Dimensions of branched polymers formed in simultaneous long‐chain branching and random scission

In free‐radical olefin polymerizations, the polymer‐transfer reactions could lead to chain scission as well as the formation of long‐chain branches. The Monte Carlo simulation for free‐radical polymerization that involves simultaneous long‐chain branching and random scission is used to investigate detailed branched structure. The relationship between the mean‐square radius of gyration 〈s²〉 and degree of polymerization P as well as that between the branching density and P is the same for both with and without random scission reactions—at least for smaller frequencies of scission reactions. The 〈s²〉 values were larger than those calculated from the Zimm–Stockmayer (Z‐S) equation in which random distribution of branch points is assumed, and therefore, the Z‐S equation may not be applied for low‐density polyethylenes. The elution curves of size exclusion chromatography were also simulated. The molecular weight distribution (MWD) calibrated relative to standard linear polymers is much narrower than the true MWD, and high molecular weight tails are clearly underestimated. A simplified method to estimate the true MWD from the calibrated MWD data is proposed. The MWD obtained with a light scattering photometer in which the absolute weight‐average molecular weight of polymers at each retention volume is determined directly is considered a reasonable estimate of the true MWD. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2960–2968, 2001     

ANALYSIS OF BRANCHING DISTRIBUTION IN POLYETHYLENES BY DIFFERENTIAL SCANNING CALORIMETRY

Short chain branching has been characterized using thermal fractionation, a stepwise isothermal crystallizationtechnique, followed by a melting analysis scan using differential scanning calorimetry. Short chain branching distributionwas also characterized by a continuous slow cooling crystallization, followed by a melting analysis scan. Four differentpolyethylenes were studied: Ziegler-Natta gas phase, Ziegler-Natta solution, metallocene, constrained-geometry single sitecatalyzed polyethylenes. The branching distribution was calculated from a calibration of branch content with meltingtemperature. The lamellar thickness was calculated based on the thermodynamic melting temperature of each polyethyleneand the surface free energy of the crystal face. The branching distribution and lamellar thickness distribution were used tocalculate weight average branch content, mean lamellar thickness, and a branch dispersity index. The results for the branchcontent were in good agreement with the known comonomer content of the polyethylenes. A limitation was that high branchcontent polyethylenes did not reach their potential crystallization at ambient temperatures. Cooling to sub-ambient wasnecessary to equilibrate the crystallization, but melting temperature versus branch content was not applicable after cooling tobelow ambient because the calibration data were not performed in this way.     

Ultrahigh Branching of Main‐Chain‐Functionalized Polyethylenes by Inverted Insertion Selectivity

Branched polyolefin microstructures resulting from so‐called “chain walking” are a fascinating feature of late transition metal catalysts; however, to date it has not been demonstrated how desirable branched polyolefin microstructures can be generated thereby. We demonstrate how highly branched polyethylenes with methyl branches (220 Me/1000 C) exclusively and very high molecular weights (ca. 10⁶ g mol^?1), reaching the branch density and microstructure of commercial ethylene–propylene elastomers, can be generated from ethylene alone. At the same time, polar groups on the main chain can be generated by in‐chain incorporation of methyl acrylate. Key to this strategy is a novel rigid environment in an α‐diimine Pd^II catalyst with a steric constraint that allows for excessive chain walking and branching, but restricts branch formation to methyl branches, hinders chain transfer to afford a living polymerization, and inverts the regioselectivity of acrylate insertion to a 1,2‐mode.     

Ultrahigh Branching of Main-Chain-Functionalized Polyethylenes by Inverted Insertion Selectivity

Branched polyolefin microstructures resulting from so-called “chain walking” are a fascinating feature of late transition metal catalysts; however, to date it has not been demonstrated how desirable branched polyolefin microstructures can be generated thereby. We demonstrate how highly branched polyethylenes with methyl branches (220 Me/1000 C) exclusively and very high molecular weights (ca. 10⁶ g mol⁻¹), reaching the branch density and microstructure of commercial ethylene–propylene elastomers, can be generated from ethylene alone. At the same time, polar groups on the main chain can be generated by in-chain incorporation of methyl acrylate. Key to this strategy is a novel rigid environment in an α-diimine Pd^II catalyst with a steric constraint that allows for excessive chain walking and branching, but restricts branch formation to methyl branches, hinders chain transfer to afford a living polymerization, and inverts the regioselectivity of acrylate insertion to a 1,2-mode.     

Complementarity of universal calibration SEC and 13C NMR in determining the branching state of polyethylene

The quantitation of long‐chain branching (LCB) and short‐chain branching (SCB) in polyethylene (PE) was accomplished with a combination of carbon nuclear magnetic resonance (¹³C NMR) spectroscopy and size exclusion chromatography (SEC) with universal calibration. We demonstrate how the spectroscopic and chromatographic techniques can supplement each other, as neither is capable individually of completely describing the molecular architecture imparted by the various types of branching. The essential lack of impact of SCB on the hydrodynamic volume imposes a limit on SEC for determining this type of branching, whereas highly effective LCB in the PE molecule may not offer a statistically large enough amount of long chains for accurate determination by NMR. A variety of examples are given for PE, showcasing the advantages and shortcomings of each analytical method and their complementarity. Additionally, the importance of choosing an appropriate linear standard and viscosity shielding ratio (ϵ) for the Zimm–Stockmayer branching calculations employed for analyzing SEC data is emphasized with an examination of the effect on the results of using a branched standard and various ϵ values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3120–3135, 2000     

Structural analysis of polyethene prepared with rac‐dimethylsilylbis(indenyl)zirconium dichloride/methylaluminoxane in a high‐temperature,continuously stirred tank reactor

A study of ethene solution polymerization with the rac‐dimethylsilylbis(indenyl)‐zirconium dichloride/methylaluminoxane catalyst system in a high‐temperature (140 °C), continuously stirred tank reactor system was carried out. ¹³C NMR, gel permeation chromatography, Fourier transform infrared, and rheological measurements were used for polymer analyses. Polyethylenes with low molecular weights (weight‐average molecular weight ≈ 35–55 kg/mol) and small amounts of methyl, ethyl, and long‐chain branching were produced. ¹³C NMR measurements showed that the long‐chain and methyl branches increased and that the ethyl branch contents decreased with decreasing monomer concentrations. At high monomer concentrations, the chain transfer to the coordinated monomer was concluded to be the predominant chain termination mechanism, whereas the chain transfer to aluminum was dominant at low monomer concentrations, which was evidenced by the fact that the selectivity of end groups was reduced to about 50%. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3292–3301, 2002     

Synthesis of branched polyethylene by ethylene homopolymerization using titanium catalysts that contain a bridged bis(phenolate) ligand

The synthesis of branched polyethylene from single ethylene feed has been achieved by using a methylaluminoxane‐activated titanium complex bearing a tetradentate bis(phenolate) ligand with a 1,4‐dithiabutanediyl bridge 1 . This catalyst produces polyethylene with activities up to 6200 kg polymer/mol h bar. As evidenced by ¹³C NMR analyses, the polyethylenes contain ethyl, n‐butyl, and long‐chain (n‐hexyl or longer) branches in a range variable from 0.2 to 2.0%, depending on the experimental parameters. NMR and gas chromatography/mass spectrometry analyses suggest that such polymer microstructure arises from the in situ production of oligomers and their subsequent incorporation into the growing polyethylene chain. The broad molecular weight distribution of these polyethylenes indicates the presence of different catalytic species. The related catalyst system 2 bearing a longer 1,5‐dithiapentanediyl bridge produces linear polyethylene with moderate activity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2815–2822, 2004     

Production of polyolefins with controlled long chain branching and molecular weight distributions using mixed metallocene catalysts

Polyethylene with long‐chain branches can be produced with certain metallocene catalysts, such as monocyclopentadienyl derivatives, by incorporation of macromonomers formed in‐situ into the polymer backbone. This investigation demonstrates how dual metallocene systems can be used to control and enhance the level of long chain branching of polyethylene made with these catalysts. For instance, a catalyst that favors long chain branch formation, such as Dow's constrained geometry catalyst, can be combined with another metallocene that produces macromonomers at a faster rate. In this way, the concentration of macromonomers in the reactor increases, thus favoring the formation of long chain branches. This leads, however, to a complex microstructural control problem, since both the molecular weight and long chain branch distribution are affected simultaneously by the presence of the second catalyst. Several mathematical models will be used to describe this challenging microstructural control problem.     

Viscoelastic properties of branched polyethylene melts

The dynamic mechanical properties of branched polyethylenes in the molten state were determined in the frequency range 10^?3–10 radians/sec. The materials tested have remarkably similar rheological properties even though they vary greatly in molecular weight and molecular weight distribution. The similarity in properties is attributed to the influence of long chain branching on the relaxation spectra. A mechanistic argument is proposed to relate the observed behavior to molecular entanglement coupling. The concept of entanglement coupling involving long-chain branching leads to the expectation that the quasi-Newtonian and non-Newtonian viscosities of branched polymers may be either greater or less than those of linear polymers of the same species, which have comparable molecular weights. This is borne out by experiment.     

Relative quantification of long chain branching in essentially linear polyethylenes

The aim of this work is to describe a method whereby low levels of long chain branching, LCB, can be quantified on a relative basis for whole, unfractionated, and essentially linear ethylene/α-olefin copolymers. The method is based on a well established, relatively fast and robust experiment, namely the measurement of the linear viscoelastic properties by a single, isothermal, small amplitude oscillatory shear experiment. The analysis of the data is predicated on the use of the so-called van Gurp-Palmen plots (the phase angle, δ (=tan⁻¹(G″/G′)), plotted against the absolute value of the dynamic complex modulus, |G∗| = (G′²+G″²)^1/2). From this plot, the value of δ at |G∗| = 10 kPa is recorded, and it is demonstrated that the amount of LCB inversely correlates with such value of the phase angle, δ. Depending on the desired frequency range, the experiment duration varies between 15 and 60 min rendering this technique well suited for high throughput parallel testing. Its applicability is critically examined with a wide variety of commercial ethylene/α-olefin copolymers. Moreover, we have improved on the long chain branching index (LCBI) proposed by Shroff and Mavridis [Shroff RN, Mavridis H. Long-chain-branching index for essentially linear polyethylenes. Macromolecules 1999;32:8454-64] by basing it on data of truly linear polyethylenes (hydrogenated anionically synthesized polybutadienes) instead of apparently linear commercial polyethylenes.     

Microstructure characterization of polyethylene using thermo-rheological methods

In the present work, we use the viscoelastic moduli of a large number of industrially available polyethylenes in order to evaluate/test some of the previously proposed correlations between levels of long chain branching and polydispersity with the rheological properties. These correlations together with some new ones can be used to correct for the effects of polydispersity or long chain branching in order to assess the effect of these two molecular features on the rheological properties independently. The effects of short and long chain branching are studied providing a methodology to detect rheologically levels of short and long chain branching.     

Dimethyl‐methylphenyl copolysiloxanes by dimethylsilanolate‐initiated ring opening polymerization. Evidence for linearity of the resulting polymer structures

Recently, we reported that dimethylsilanolate‐initiated anionic ring opening polymerization of dimethylsiloxy‐ and diphenylsiloxy‐cyclic siloxanes results in polymer chain branching by dimethylsilanolate‐induced cleavage of only one Si‐C_Ar side bond in diphenylsiloxy repeat units, leading to formation of “Ph‐T‐branches”, and not extending to the cleavage of the second phenyl group. We attributed this behavior to electronic structures of the participating dimethylsiloxy‐, diphenylsiloxy and Ph‐T‐branch silicons and predicted that copolymers prepared by this synthetic route from dimethylsiloxy‐ and methylphenylsiloxy‐cyclics should not undergo branching at all but should have perfect linear chain configuration. Here, we describe results of a study of two such dimethylsilanolate‐initiated ring opening polymerizations of dimethylsiloxy‐ and methyphenylsiloxy‐cyclic tetramers and characterization of the resulting polymers by SEC‐MALS‐VIS, Mark‐Houwink‐Sakurada relationship and ²⁹Si NMR. The results obtained clearly confirmed our prediction of expected linearity of these polymer chains and also indicated that the resulting polymers were completely amorphous even at as low methylphenylsiloxy‐content as 3.9 mol %. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1122–1129     

A basis for the determination of branching in polymers by use of gel-permeation chromatography

The technique for determining branching in polymers by using a combination of GPC and intrinsic viscosity data has been extended beyond current methods. Equations used in these analyses are presented. The derivations are based upon the assumption that branching is present only when there is a measurable reduction in the intrinsic viscosity. Techniques for calculating the functionality of the star branch point in starbranched polymers are given. Three random-branching parameters are calculated from a knowledge of the average branching density, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar \lambda $\end{document}: (a) the lowest molecular weight branched polymer that can be measured, M?^*; (b) the average molecular weight between branch points, M?_bp; (c) the weight percentage of polymer that is branched. The applicability of this technique is demonstrated by using an analysis of published data on characterized fractions of a randomly branched polystyrene.     

Simulating Light Scattering Behavior of Branched Molecules

Monte Carlo simulations reveal long chain branching (LCB) topology based on kinetics of systems like low‐density polyethylene (ldPE). Examining the topologies computed shows the majority of branch arms to be short as compared to backbone length, while also a significant branch‐on‐branch fine structure is observed. Until now, predicting scattering function P ⁻¹(θ) from LCB has only been successful for structures like simple combs or stars. Topologies in graph theoretical form are used to predict scattering function P ⁻¹(θ) and by summating intramolecular distances, accounting for branching and excluded volume. Experimental size exclusion chromatography with multiangle light scattering can be brought in line with the predicted branching character. Branching is less than predicted due to a different fine structure in ldPE leading to stronger size contraction.     

Comparing Long‐Chain Branching Mechanisms for Ethylene Polymerization with Metallocenes and Other Single‐Site Catalysts: What Simulated Microstructures Can Teach Us

Three different long‐chain branch (LCB) formation mechanisms for ethylene polymerization with metallocenes in solution polymerization semi‐batch and continuous stirred‐tank reactors are modeled to predict the microstructure of the resulting polymer. The three mechanisms are terminal branching, C–H bond activation, and intramolecular random incorporation. Selected polymerization parameters are varied to observe how each mechanism affects polymer microstructure. Increasing the ethylene concentration during semi‐batch polymerization reduces the LCB frequency of polymers made with the terminal branching and intramolecular mechanisms, but has no effect on those made with the C–H bond activation mechanism, which disagrees with most previous data published in the literature. The intramolecular mechanism predicts that LCB frequencies hardly depend on polymerization time or ethylene conversion, which also disagrees with the published experimental data for these systems. For continuous polymerization reactors, experimental data relating polydispersity to LCB frequency can be well described with the terminal branching mechanism, but both C–H bond activation and intramolecular models fail to describe this experimental relationship. Therefore, detailed simulations confirm that the terminal branching mechanism is indeed the most likely mechanism for LCB formation when ethylene is polymerized with single‐site coordination catalysts such as metallocenes in solution polymerization reactors.     

Size‐exclusion chromatography coupled to multiangle light scattering detection of long‐chain branching in polyethylene made with phillips catalyst

Size‐exclusion chromatography coupled to multiangle light scattering (SEC‐MALS) has been used to detect long‐chain branching (LCB) in polyethylene (PE) from Cr/silica catalysts for the first time. The observed LCB response to several catalyst and reactor variables mostly confirms earlier conclusions drawn from rheological measurements. However, SEC‐MALS has also shed additional light on a few previously unanswered questions. Above all, SEC‐MALS shows the placement of branching within the MW distribution, which was not previously known, and which may explain some of the unique molding behavior of Cr‐derived PE. This new SEC‐MALS data also provide insight into the mechanism of LCB formation, which is discussed. Like earlier studies based on rheology, this new study demonstrates that the commonly accepted view of macromer incorporation may be overly simplistic. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Size Exclusion Chromatography of Polymers With Random Tetrafunctional Branching

Abstract

The behaviour of polydisperse branched copolymers of methyl methacrylate with a small amount of randomly situated tetrafunctional ethylenedimethacrylate units was investigated by means of size exclusion chromatography (SEC). A procedure has been suggested for the conversion of apparent values of molecular parameters of real polymer branched systems (M_{n, app}; M_{w, app} obtained from SEC data by calibration of the separation system using a linear polymer) into actual values. This was made possible by off-line coupling of SEC and viscometry. The branching was characterized by the weight average number of branching sites in the macro-molecule, m_w, and the branching index, y.     

Rheological investigation of the influence of molecular structure on natural and accelerated UV degradation of linear low density polyethylene

Metallocene and Ziegler-Natta (ZN) linear low density polyethylenes (LLDPEs) of different branch types and contents as well as linear high density polyethylene (HDPE) were exposed to natural and accelerated weather conditions. The degree of UV degradation of exposed samples was measured by rheological techniques and results were compared with unexposed polymers. Dynamic shear measurements were performed in an ARES rheometer in the linear viscoelastic range. The degree of enhancement or reduction in viscosity and elasticity was used as a measure of the degree of cross-linking or chain scission, respectively. The degradation results of LLDPE suggest that both cross-linking and chain scission are taking place. Chain scission dominated the degradation at high levels of short chain branching (SCB) and long exposure times. The degradation mechanism of m-LLDPE and ZN-LLDPE is similar; however, m-LLDPE showed a higher degradation rate than ZN-LLDPE of similar M_w and average SCB. ZN-LLDPE was found to be more stable than a similar m-LLDPE. Comonomer type had little influence on degradation. Dynamic shear rheology was very useful in revealing the influence of different molecular parameters and it exposed the degradation mechanism.     

Changes in sol fraction during peroxide crosslinking of linear low-density polyethylenes with homogeneous distribution of short chain branching

FTIR measurements of sol fractions were carried out in order to assess side reactions during dicumyl peroxide (DCP) crosslinking of linear low density polyethylenes (LLDPEs) with homogeneous distribution of short chain branching. The changes of methyl and olefinic unsaturation concentration were measured as a function of degree of branching and DCP content. The changes of methyl and vinylidene concentration indicate that the scission probability has greater significance for the samples with initial branch content above 31 CH₃/1000 C and increases with increasing DCP concentration. The analysis of trans-vinylene concentration indicates that the probability of disproportionation also increases with increasing DCP content. The changes of methyl concentration in the sol fraction of the sample containing initially ca. 23 CH₃/1000 C with increasing DCP content could be interpreted using the dependence of crosslinking efficiency on branch content found previously for some range of branch concentration. © 1995 John Wiley & Sons, Inc.