Long-chain Branching Research Articles

Development of a model for granule-bound starch synthase I activity using free-energy calculations

Starch is a branched polymer of glucose with two components, both of which have (1 → 4)-α linear links and (1 → 6)-α branch points: amylopectin, of high molecular weight with many short branches, and amylose, of lower molecular weight and only a few long-chain branches. Granule-bound starch synthase I (GBSSI) is one of the main enzymes controlling amylose synthesis and chain-length distribution. As production of different GBSSI mutants is time-consuming and laborious, molecular dynamics (MD) simulations are used here to predict the binding of different GBSSI mutants to a representative amylose fragment. The simulations were atomistic, with explicit solvent and docking, a method successfully used to understand the binding of wild-type GBSSI to amylose fragments. The binding of GBSSI to G5 (a pentasaccharide amylose fragment) is combined with free-energy calculations employing a thermodynamic integration method to predict the effects of mutations on enzyme activity. Ten GBSSI mutants with different enzyme activities were analyzed to find the structural and energy changes among different single amino-acid mutants and their possible relationship to starch characteristics. Comparing the structural changes and the relative binding free energy of G5 to the wild type GBSSI and GBSSI mutants, it was found that mutants with negative binding energy (lower than −2.0 kcal/mol) are more likely to have higher enzyme activity and amylose content compared to the wild type. This theoretical paper used simulations and robust free energy calculations to interpret in planta data with potential predictions as to what mutants might be generated to give desired properties. This study can be used to help develop grains with improved functional properties.

Eliminating the thermal degradation of polylactic acid by the modification of a macromolecular epoxy‐type chain extender

AbstractA novel macromolecular epoxy chain extender was synthesized and used to modify the PLA resin for developing conventional melt extrusion technology. Fourier‐transform infrared spectroscopy (FTIR), gel permeation chromatography (GPC), and 1H nuclear magnetic resonance (1H NMR) characterized the successful synthesis. For the first time, the molecular weight plays a key role in preventing thermal degradation and chain extension were discussed experimentally. Macromolecular chain extender showed superior advantages in that the chain extender with higher molecular weight was easier to get the long chain branched (LCB) structure in the modification of PLA. The characterization by rotational rheometer, GPC, melt index, chemical titration, and differential scanning calorimeter (DSC), results demonstrate that the macromolecular epoxy chain extender could decrease the concentration of terminal carboxyl groups and increase with only 0.5% dosage. At a concentration ≥2%, there were a large number of long chain branched structures in the chain extension system for modified PLA. It showed better melt strength and would influence the crystallinity of PLA which would significantly improve the processability of PLA, especially in high‐temperature extrusion, blow molding, spinning, and other processing technologies and applications.

Theoretical Insights into Midchain Radicals and Branching Characteristics in Solution Copolymerization of Ethylene and Vinyl Acetate.

The kinetics of intermolecular chain transfer to polymer (CTP) and chain transfer to monomer (CTM), as well as backbiting in solution copolymerization of ethylene and vinyl acetate (VAc), are calculated by density functional theory. An intrinsic rate coefficient for each reaction type, whose Arrhenius parameters are expressed as functions of unreacted monomer composition, is extracted from calculated elementary reactions, and hence it applies to a wide range of fragment compositions of EVA. Backbiting controls the generation of midchain radicals (MCRs) on the backbone, and its rate maximizes at a medium fraction of VAc in the unreacted monomers. CTP plays an insignificant role in MCR generation even at high conversion rates due to its low pre-exponential factor. The concentration of MCRs is quantified and is close to that of ECRs at high conversions and high fractions of VAc in monomers. Additionally, branching characteristics are explored; concentrations of short-chain branching (SCB) and long-chain branching (LCB) are about 0.7-2.5 and 0.1-0.4%, respectively, and drop with VAc fraction rapidly. The role of the migration of MCRs is highlighted, which transforms about 10% of SCB points into LCB points. Disagreeing with insights from laboratory experiments, it is the migration, rather than CTP, which increases the LCB concentration at high conversions.

Ammoniated Zinc Oxide Nanoparticles for Preparing High-Melt-Performance Poly(lactic acid) Bearing Dual Hybrid Long-Branched Chains by Degrading and Restructuring Chains

Ammoniated Zinc Oxide Nanoparticles for Preparing High-Melt-Performance Poly(lactic acid) Bearing Dual Hybrid Long-Branched Chains by Degrading and Restructuring Chains

Molecular and thermo-mechanical assessment of long-chain branched polypropylene: Effect of irradiation dose, multifunctional monomer content and molecular weight

The influence of irradiation dose, trimetylolpropane trimethacrylate (TMPTMA) amount, as a three-functional monomer, and polypropylene (PP) molecular weight on the performance of irradiation technique to create long chain branched PP (LCB-PP) was investigated through molecular, rheological and thermo-mechanical characterizations. With increasing doses or amount of TMPTMA, a reduction in molar mass and an increment in long chain branches (LCBs) number as well as a change in the topology of LCBs from star to tree-like were found. PP grade with low molar mass had more branching ability and its LCBs topology was different. Irradiation declined the glass transition and melting temperature of PP, while it did not affect its crystallization temperature and its degree. Two opposing effects of molar mass reduction and LCBs formation controlled the tensile strength and toughness of irradiated PP samples.

Branched thermotropic liquid crystal polymer with favourable processability and dielectric properties

Thermotropic Liquid Crystal Polymer (TLCP) has emerged as a promising material for 5G mm-wave antennas due to its low dielectric constant and loss at high frequencies. However, its low melt viscosity, inadequate melt elasticity, and rigid rod-like macromolecular chain with easy orientation pose a significant challenge in the production of isotropic films. In this study, in order to improve the melt viscosity and melt elasticity of TLCP, a multifunctional epoxide-based branching agent (ADR 4468) was applied to produce branched TLCP. The impact of the branched structure on linear viscoelastic, thermal, mechanical, and dielectric performance was investigated. Results from linear rheological characterizations indicated that complex viscosity and storage modulus of modified TLCP samples were significantly enhanced, indicating the presence of long-chain branches. The mechanical performance of modified samples was scarcely affected by the concentration of ADR 4468, with a tensile strength of approximately 245 MPa, and Charpy notched impact strength of approximately 30 KJ/m2. However, with an increase in ADR 4468 content, the dielectric constant increased (from 3.25 to 3.30 at 10 GHz) as well as the dielectric loss (from 1.36 × 10−3 to 2.14 × 10−3 at 10 GHz). Based on the overall performance, the optimal content of ADR 4468 was found to be about 2–3 wt%. These findings offer insights into the potential applications of modified TLCPs as substrates for 5G mm-wave antennas.

Insights into the effect of different macromolecular architectures on the charring ability of polyethylene

The induction period preceding the ignition is a fundamental stage in controlling the protection of polymeric materials from fire. In fact, at this stage, the formation of a non-pyrolyzable carbonaceous layer (char) onto the material surface could prevent the development of a sustained flame, hence delaying or preventing polymer burning. In this work, the charring ability of four samples of high- and low-density polyethylene was evaluated in different scenarios, namely isothermal oxidative conditions and cone calorimetry tests at different heat fluxes, aiming at assessing the possible influence of the polymer macromolecular architecture on their charring ability. First, the selected polymers were characterized from a thermal and rheological point of view; the obtained results allowed for disclosing the different microstructure of the materials, in terms of molecular weight and possible presence of short- or long-chain branching. Then, isothermal thermogravimetric analyses and cone calorimetry tests were performed, demonstrating a different charring ability of the investigated polyethylenes. Finally, the observed behaviours were correlated to the different chemical structure and to the specific macromolecular architecture of the polymers, allowing a systematic evaluation of the relationship between the molecular weight or the presence of branched structures and the mechanism and rate of char formation.

Imperative role of SBS molecular structure on the performance properties of modified binders and asphalt mixes

ABSTRACT The current study evaluates the impact of SBS molecular structure (L-SBS, B-SBS, HV-SBS, and DB-SB) and concentration on asphalt mix performance. Polymers were characterized using GPC, FTIR, melt rheology, and DSC analysis. GPC analysis indicates that BSBS has the highest molecular weight, while DB-SB has the lowest. FT-IR studies show differences in vinyl content among the four polymers. Asphalt mixture study resonated binder study where B-SBS polymer outperformed their counterparts. Results showed that compared to widely used L-SBS polymer, B-SBS copolymer generates ≈ 33 %, 26 % and 18 % more fatigue resistance, rutting resistance and stiffness behaviour, respectively, at a polymer content of 4.5 wt.%. The combined effect of higher molecular weight, triblock structure and the long-chain branching in B-SBS copolymer contributes to the discussed outcome which facilitates its utilization for high-stressed pavement sections at upper and intermediate service temperatures. However, L-SBS and HV-SBS polymers depict almost similar mixture performance due to their alike molecular structure. Moreover, the presence of a di-block structure and lower molecular weight results in inferior performance for mixes prepared with DB-SB polymer. The results clearly signify the dominance of polymer molecular structure in identifying the mixes’ performance properties at respective polymer content.

Influence of a Multiple Epoxy Chain Extender on the Rheological Behavior, Crystallization, and Mechanical Properties of Polyglycolic Acid

This study investigated the impact of a multiple epoxy chain extender (ADR) on the rheological behavior, crystallization, and mechanical properties of polyglycolic acid (PGA). Tests of the torque and melt mass flow rate and dynamic rheological analysis were conducted to study the rheological behavior of PGA modified with ADR. The rheological results of the modified PGA showed a significantly increased viscosity and storage modulus with an increase in the ADR amount, which could be attributed to the chain extension/branching reactions between PGA and ADR. It was proved that ADR could be used as an efficient chain extender for tailoring the rheological performance of PGA. The Han plot of the modified PGA showed a transition of viscous behavior to elastic behavior, while the ADR content was increased from 0 to 0.9 phr. The formation of long-chain branches (LCBs) was confirmed via the Cole–Cole plot and weighted relaxation spectrum, wherein the LCBs substantially changed the rheological behavior of the modified PGA. The vGP plots predicted a star-type topological structure for the LCBs. The results of non-isothermal crystallization kinetics suggested that the crystallization of the modified PGA was predominantly homogeneous nucleation and three-dimensional growth. The crystallinity decreased slightly with the increase in the ADR amount. Compared to neat PGA, the modified PGA samples exhibited better tensile and flexural performances.

The method of moments used in polymerization reaction engineering for 70 years: An overview, tutorial, and minilibrary

AbstractIn the last seven decades, the method of moments (MoM) has become an invaluable tool in the field of polymerization reaction engineering, due to the simplicity of translating a complex set of population balance equations (PBE) into a system with a limited number of equations. In this work, we offer an overview of the MoM, describing the derivation of the moment equations in a basic kinetic mechanism. Some tools and strategies for the derivation of the moment equations are reviewed and explained in detail, such as the binomial theorem, the method of series expansion and pattern identification (SEPI), extensively used by the community, and a graphical approach of summation inversion. The treatment for multivariate distributions is also exposed, taking advantage of the complete and partial moment techniques. The derivation of the MoM contribution by kinetic mechanisms beyond the basic ones or involving special difficulties, such as depropagation, long chain branching (LCB), random chain scission, LCB and β‐scission, short chain branching (SCB) and scission, internal double bond (IDB) (polymerization), termination by combination, reversible deactivation radical polymerization (RDRP), and intermolecular transesterification reactions (ITRs), are explained in a tutorial way. Additionally, the fundamentals of the MoM in copolymerization and the application of the pseudo‐homopolymerization approach are briefly described. An introduction of the MoM to emulsion polymerization is also presented. Finally, some advanced applications of MoM in recent works are exposed: MoM models with chain‐length dependent or diffusion‐controlled termination, and the extension of the MoM for the prediction of the molecular weight distribution (MWD).

Preparation of clay-supported sodium benzoate and its effect on the rheology, crystallization and foaming of long chain branched polypropylene

The foaming of PP has encountered challenges because of its low melt strength and semi-crystalline characteristics. Introducing long chain branching (LCB) onto the PP backbone and the addition of particles as cell nucleating agent are the commonly used methods to improve the cell structure of PP foams. In this paper, clay-supported sodium benzoate (NaB-OMMT) was prepared from Na-montmorillonite (Na-MMT) via the partial ion exchange reaction with surfactant and subsequent reaction with benzoic acid. The as prepared NaB-OMMTs were then applied to prepare LCBPP/NaB-OMMT nanocomposites and their foams. The dispersion state of clay, crystallization behaviors and rheological properties of the nanocomposites, as well as the cell structure and compression properties of the foams were investigated. The results show that clay layers are mostly exfoliated in the nanocomposites with low NaB-OMMT content, while intercalated layers dominant with the content reaches 2% or higher. The melting temperature of the nanocomposites decreases and the crystallinity increases, while the spherulite size decreases compared to LCBPP. The melt viscosity and elasticity of nanocomposites increase significantly when the content of NaB-OMMT reaches 2% or higher. LCBPP/NaB-OMMT nanocomposites foams exhibit higher cell density, smaller cell size and its standard deviation. Therein, the foam with 1% of NaB-OMMT shows the maximum cell density and the minimum cell size. It is concluded that the cell structure of the foam is highly dependent on the content, dispersion state and structure of the cell nucleating agent. When NaB is supported on well dispersed and exfoliated clay layers, the cell nucleation efficiency is significantly enhanced. The compression properties of the foams depend on their cell structures and exhibit the similar variation trend with the latter with the content of NaB-OMMT increasing.

Fracture in elongational flow of two low-density polyethylene melts

Samples of two commercial low-density polyethylene melts were investigated with respect to their fracture behavior in controlled uniaxial extensional flow at constant strain rate in a filament stretching rheometer. In order to assess the possible influence of grain boundaries on fracture, the samples were prepared by three different types of pre-treatment: by compression molding of (1) virgin pellets used as received, (2) pellets homogenized in a twin-screw extruder, and (3) pellets that were milled into powder by cryogenic grinding under liquid nitrogen. The elongational stress growth data were analyzed by the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model developed by Wagner et al. (Rheol. Acta 61, 281-298 (2022)) for long-chain branched (LCB) polymer melts. The EHMMSF model quantifies the elongational stress growth including the maximum in the elongational viscosity of LDPE melts based solely on the linear-viscoelastic relaxation spectrum and two nonlinear material parameters, the dilution modulus GD and a characteristic stretch parameter {overline{lambda}}_m. Within experimental accuracy, model predictions are in excellent agreement with the elongational stress growth data of the two LDPE melts, independent of the preparation method used. At sufficiently high strain rates, the fracture of the polymer filaments was observed and is in general accordance with the entropic fracture criterion implemented in the EHMMSF model. High-speed videography reveals that fracture is preceded by parabolic crack opening, which is characteristic for elastic fracture and which has been observed earlier in filament stretching of monodisperse polystyrene solutions. Here, for the first time, we demonstrate the appearance of a parabolic crack opening in the fracture process of polydisperse long-chain branched polyethylene melts.

CRYSTAF, DSC and SAXS Study of the Co-Crystallization, Phase Separation and Lamellar Packing of the Blends with Different Polyethylenes.

The crystallization of polyethylene (PE) blends is a highly complex process, owing to the significant differences in crystallizability of the various PE components and the varying PE sequence distributions resulting from short- or long-chain branching. In this study, we examined both the resins and their blends through crystallization analysis fractionation (CRYSTAF) to understand the PE sequence distribution and differential scanning calorimetry (DSC) to investigate the non-isothermal crystallization behavior of the bulk materials. Small-angle X-ray scattering (SAXS) was utilized to study the crystal packing structure. The results showed that the PE molecules in the blends crystallize at different rates during cooling, resulting in a complicated crystallization behavior characterized by nucleation, co-crystallization, and fractionation. We compared these behaviors to those of reference immiscible blends and found that the extent of the differences is related to the disparity in crystallizability between components. Furthermore, the lamellar packing of the blends is closely associated with their crystallization behaviors, and the crystalline structure varies significantly depending on the components' compositions. Specifically, the lamellar packing of the HDPE/LLDPE and HDPE/LDPE blends is similar to that of the HDPE component owing to its strong crystallizability, while the lamellar packing of the LLDPE/LDPE blend is approximately an average of the two neat components.

Microcellular extrusion foaming of long-chain branched polyamide 6 composites

In this study, by introducing the long-chain branched (LCB) structure into the polyamide 6 (PA6) matrix, low-density microcellular PA6 composite foams with favorable cell morphology were prepared using supercritical CO2 extrusion foaming. PA6/talc composites with varying degrees of LCB were prepared using a twin-screw extruder. Rheological tests showed that the LCB-4.0 T sample with an ultra-high LCB degree had more apparent strain-hardening behavior and higher instantaneous elongational viscosity of 4.40 × 108 Pa·s. Isothermal crystallization tests revealed that LCB-4.0 T had lower crystallization rate. The effect of the degree of LCB on the gas solubility of CO2 in the PA6 composites was also examined. The foamability of the PA6/talc composites was verified via continuous extrusion foaming. High-performance PA6 composite foams with an average cell size as low as 66.7 µm, cell density as high as 2.53 × 107 cells/cm3, expansion ratio as high as 11.8, and foaming temperature window as wide as 16 °C were successfully obtained.

Rheological and Mechanical Study of Comb-Branched Polyolefin Elastomers Containing Macromer Residues

Comb-polyolefin elastomers (CPOEs) with crystalline long-chain branches (LCBes) demonstrate superior mechanical properties and processability. However, fully understanding the effect of LCBes on their material performance remains a huge challenge due to the residue of unreacted polyethylene macromers (PE-Ms). Here, we report a method of blending CPOEs with PE-Ms to study the structure–activity relationship of CPOEs via extrapolation. CPOE samples with different numbers of LCBes (q) between 0.0 and 9.9 and PE-Ms with an Mw value similar to the LCBes were prepared and studied. Blending CPOEs with 20–40 wt % of PE-Ms increased the melt fluidity and reduced the zero-shear viscosity (η0) value from 4590 Pa·s to 980 Pa·s without causing phase separation. These CPOEs exhibit dynamic responses with a similar temperature dependence where the time shift factors could be fitted by the same Williams–Landel–Ferry parameters with C1 at 4.88 and C2 at 443 K. For CPOEs with LCBes, as q increased from 1.1 to 9.9, the number of entanglements between the graft points (Zg) decreased from 11.78 to 0.93, and the chain conformation changed from sparse comb (SC) to dense comb (DC), respectively. The maximum η0 value of CPOEs occurs at the turning point of SC and DC, where Zg is equal to the entanglement number of the branched chain −Zbc of 4.72. Our study distinguished the different effects between the grafted and free PE-Ms on the CPOEs, enabling an in-depth understanding of macromolecular engineering in polymer and facilitating the future development of higher-performance CPOEs or other grafted polymers.

Modeling elongational viscosity and brittle fracture of 10 polystyrene Pom-Poms by the hierarchical molecular stress function model

A Pom-Pom polymer with qa side chains of molecular weight Mw,a at both ends of a backbone chain of molecular weight Mw,b is the simplest branched polymer topology. Ten nearly monodisperse polystyrene Pom-Pom systems synthesized via an optimized anionic polymerization and a grafting-onto method with Mw,b of 100 to 400 kg/mol, Mw,a of 9 to 50 kg/mol, and qa between 9 and 22 are considered. We analyze the elongational rheology of the Pom-Poms by use of the hierarchical multi-mode molecular stress function (HMMSF) model, which has been shown to predict the elongational viscosity of linear and long-chain branched (LCB) polymer melts based exclusively on the linear-viscoelastic characterization and a single material parameter, the so-called dilution modulus GD. For the Pom-Poms considered here, we show that GD can be identified with the plateau modulus {G}_{N}^{0}={G}_{D}, and the modeling of the elongational viscosity of the Pom-Poms does therefore not require any fitting parameter but is fully determined by the linear-viscoelastic characterization of the melts. Due to the high strain hardening of the Pom-Poms, brittle fracture is observed at higher strains and strain rates, which is well described by the entropic fracture criterion.Graphical abstract

Tandem coordinative chain transfer polymerization for long chain branched Polyethylene: The role of chain displacement

The controlled introduction of long chain branches (LCBs) in the commonly linear structure of polyolefins has been frequently pursued by researchers to improve their melt processability. To account for that, we introduce a new tandem dual catalytic system for the formation of LCB in ethylene polymerization. Coordinative chain transfer polymerization in the first step produces Al-alkyls via frequent transfer of growing polymer chains from the single-site α-diimine nickel polymerization catalyst to AlEt2Cl chain transfer agent (CTA). Next, the displacement catalyst, Ni(acac)2, converts the dormant alkyl chains into macromers through a β-hydride elimination and retrieves the Al-based CTA. Due to the high comonomer affinity of the polymerization catalyst, the released macromers are incorporated in growing polymer chains. By repeating this reaction cycles, a branch-on-branch structure is formed. Interestingly, a separate cocatalyst is not required, as AlEt2Cl serves as both the cocatalyst and the CTA for the CCTP system. This reaction scheme employs the “nickel-effect” mechanism for the formation of LCB in coordinative polymerization for the first time. The efficiency of the proposed mechanism in the formation of LCBs is confirmed by comprehensive rheological studies and NMR spectroscopy. Moreover, density functional theory (DFT) simulations rationalize the formation of LCBs through the proposed Ni-based displacement reaction.

Molecular structure and linear-non linear rheology relation of rice starch during milky, dough, and mature stages

Immature rice has potential to be used as healthy food. The relation between molecular structure and rheological properties was investigated. The lamellar repeating distance (8.42–8.63 nm) and crystalline thickness (4.60–4.72 nm) were not different among stages indicating a complete lamellar structure even at early stage. The relative crystallinity was higher in dough (39.62 %) than milky (36.69 %) and mature starch (35.22 %) caused by molecular structure, amylose, and amylose-lipid complex. The short amylopectin branched chains (A and B1) in dough starch were easily entangled resulted in higher Payne effect and elastic dominant. Dough starch paste exhibited higher G′Max (738 Pa) than milky (685 Pa) and mature (645 Pa) starch. In a non-linear viscoelastic regime, small strain hardening was found in milky and dough starch. Mature starch showed the highest plasticity and shear thinning at high-shear strains as the long-branched chains (B3) microstructure was disrupted, disentangled, followed by chain orientation along shear.

Construction of fully biodegradable poly(L-lactic acid)/poly(D-lactic acid)-poly(lactide-co-caprolactone) block polymer films: Viscoelasticity, processability and flexibility

Development of biodegradable polymer films is essential for sustainable energy conservation and ecological protection. In this work, to improve the processability and toughness of poly(lactic acid) (PLA) films, poly(lactide-co-caprolactone) (PLCL) segments were introduced into poly(L-lactic acid) (PLLA)/poly(D-lactic acid) (PDLA) chains via chain branching reactions during reactive processing, and fully biodegradable/flexible PLLA/D-PLCL block polymer with long-chain branches and stereocomplex (SC) crystalline structure was prepared. Compared with neat PLLA, PLLA/D-PLCL exhibited much higher complex viscosity/storage modulus, lower tanδ values in terminal region and obvious strain-hardening behavior. Through biaxial drawing, PLLA/D-PLCL films were prepared, which showed improved uniformity and non-preferred orientation. With increasing draw ratio, the total crystallinity (Xc) and Xc for SC crystal both increased. By introduction of PDLA, the two phases of PLLA and PLCL penetrated and entangled with each other, and the phase structure transformed from “sea-island” structure to “co-continuous network” structure, which was beneficial for exerting the toughening effect of flexible PLCL molecules on PLA matrix. The tensile strength and elongation at break of PLLA/D-PLCL films increased from 51.87 MPa and 28.22 % of neat PLLA film to 70.82 MPa and 148.28 %. This work provided a new strategy for developing fully biodegradable polymer films with high performance.

Rigid Triptycene-Based Di- and Trinuclear Salicylaldiminato Nickel Cooperative Polymerization Catalysts

A multimetallic structure with a rigid linker can poise more than one catalytically active site in close proximity to control their reaction pathways in ethylene (co)polymerization by intermetallic cooperativity. This elegant concept was mainly limited to bimetallic systems. We report the synthesis of a series of mono-, bi-, and trinuclear salicylaldiminato Ni(II) catalysts based on a triptycene backbone. In ethylene (co)polymerization, the bimetallic nickel catalyst not only showed higher activity than the mononickel catalyst but also achieved an enhanced incorporation rate of α-olefin and the polar amino olefin, while the trimetallic nickel catalysts were thermally robust up to 100 °C and achieved a unique long-chain branching level up to an 81% mole ratio of all. Trinuclear nickel catalysts were found to be very less active for ethylene copolymerization with 1-hexene due to the increased steric hindrance. Although the catalytic result is worse than expected, especially for trinickel complexes, this work is still meaningful for the development of multinuclear catalysts that can mediate important catalytic reactions with enhanced efficiency and cooperativity.