Degree Of Long-chain Branching Research Articles

A statistical approach towards determining the governing parameters in volume expansion behavior of polypropylene foams

This study delves into the complex relationship between molecular structures and properties within polypropylene (PP) foams, with a particular focus on how various material parameters influence foamability. Multiple linear regression was adopted to efficiently assess the impact of eleven material parameters on foam expansion behavior. A primary finding is the significant role of branching index (g'vis) in shaping the expansion profile (i.e., the foaming window, maximum expansion ratio (Φmax), and optimum foaming temperature (Toptimum)). Additionally, Z-average molecular weight (Mz) is identified as crucial factor influencing the foaming window. Furthermore, the Winter-Chambon parameter n, indicator of the relaxation behavior of a resin in the terminal zone, is distinguished as a key parameter in determining Φmax. The crystallization temperature (Tc) also plays a pivotal role, particularly in its relationship with Toptimum. The research further highlights the significance of long-chain branching (LCB) and suggests strategies for cost reduction by minimizing the degree of LCB without compromising foaming performance, achievable through the adjustment of Mz and n. This strategy was exemplified through the comparison of two LCB PP resins, PP-12 and PP-22, demonstrating the feasibility of achieving similar foamability with adjustments in material parameters. The findings offer a detailed assessment of these parameters' influence on foamability, presenting valuable guidelines for optimizing PP foam production and customizing material properties for targeted applications.

Coupling Kinetic Modelling with SAOS and LAOS Rheology of Poly(n-butyl acrylate).

A kinetic model based on fundamentals of radical polymerization and literature known rate parameters for the polymerization of n-butyl acrylate is validated against molecular analysis and rheological data. The model is used to predict conversion, molar mass distribution, and branching densities in form of short and long chain branching. Rheological measurements of synthesized model polymers are evaluated along the Carreau-Yasuda and Van Gurp-Palmen presentations, allowing to detect small differences in the degree of long chain branching. Contributions of anharmonics to viscoelastic response in large amplitude oscillations are small and differences between the products are dominated by the differences in molar mass.

Biaryl Group 4 Metal Complexes as Non‐Metallocene Catalysts for Polyethylene with Long Chain Branching

A series of biaryl Group 4 complexes with a bidentate and a tridentate pincer ligand have been synthesized and characterized. The complexes have been applied as metallocene analogues for the controlled polymerization of ethylene and the copolymerization of ethylene and 1‐hexene, with a particular focus on the control of the degree of long chain branching in these polymers.

Toughening mechanism of long chain branched polyamide 6

Polyamide 6 (PA6) materials with different degrees of long chain branching (LCB) were prepared via extrusion through varying the addition of chain extender. The LCB degree was quantitatively determined by using a rheological method based on macromolecular dynamic models. The topological structures of long-chain branching and crosslinked network were effectively distinguished through rheological percolation analysis so that modified PA6 with ultra-high LCB level was obtained. The XRD analysis indicated that LCB modification favored the generation of the γ-form, and the γ-form content of LCB-PA6 increased with increasing degree of LCB, which could provide a reasonable explanation for the high Izod impact strength of ultra-high LCB-PA6. Another reason for the great enhancement of impact toughness was the strong interfacial interaction between LCB molecules and virgin PA6 matrix. A large number of fibrillar ligaments and cavities during crack propagation were observed in the SEM analysis.

Structure and Property of Microinjection Molded Poly(lactic acid) with High Degree of Long Chain Branching

Long chain branches (LCB) are successfully grafted to linear poly(lactic acid) (PLA) using functional group reactions with pentaerythritol triacrylate (PETA) and tetraethylthiuram disulfide (TETDS)...

Shear-induced enhancements of crystallization kinetics and morphological transformation for long chain branched polylactides with different branching degrees.

The effects of long chain branching (LCB) degree on the shear-induced isothermal crystallization kinetics of a series of LCB polylactides (LCB PLAs) have been investigated by using rotational rheometer, polarized optical microscopy (POM) and scanning electron microscopy (SEM). Dynamic viscoelastic properties obtained by small-amplitude oscillatory shear (SAOS) tests indicate that LCB PLAs show more broadened relaxation time spectra with increasing LCB degree. Upon a pre-shear at the shear rate of 1 s−1 LCB PLAs show much faster crystallization kinetics than linear PLA and the crystallization kinetics is enhanced with increasing LCB degree. By modeling the system as a suspension the quantitative evaluation of nucleation density can be derived from rheological experiments. The nucleation density is greatly enhanced with increasing LCB degree and a saturation in shear time is observed. Crystalline morphologies for LCB PLAs observed by POM and SEM demonstrate the enhancement of nucleation density with increasing LCB degree and a transformation from spherulitic to orientated crystalline morphologies. The observation can be ascribed to longer relaxation time of the longest macromolecular chains and broadened, complex relaxation behaviors due to the introduction of LCB into PLA, which is essential in stabilizing the orientated crystal nuclei after pre-shear.

Branching degree and rheological response correlation in peroxide-modified linear low-density polyethylene

Correlations between rheological behavior and degree of long chain branching (LCB) of linear low-density polyethylene (LLDPE) upon a peroxide (dicumyl peroxide [DCP]) modification process under various conditions are discussed in this paper. The gel content analysis revealed negligible insoluble crosslinked fraction implying that incorporation of DCP to LLDPE predominately leads to branching rather than crosslinking. The slight changes in average molecular weight and molecular weight distribution induced by peroxide modification under various conditions revealed that formation of low-molecular-weight fractions due to chain scission is also negligible. The changes in terminal, trans, and pendant double bonds concentration of the modified samples with different amounts of peroxide were well depicted by Fourier transform infrared spectroscopy. Considering insignificant changes in molecular weight and molecular weight distribution during peroxide modification, the deviation observed in zero-shear-rate viscosity (η0) values of the modified LLDPE with that of power-law equation related to the linear PEs could be reliably attributed to the presence of LCB in the peroxide modified samples. Increasing the DCP content at roughly constant molar mass led to increasing of η0 values as a result of increased degree of LCB. The increase in η0 values was ascribed to prolonged relaxation times of the polymer molecules due to the retarded reptation motion-driven relaxation mechanism. Copyright © 2014 John Wiley & Sons, Ltd.

Revisiting the long-chain branch formation mechanism in metallocene catalyzed polyethylenes

The effect of polymerization parameters, such as pressure (ethylene concentration), temperature and comonomer type and concentration, on several long-chain branched (LCB) ethylene homopolymers and ethylene/α-olefin copolymers was investigated with respect to their degree of long-chain branching. Common long-chain branched metallocene polyethylenes (LCB-mPEs) and comb-like LCB-PEs, which have high viscosity and significantly differ from conventional LCB-mPEs, have been used to evaluate different proposed mechanisms for LCB-formation based on available characterization methods. The correlations between polymerization parameters and degree of long-chain branching were compared with the correlations predicted by different formation mechanisms (intermolecular auto-copolymerization by re-incorporation of β-hydride terminated chains, intramolecular insertion of stored vinyl terminated chains, chain walking and σ-bond metathesis reactions) to elucidate which of these mechanisms is the correct one. The intermolecular auto-copolymerization mechanism was found to be the predominant mechanism behind LCB-formation in slurry phase polymerization. However, σ-bond metathesis reactions cannot be entirely ignored.

Effects of long chain branching on melt fractures in capillary extrusion of metallocene‐catalyzed linear low‐density polyethylene melts

AbstractTo investigate the effect of long chain branching (LCB) on melt fractures of metallocene‐catalyzed linear low‐density polyethylene (mLLDPE), we prepared a series of sparsely long‐chain‐branched mLLDPEs with well‐defined degrees of LCB. Gross melt fractures were observed to decrease as the degree of LCB increases. This is in accordance with a prediction based on the observation that LCB enhances chain entanglement and consequently increases the melt strength of a polymer. However, sharkskin melt fracture (SMF) was observed to be more severe with the degree of LCB. There have been debates over the effect of LCB on SMF. According to a well‐known mechanism of SMF, SMF is expected to decrease with the degree of LCB. Therefore, the majority of research groups believe that SMF decreases with the degree of LCB. This study clearly shows that the SMF becomes more severe with an increase of the degree of LCB and suggests another possible mechanism for the SMF. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Correlations between the Characteristic Rheological Quantities and Molecular Structure of Long-Chain Branched Metallocene Catalyzed Polyethylenes

Different rheological quantities, such as the zero shear-rate viscosity η0 and the linear steady-state elastic compliance Je0 of long-chain branched metallocene-catalyzed ethene homopolymers and ethene-/α-olefin copolymers with a polydispersity Mw/Mn ≈ 2, were correlated with the molar mass Mw and degree of long-chain branching λ. A linear reference for the δ(|G*|) plot was used to show the effect of long-chain branches on this rheological property. The linear steady-state elastic compliance Je0 correlated with the zero shear-rate viscosity increase factor η0/η0lin and the characteristic phase angle δc. However, the latter only works when compensating for the influence of the molar mass on Je0 by the relationship between Je0 and Mw established elsewhere (Stadler and Munstedt, JoR, 2008). The characteristic phase angle δc and zero shear-rate viscosity enhancement factor η0/η0lin are linked to each other by the linear dependencies for the type I and type II viscosity functions.

Anionic Synthesis and Rheological Characterization of Poly(p‐methylstyrene) Model Comb Architectures with a Defined and Very Low Degree of Long Chain Branching

A method is presented for the synthesis of defined sparsely branched polystyrene-based homopolymer model combs. By the use of poly(p-methylstyrene) (PpMS) as backbone and side chains, a low, but well controlled amount of branching of typically less than 1 mol-% (e.g., 1 branch per approx. 200 backbone C-atoms) can be achieved. The used anionic synthesis offers full control of the molecular weight in combination with low polydispersity. Molecular weight and polydispersity were determined by SEC-MALLS, confirming the well defined synthesis with low polydispersity ($\overline {{\rm M}} _{{\rm w}} /\overline {{\rm M}} _{{\rm n}} $ < 1.07). The melt rheological properties of the synthesized linear and comb polymers were obtained in both oscillatory shear and uniaxial extensional flow. Using the so-called van Gurp-Palmen plot, clear differences between both synthesized topologies are clearly seen. The appearance of a second minimum for lower values of the complex modulus in shear is a clear indication of a second relaxation process attributable to the entangled side chains. The presence of the entangled side chains is responsible for the observed strain hardening obtained in extensional viscosity experiments, as compared to the linear polymers. These model samples open up the possibility to compare different advanced rheological methods, e.g., FT-rheology or extensional rheology, towards limiting sensitivity.

Structural determination of ethylene‐propylene‐diene rubber (EPDM) containing high degree of controlled long‐chain branching

AbstractThis work highlights an attempt to characterize the degree and nature of long‐chain branching (LCB) in an unknown sample of ethylene‐propylene‐diene rubber (EPDM). Two EPDM rubbers selected for this study were comparable in comonomer compositions but significantly different with respect to molar mass and the presence of LCB. Both rubbers contained 5‐ethylidene‐2‐norbornene (ENB) as diene. Solution cast films of pure EPDM samples were used for different characterization techniques. 1H‐NMR, and 13C‐NMR were used for assessing the comonomer ratios and LCB. Size exclusion chromatography (SEC) equipped with triple detector system was used to determine the molar mass (both absolute and relative) and polydispersity index (PDI). Presence of branching was also detected using sec‐viscometry. Rheological analysis has also been used for characterizing LCB. Finally, on the basis of the experimental findings and the available theories, an attempt was made to identify the chemical nature and degree of LCB. This study reveals the possibility of detailed characterization of molecular architecture of EPDM containing LCB by comparing with an essentially linear EPDM in light of an existing theory. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

The influence of porosity on the Phillips Cr/silica catalyst 2. Polyethylene elasticity

AbstractThe Phillips Cr/silica catalyst produces low levels of long chain branching (LCB) in polyethylene, which have a powerful influence on industrial molding behavior. Although many catalyst and reactor variables determine the degree of LCB, perhaps the most significant of these is the morphology of the silica support. In this study many different types of silicas were converted into Cr/silica catalysts, which were tested in ethylene polymerization, and the resultant polymer elasticity was then determined. In some experiments, the surface area of the catalyst seemed to correlate quite well with polymer elasticity. In other tests, however, no connection with surface area was evident but the pore volume was quite influential. Together, all these studies suggest that it is the degree of structural reinforcement of the silica matrix, rather than any one physical measurement of porosity, that influences elasticity. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 845–865, 2009

Molecular, rheological, and crystalline properties of low‐density polyethylene in blown film extrusion

AbstractThe molecular weight and its distribution, degree of long chain branching and cooling rate strongly influence crystallinity during processing, which in turn determines the processability and the ultimate properties of the blown film. Generally a decrease in the number of branches and molecular weight of the polymer and the cooling rate results in an increase of the crystallinity. Length of the main chain and extent of branching in low‐density polyethylene (LDPE) are also factors that affect melt rheology and film crystallinity. Long chain branched polyethylene is suitable in the blown film process due to its better melt strength for bubble stability. The objective of this article is to describe the effect of molecular properties (e.g. molecular weight and its distribution, degree of long chain branching etc) of LDPE on film crystallinity at different cooling rates of blown film extrusion. Two different grades of LDPE were selected to investigate molecular characteristics, crystallinity, and rheology. The resins were processed in a blown film extrusion pilot plant using four different cooling rates. Molecular, rheological, and crystalline properties of the resins were key parameters considered in this study. POLYM. ENG. SCI., 47:1983–1991, 2007. © 2007 Society of Plastics Engineers

A Study of the Use of Oscillatory Flow to Characterize Isotactic and Syndiotactic Poly(propylene)s

AbstractSummary: A rheological characterization of poly(propylene)s (PP) of different tacticity, monomodal and bimodal molecular distribution and long chain branching (LCB), is presented. Loss factor δ plotted as a function of the complex modulus G* allows to discriminate syndiotactic from isotactic PPs, as well as syndiotactic monomodal from bimodal samples. However, using such rheological plots is not effective to investigate the broadness of the molecular weight distribution and other rheological techniques are proposed. Isotactic and syndiotactic PPs submitted to electro beam irradiation give rise to thermorheological complexity, associated to LCB. The degree of LCB is estimated using complex viscosity results. Syndiotactic poly(propylene)s are more prone to give long branches than isotactic samples.A symptom of long chain branching is detected in irradiated syndiotactic PPs.magnified imageA symptom of long chain branching is detected in irradiated syndiotactic PPs.

An Evaluation of Dilution Rheology for the Characterization of Long Chain Branching of Polyethylenes

Abstract The purpose of this paper was to re-evaluate the novel rheological method of Crosby et al. [J. Rheol. 46 (2002) 401] to characterise long chain branching (LCB) in polyethylenes (PE) using the rheology of concentrated solutions. The feasibility of this dilution method centred on knowing the class of branched material and the molecular tube theory-based technique for the determination of two topological parameters (n, bU), where n is the number of entanglements between branch points while bU is the probability of meeting a branch point when tracing along the molecule from a random monomer against the direction of polymerisation. This paper proposes new possible approaches to calculate the two topological parameters (n, bU) set for metallocene polyethylenes (mPE), and their ambiguity discussed, as the results are dependent on the approach taken, though the previous authors mentioned only one. In addition, their approach requires an input value of LCB/1000C obtained from the standard analytical solution (SEC-V or SEC-LALLS) methods, hence, until now, without proper demonstration of the potential advantage of the dilution rheology method for LCB characterisation, as the main premise of their published article was to characterise the degree of LCB via rheological measurements without recourse to other methods of LCB characterisation.

Modeling the linear viscoelastic properties of metallocene-catalyzed high density polyethylenes with long-chain branching

The hierarchical model modified by Park et al. (2005) is applied to single-site metallocene-catalyzed high density polyethylene (mHDPE) to predict the effect of long-chain branching (LCB) on the linear viscoelastic properties. In this work we generate the distributions of molecular weight and LCB of mHDPE for the hierarchical model predictions using a Monte Carlo simulation of Costeux et al. (2002), where the simulation parameters are obtained from the average molecular weight and the degree of LCB. The parameters needed in the hierarchical model are determined from experimental data for linear polyethylenes. The model predicts the experimental data well, reveals the effect of LCB on the linear viscoelastic properties of mHDPE, and indicates the possibility of inferring branching levels from measurements of linear viscoelastic properties of mHDPEs.

Effect of long branches on the rheology of polypropylene

In order to study the rheology of long chain branched polymers, branches have been added on linear polypropylene precursors in varying amounts using reactive modification with peroxydicarbonates. The branched polypropylene samples show distinct strain hardening, something absent from the linear melt; this considerably improves the melt strength of the modified polymer. The zero shear viscosity and the elasticity measured by the relaxation spectrum also increase with the number of branches per molecule. Two models are applied to describe strain hardening of the viscosity during the course of elongation. The model parameters were found to vary systematically with the degree of branching and, therefore, their values can be used as a measure of this. Consequently, fluidity, elasticity, strain hardening, and melt strength are all related to the degree of long chain branching.

The effect of long chain branching on the processability of polypropylene in thermoforming

AbstractLinear polypropylene was modified by reaction with peroxydicarbonates in a twin screw extruder to obtain varied degrees of long chain branching. The melt strength and the elasticity of the modified polymers were found to increase with the modification. The processability in foaming and thermoforming processes improved with branching and showed an optimum, beyond which higher degrees of long chain branching appeared not to help any further. The branched PP samples showed distinct strain hardening in the elongational viscosity, which was absent from the original linear melts. Melt strength, elasticity and strain hardening increased with the increase of the number of long chain branches on the main chain. The effect of molecular weight and molecular weight distribution of the precursor on the improvement of the processability of the polymer was examined. Polym. Eng. Sci. 44:973–982, 2004. © 2004 Society of Plastics Engineers.

Shear-Induced Crystallization in Novel Long Chain Branched Polypropylenes by in Situ Rheo-SAXS and -WAXD

The characteristic properties of a new class of long chain branched isotactic polypropylene (LCB-iPP) polymers and the effects of its molecular architecture on the nature of orientation-induced crystallization precursor structures and crystallization kinetics in flow were investigated. In these polymers, long chain branching (LCB) was introduced via in situ polymerization of propylene and a diene monomer using the metallocene catalyst technology. The LCB-iPP polymers exhibited improved melt strength and mechanical properties, such as flexural modulus and tensile yield strength. As determined by gel permeation chromatography coupled with multiangle laser light-scattering (GPC−MALLS) analysis, it was noted that the LCB-iPP polymers had a significant population of highly branched chains in the high molecular weight component of the molecular weight distribution. Dynamic viscoelastic properties obtained by small-amplitude oscillatory shear technique showed that the increase in the degree of LCB caused a broadening of the melt relaxation spectrum, especially in the longest relaxation time regime. The effects of the unique molecular architecture of the LCB-iPP polymers on shear-induced crystallization development was investigated by in situ rheo-SAXS (small-angle X-ray scattering) and -WAXD (wide-angle X-ray diffraction) techniques. The results showed that upon application of a step shear (rate = 60 s-1, ts = 0.25 s, T = 140 °C), the oriented crystals fraction was substantially higher in the LCB-iPP polymers than that in the linear iPP polymer. The shear-induced crystallization rate of the LCB-iPP polymers was analyzed by an Avrami model; the value of Avrami exponent, n, ranged from 1.8 to 2.8 indicating a rod or disklike crystal growth geometry. In addition, the crystallization kinetics was enhanced by more than an order of magnitude when compared to linear iPP polymer under shear. The details of the crystalline phases determined from the WAXD data showed that, in addition to monoclinic α-form crystals, they were triclinic γ-form crystals. The contribution of γ-form crystals to the total crystalline phase was independent of the LCB level and was attributed to the regio defects of the chain. Enhancements in various mechanical properties as well as their strong crystal orientation and improved crystallization kinetics in flow, are due to the unique molecular architecture of these LCB-iPP polymers, which in turn are strongly coupled to their broadened and complex relaxation behavior.