched) polyethylene whole polymers, as well as in a series of fractions, have been studied for two different extreme crystallization modes. Concomitantly, thermodynamic properties of the same samples have also been determined. After isothermal crystallization at elevated temperatures, spherulitic structures are found in all the whole polymer samples. On the other hand, after rapid crystallization a variety of different types of supermolecular structures are observed which are shown to depend systematically on the concentration of side-chain branches and the relative proportion of high molecular weight species in the sample. This temperature dependence of the morphological forms is opposite to that previously reported for linear polyethylene. The studies with the fractions show that the individual species are not the cause of this behavior; rather, the total composition is the important factor. The thermodynamic properties are also quite different from those of linear polyethylene in showing virtually no molecular weight dependence and being governed primarily by the concentration of short-chain branches. The degrees of crystallinity as determined from density and enthalpy of fusion measurements do not vary much with the two extreme crystallization conditions employed, are not sensitive to the morphology, and differ from one another, even when well-developed spherulites are formed. A major influence of the branching concentration on these properties is clearly indicated.     

Simulation of the effects of chain architecture on the sorption of ethylene in polyethylene

An osmotic ensemble hyperparallel tempering technique has been developed to study the solubility of ethylene in amorphous linear low-density polyethylene of different chain architectures. The NERD united-atom force field (Nath, Escobedo, and de Pablo revised united-atom force field) is used in all simulations. We have investigated the effect of polyethylene chain length and branching on ethylene solubility. In this study, we have considered short-chain branching of amorphous linear low-density ethylene-1-hexene copolymers under typical polymerization reactor conditions. It is observed that, in the polymer, ethylene prefers to reside in the vicinity of polymer chain ends. This clustering causes a decrease in ethylene solubility with polymer chain length. When short-chain branches are introduced to a linear polymer chain, however, the chain-end clustering effect is counteracted by a higher density, thereby leading to an ethylene solubility almost identical to that in the linear polymer.     

Characterization of linear low-density polyethylene: Cross-fractionation according to copolymer composition and molecular weight

The structure of ethylene copolymers modified by α-olefins has become an area of intense investigation since the successful commercialization of so-called linear low-density polyethylene (LLDPE) resins. The molecular structure of a series of typical commercial LLDPE copolymers was investigated and compared to LDPE and HDPE. The commercial LLDPE resins studied contained about 7% by weight of butene-1. The resins were fractionated according to short-chain branching content by a technique called temperature rising elution fractionation. Size exclusion chromatography, x-ray diffraction, ¹³C nuclear magnetic resonance, intrinsic viscosity, and differential scanning calorimetry were used to fully characterize the whole polymers as well as fractions of a selected LLDPE resin. A broad set of data was assembled in this work to investigate the short-chain branching, long-chain branching, and the molecular-weight distribution of these commercial resins. The melting behavior of the LLDPE resins was found to be strikingly different from that of LDPE and HDPE. The broad and multimodal melting envelope of the LLDPE resins was found to be due to a broad and multimodal short-chain branching distribution. No significant long-chain branching was found in the LLDPE resins. The short-chain branching was found to decrease with the increase of molecular weight in a typical commercial LLDPE resin. The unique physical properties of these resins are certainly strongly controlled by the expression of the distinctive heterogeneous comonomer incorporation in the solid-state morphological structure. The physical and mechanical properties of these materials should be ultimately understandable on the basis of the unique morphology which results from the extremely heterogeneous incorporation of modifying α-olefin in these commercial LLDPE resins.     

Novel mechanism for the formation of long-chain branching in polyethylene

Polyethylene produced by a vanadium-based polymerization catalyst contains long-chain branching as determined by NMR and rheology, even though the polymer has very low levels of vinyl unsaturation. A new mechanism is proposed for the formation of the long-chain branching, which involves C H bond activation of the polyethylene backbone through a σ-bond metathesis reaction, followed by ethylene insertion at the new V C bond. Consistent with the proposed C H bond activation mechanism, the polymerization catalyst was also found to insert ethylene into the C H bonds of alkanes such as heptane. A bridged metallocene catalyst was also found to activate C H bonds of alkanes suggesting this new mechanism may explain the formation of long-chain branching in some metallocene-produced polyethylene. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2889–2898, 1998     

Gel permeation chromatography of branched polyethylene

The effect of long-chain branching must be considered in gel permeation chromatography to evaluate the molecular weight polydispersity of branched polyethylenes. Osmotic molecular weights of fractions of branched polyethylene were correlated with elution volumes; weight-average and number-average molecular weights of a branched polyethylene were determined. Molecular weight changes on crosslinking polyethylene by ionizing radiation are accompanied by branching and cannot be simply interpreted by gel permeation chromatography.     

DETERMINATION OF BRANCHING DISTRIBUTION IN HIGH cis-1,4-POLYBUTADIENE BY GPC AND AUTOMATIC VISCOMETRY

Based on the methods reported by Ambler and Kraus, a method has been developed for the determination of long-chain branching distribution in polymers by the combined use of GPC and intrinsic viscosity data of polymer fractions. In this method, g_i, λ_i, G_i, m_i, the weight percentage of polymer that is branched, etc. can be used simultaneously to characterize the distribution, degree and content of branching in polymers. Some relations between molecular weight polydispersity and branching polydispersity in Nickel-based high cis-1,4-polybutadiene samples are discussed. It was found that the number of long branches λ. per unit molecular weight is a function of molecular weight and all of the samples are highly branched at a molecular weight of about 10~6.     

Processability improvement of polyolefins through radiation-induced branching

Radiation-induced long-chain branching for the purpose of improving melt strength and hence the processability of polypropylene (PP) and polyethylene (PE) is reviewed. Long-chain branching without significant gel content can be created by low dose irradiation of PP or PE under different atmospheres, with or without multifunctional branching promoters. The creation of long-chain branching generally leads to improvement of melt strength, which in turn may be translated into processability improvement for specific applications in which melt strength plays an important role. In this paper, the changes of the melt flow rate and the melt strength of the irradiated polymer and the relationship between long-chain branching and melt strength are reviewed. The effects of the atmosphere and the branching promoter on long-chain branching vs. degradation are discussed. The benefits of improved melt strength on the processability, e.g., sag resistance and strain hardening, are illustrated. The implications on practical polymer processing applications such as foams and films are also discussed.     

Low-density polyethylene: Variation of branching frequency with molecular weight and its influence on molecular weight as determined by gel-permeation chromatography

A method for determining long-chain branching frequency and molecular weight averages for unfractionated low-density polyethylene (LDPE) by the combined use of gel-permeation chromatography (GPC) and intrinsic viscosity data has been reported (GPC–IV method). The method assumes that the number of long branches λ per unit molecular weight is a constant independent of molecular weight. Recent data reported on λ as a function of molecular weight M in commercial LDPE indicate that this assumption is not generally valid, and concern has been expressed as to the size of the errors in molecular weights calculated using this assumption. The errors associated with assuming that λ is constant were evaluated in this study by first determining the way in which λ varies with M for two typical commerical LDPE resins by fractionation and application of the GPC–IV method to representative fractions. The experimentally determined relations between λ and M were then employed in the calculation of molecular weight and molecular size averages from GPC–IV data on the original unfractonated samples. Although it was found that λ increases with molecular weight for both samples, the results indicate that the error involved in assuming that λ is a constant is no greater than the precision with which molecular weight averages can be evaluated by GPC.     

High‐density polyethylene fractionation with supercritical propane

During the development of column extraction techniques, two methods of separation were identified. The first method is based on altering polymer solubility by varying the ratio of solvent in a solvent/nonsolvent mixture at a constant temperature above the polymer melting point (gradient solvent elution fractionation). This method fractionates polymers according to molecular weight. The second method is based on altering polymer solubility by varying solvent temperature (temperature rising elution fractionation—TREF). TREF fractionates semicrystalline polymers with respect to their crystallizability, independently of molecular weight effects. In the present article, supercritical propane will be used to fractionate a high‐density polyethylene sample by molecular weight and short chain branching. The main advantage of supercritical fluid fractionation is that large polymer fractions with narrow molecular weight distributions (isothermal fractionation) or narrow short chain branching distributions (isobaric fractionation) can be obtained without using hazardous organic chlorinated solvents. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 553–560, 1999     

Another Look at Long-Chain Branching

Long-chain branching can occur during radical polymerization and is especially important for polyethylene. An improved method of calculating the effect of long-chain branching on molecular weight distribution is presented. This method uses a probability treatment. The results are more consistent with both kinetic theory and experimental data than the results of previous long-chain branching calculations. In contrast to previous calculations, the present work shows that generation cannot occur from long-chain branching alone.     

On the transition from paraffinic to polymeric behavior: Mechanical properties

An attempt has been made to determine what influence chain folds may have on the α and γ mechanical loss peaks in linear polyethylene. In so doing, one long-chain n-paraffin (C₉₄H₁₉₀) and two low molecular weight polyethylene fractions have been examined with mechanical relaxation, differential scanning calorimetry (DSC), and low-angle x-ray diffraction techniques. The data suggest that chain folds play a prominent role in both the α and γ processes but that other factors such as polydispersity and/or branching are also important.     

Long-Chain Branching under Conditions of Nonuniform Branching Probability

Abstract

Long-chain branching can occur during free radical polymerization and is especially important for polyethylene. An improved method of calculating the effect of long-chain branching on molecular weight distribution was presented in an earlier paper in which the assumption was made that the probability of branching at each monomer unit was constant throughout the polymerization. A method of including a nonuniform probability of branching in the calculations is presented. Calculation results show that the predictions of the two mathematical models are similar and both models fit published data on polyethylene equally well.     

Molecular weight distribution and molecular structure of polyethylene produced by radiation-induced polymerization

The molecular weight distribution of polyethylene produced by radiation was calculated according to a kinetic scheme. The calculated molecular weight distribution was compared with the results deduced from gel-permeation chromatography. The observed distribution curve from GPC was broader and showed a lower degree of polymerization than the calculated one. Discrepancies between observed and calculated curves can be explained if the polymer contains nonsteady-state products and if the reaction mechanism includes chain transfer to dead polymer. By this reaction long-chain branching would occur. Several long-chain branches per polymer molecule were indeed found, as inferred from solution properties.     

A simulation model for long-chain branching in vinyl acetate polymerization: 1. Batch polymerization

A new simulation model for the kinetics of long-chain branching formed via chain transfer to polymer and terminal double-bond polymerization is proposed. This model is based on the branching density distribution of the primary polymer molecules. The theory of branching density distribution is that each primary polymer molecule experiences a different history of branching and provides information on how each primary polymer molecule is connected with other chains that are formed at different conversions, therefore making possible a detailed analysis on the kinetics of the branched structure formation. This model is solved by applying the Monte Carlo method and a computer-generated simulated algorithm is proposed. The present model is applied to a batch polymerization of vinyl acetate, and various interesting structural changes occurring during polymerization (i.e., molecular weight distribution, distribution of branch points, and branching density of the largest polymer molecule) are calculated. The present method gives a direct solution for the Bethe lattice formed under nonequilibrium conditions; therefore, it can be used to examine earlier theories of the branched structure formation. It was found that the method of moments that has been applied successfully to predict various average properties would be considered a good approximation at least for the calculation of not greater than the second-order moment in a batch polymerization. © 1994 John Wiley & Sons, Inc.     

Effect of molecular structure on polyethylene melt rheology. II. Shear-dependent viscosity

The investigation of the effect of molecular structural variables on the melt viscosity of polyethylene was extended to the shear dependent region by application of a reduced variables treatment following, in a formal sense, that of Bueche. Viscosity–shear rate data were obtained for a series of experimentally polymerized linear polyethylene samples having a range of molecular weights and molecular weight distributions as characterized primarily by gel permeation chromatography. These data could be superimposed on a single reduced variables flow curve using parameters which were a function only of temperature, limiting Newtonian viscosity, M?_w, and M?_w/M?_n. The same treatment was successfully applied also to branched (low-density) fraction data discussed in a previous paper, with additional correction for long-chain branching. However, different reduced variables curves were obtained for the branched and linear cases.