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     

4种低密度聚乙烯树脂的链结构及其性能

选用4种商品化的具有不同熔体流动速率的低密度聚乙烯(LDPE),利用高温凝胶渗透色谱仪(HT-GPC)、碳核磁共振谱仪(¹³C NMR)、差示扫描量热仪(DSC)和流变仪研究其链结构特点及其流变性能。 按照相对分子质量的差异分成两组,D-1和Q-1,D-3和Y-1,每组的两个样品具有相近的平均相对分子质量。 ¹³C NMR的结果表明,4种LDPE都既含有短链支化又含有长链支化,且短链支化含量均高于长链支化含量;而短链支化中丁基含量最多。 连续自成核退火热分级(SSA)结果表明,树脂中均含有不同长度的可结晶的亚甲基序列,即每种树脂分子链内的短链支化分布不均匀。 探讨了相对分子质量及其分布、亚甲基序列长度及其分布、支化含量、结晶度等因素对树脂熔融行为、流变行为和薄膜力学性能的影响,发现Q-1的低相对分子质量尾端和Y-1的长链支化含量均影响熔体流动速率,平均亚甲基序列长度决定熔融峰的位置,结晶度直接影响薄膜的力学性能。 基于上述结果,建立结构与性能的关联。     

Synthesis and Rheological Investigation ofModel Symmetric 3-Arm Star Polyethylene简

A variety of linear and 3-arm star polyethylene （PE） model polymers covering a wide range of molecular weight are synthesized by the living polymerization of butadiene and the subsequent hydrogenation. Several rheological parameters of these model linear and 3-arm star PE samples are analyzed for detecting the long chain branching （LCB） structure. It is found that the analyses based on zero shear viscosity, vGP plot and flow activation energy are very sensitive to the 3-arm star PEs. The information on the presence of LCB can be obtained with these methods even for low molecular weight samples, which can not be determined by GPC-MALLS. However the information about the LCB structure can not be obtained by the rheological methods alone.     

Effect of branching and molecular weight on the viscoelastic properties of poly(butyl acrylate)

A series of poly(butyl acrylate) samples were prepared by emulsion polymerization with a range of molecular weights and degrees of chain branching. Characterization was performed with NMR (giving the fraction of branching, ranging from approximately 0 to 7%), gel permeation chromatography, viscometry, and determination of the gel fraction. The dynamic mechanical response, that is, the frequency dependence of the storage and loss moduli G′(ω) and G″(ω) was measured from 0.02 to 200 Hz. The occurrence of a significant insoluble fraction in the sample meant that full characterization of the molecular weight distribution was not possible, and so an unambiguous separation of the dependencies of the mechanical response on the degree of long‐chain branching (LCB) and short‐chain branching (SCB) and the molecular weight could not be made; however, trends dependent on the molecular weight alone were insufficient to model the results. At high frequencies, all trends in G′(ω) and G″(ω) could be ascribed to molecular weight dependencies; at low frequencies, the effects of both the molecular weight and total degree of branching could be inferred, with more highly branched samples showing lower storage and loss moduli. Although the relative amounts of SCB and LCB could not be determined, no dynamic features attributable to LCB were observed. The low‐frequency trends could be semiquantitatively fitted with reptation and retraction theory if it was assumed that an increased degree of SCB led to an increased tube size. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3335–3349, 2002     

Crystallization and melting of narrow composition distribution polyethylenes: Investigation and implications of crystal thickening

The crystal structure produced during the isothermal crystallization of polyethylene (PE) copolymers with a broad range of comonomer concentrations was determined by the measurement of the melting endotherms directly after crystallization. PE copolymers with higher concentrations of short‐chain branches (≥10 branches per 1000 total carbon atoms) exhibited strong resistance to crystal thickening during isothermal crystallization. Negligible thickening, estimated to be only about 0.1 nm in 10 min of isothermal crystallization, was observed. The side‐chain branches apparently acted as limiting points of chain incorporation into the crystals, which exhibited great resistance to the modification of their position, that is, crystal thickening. Even with long periods (up to 8 h) of isothermal storage, crystal thickening was very small or negligible, about 0.3 nm. The crystal thickness was calculated from differential scanning calorimetry data. The behavior of copolymers with lower branching concentrations and the unbranched PE homopolymer was quite different from that of the copolymers with higher branching. Polymers with low or no branching exhibited the initial crystallization of a thinner crystal population, which thickened substantially with increasing time. The thickening observed for these lower or unbranched polymers was an order of magnitude larger, that is, 1.6–2.0 nm in 10 min of isothermal crystallization. Copolymers with higher concentrations of branching had relatively short sequence lengths of ethylene units between branch points, and this resulted in strong control over the crystal thickness by the branch points and great resistance to crystal thickening, even with long times of isothermal crystallization. Copolymers with low concentrations of branching had relatively long sequence lengths of ethylene units between branch points, and this resulted in little control over the crystal thickness by the branch points and rapid crystal thickening upon isothermal crystallization. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 235–246, 2003     

Detection of long-chain branches in polyethylene via rheological measurements

The detection of long-chain branches(LCB) in polyethylene is of considerable importance as the processing properties of polyethylene are strongly affected by even a small amount of LCB. While the conventional characterization techniques such as GPC-MALS and13 C NMR fail or take very long time to detect low content of LCB, we turn to the rheological method, which is more sensitive to LCB. In our study, we performed oscillatory shear test, creep test and stress relaxation test on two series of metallocene linear low density polyethylene(LLDPE), revealing that the resins with LCB show higher zero-shear-rate viscosity, retarded relaxation and higher flow activation energy than those without or with less LCB. The resins with LCB showed shear thinning at very low shear rate and their zero-shear-rate viscosities were obtained via creep test. The content of LCB was quantitatively estimated from the flow activation energy. In addition, the modulus-time curves during stress relaxation of melt of the different resins obeyed the power law. The exponent of the resins with more LCB was 0.7, different from that of the resins with less LCB, around 1.7.     

Modeling of polyethylene and poly (L-lactide) polymer blends and diblock copolymer: chain length and volume fraction effects on structural arrangement

Dissipative particle dynamics (DPD), a mesoscopic simulation approach, has been used to investigate the chain length effect on the structural property of the immiscible polyethylene (PE)/poly(L-lactide) (PLLA) polymer in a polymer blend and in a system with their diblock copolymer. In this work, the interaction parameter in DPD simulation, related to the Flory-Huggins interaction parameter chi, is estimated by the calculation of mixing energy for each pair of components in molecular dynamics simulation. The immiscibility property of PE and PLLA polymers induces the phase separation and exhibits different architectures at different volume fractions. In order to observe the structural property, the radius of gyration is used to observe the detailed arrangement of the polymer chains. It shows that the structure arrangement of a polymer chain is dependent on the phase structure and has a significantly different structural arrangement character for the very short chains in the homopolymer and copolymers. The chain length effect on the degree of stretching or extension of polymers has also been observed. As the chain length increases, the chain exhibits more stretching behavior at lamellae, perforated lamellae, and cylindrical configurations, whereas the chain exhibits a similar degree of stretching or extension at the cluster configuration.     

Determination of the crystallinity of polyethylene/α‐olefin copolymers by thermal analysis: Relationship of the heat of fusion of 100% polyethylene crystal and the density

The heat of fusion measured with differential scanning calorimetry (DSC) is typically divided by a constant value of the heat of fusion of 100% polyethylene (PE) crystal (ΔH) for the estimation of the fraction crystallinity of PE copolymers, regardless of the density [i.e., the short‐chain branching (SCB) concentration]. In this work, values of ΔH of about 288 J/g were determined with a combined DSC and X‐ray diffraction (XRD) method for a series of PE copolymers containing SCB from 0 to 50 Br/1000 C (density = 0.965–0.865 g/cc). There was no systematic change in ΔH observed across this density range. This result supports the suitability of determining the fraction crystallinity of PE of any density by the simple division of the observed heat of fusion determined by DSC by a constant value of ΔH. This DSC method yielded values of PE crystallinity in good agreement with corresponding values determined by XRD for a series of PE copolymers. The determination of ΔH involved a small precision error for higher density (lower SCB) PEs, but the precision error increased for lower density (i.e., higher SCB) PEs. This was due to the difficulty in measuring the heat of fusion for lower density PEs, which exhibited low values of the heat of fusion and melted only slightly above room temperature, and due to the difficulty of measuring lower values of crystallinity by XRD. The crystal thickness measured by small‐angle X‐ray scattering for this series of PE copolymers decreased exponentially from about 280 to 6 Å. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1637–1643, 2002     

Study of Multi-Site Nature of Supported Ziegler-Natta Catalysts in Ethylene-Hexene-1 Copolymerization

Summary: Heterogeneity of active centers (AC) of titanium-magnesium catalysts (TMC) and vanadium-magnesium catalyst (VMC) in ethylene-hexene-1 copolymerization has been studied on the base of data of polymer molecular weight distribution (MWD) deconvolution technique and copolymer fractionation onto narrow fractions. It was found that 3 and 4 Flory components (groups of active centers) are required to describe experimental MWD curves of copolymers produced over TMC with different Ti content. In the case of VMC MWD of homopolymer and copolymer are characterized by set of 5 Flory components (5 groups of AC). Different character of inter-relationship between MW and short chain branching (SCB) was found for ethylene-hexene-1 copolymers produced over different catalysts: heterogeneous type in the case of TMC and more uniform for copolymer prepared over VMC. The content of Ti affects on the slope of that profile in copolymers produced over TMC. The results indicated that TMC and VMC are different greatly on the heterogeneity of active centers to the formation of polymers with different molecular weights and to formation of copolymers with different inter-relationship between MW and short chain branching. TMC produces polymers with more narrow MWD but it contains highly heterogeneous centers regarding comonomer reactivity ratios. VMC produces polymers with broad and bimodal MWD but it contains more homogeneous centers regarding comonomer reactivity ratios.     

CRYSTAF Analysis of Polyethylene Synthesized with Phillips Catalyst

Crystallization analysis fractionation (CRYSTAF) was used for the first time to investigate the solution crystallization behavior of ethylene homopolymers and copolymers made with Phillips CrO_x/SiO₂ catalyst. Interestingly, the crystallization peak temperatures (T_p) of copolymers of ethylene and cyclopentene increased with increasing cyclopentene molar fraction in the copolymer. Comparing two factors (short chain branches (SCBs) and cyclopentene incorporation), decreasing SCB frequency is proposed as the dominant factor to explain the increase of crystallization peak temperatures with increasing cyclopentene incorporation. In addition, SCB frequency and molecular weight might be the two significant factors determining the crystallization temperature of polyethylene made with Phillips CrO_x/SiO₂ catalyst with different cocatalysts (triethylaluminum and diethylaluminum ethoxide).     

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     

Solution properties and chain conformation characteristics of cellulose tricarbanilate

Fractions of two cellulose tricarbanilate samples were characterized by light-scattering (weight-average molecular weight, second virial coefficient, mean-square radius of gyration), gel permeation chromatography (polydispersity index), and viscometry (intrinsic viscosity) in tetrahydrofuran and acetone. The intrinsic viscosity data were analyzed in terms of the theory developed for the continuous wormlike cylinder model, and the chain parameters (Kuhn statistical segment length λ^?1, chain diameter d, and shift factor M_L) were evaluated. The molecular-weight dependence of the mean-square radius of gyration in tetrahydrofuran was calculated for the Kratky—Porod chain model and compared with the experimental results. Data on the intrinsic viscosity and radii of gyration for other solvents at temperatures from 0 to 100°C were analyzed in the same way, and the effects of solvent and temperature on the statistical segment length were evaluated. Polymer—solvent interaction parameters were estimated from the second virial coefficients.     

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.     

Implications of LDPE Branching and Mw on Thermal and Mechanical Properties of PP/LDPE Blends

Summary: The influences of short chain branching (SCB) and molecular (M_w) weight of low density polyethylene (LDPE) on the solid state properties of polypropylene (PP)-LDPE blends were investigated by mechanical and thermal techniques. DSC analysis of all blends exhibit a double melting peak at all compositions studied thus suggesting that both PP and LDPE crystals exist separately in the solid state. It was found that the SCB and Mw of LDPE influenced the modulus and ultimate tensile strength of the blends. However, elongation at break seems to be independent of the molecular characteristics of the pure homopolymer especially at PP blend composition greater than 50%. LDPE with high SCB showed broader melting peaks. Addition of a small amount of a low Mw LDPE (10%) resulted in a higher elongation at break than a high Mw LDPE. There is likely a correlation between the presence of a new peak in the thermograms of PP-rich blends and the observed poor elongation at break.     

A Conditional Monte Carlo Method to Determine the Architectures of Metallocene Catalyzed Polyethylene

Two polymer molecules of the same length (n) and the same number of branch points (N) can have different properties, since they may possess distinct architectures. In this paper we present a conditional Monte Carlo algorithm for the virtual synthesis of metallocene‐catalyzed polyethylene (PE) in a continuous stirred tank reactor (CSTR). The condition for the Monte Carlo method consists of a fixed chain length distribution (CLD) and a degree of branching distribution (DBD). These distributions are calculated with a Galerkin finite element method. The synthesis method is a recursive algorithm that subsequently creates insertions of sub‐structures containing numbers of branch points according to a certain probability density function. This provides an adjacency matrix describing the connectivity between the branch points, while separately a vector containing the length of segments between branch points and terminal segments is generated. Characterization of the architectures proceeds by rheological features, seniorities and priorities, and molecular properties like the radius of gyration. Comparing the radii of gyration of metallocene polyethylene and low density PE (ldPE) shows the former to possess a more comb‐like structure on average. This is confirmed by the rheological characterization. The found bivariate seniority/priority distribution agrees well to the results of an analytical study of the same chemical system.

Constituting elements of the algorithm.     

One‐step synthesis of hyperbranched polyethylene macroinitiator and its block copolymers with methyl methacrylate or styrene via ATRP

Block copolymers of hyperbranched polyethylene (PE) and linear polystyrene (PS) or poly(methyl methacrylate) (PMMA) were synthesized via atom transfer radical polymerization (ATRP) with hyperbranched PE macroinitiators. The PE macroinitiators were synthesized through a “living” polymerization of ethylene catalyzed with a Pd‐diimine catalyst and end‐capped with 4‐chloromethyl styrene as a chain quenching agent in one step. The macroinitiator and block copolymer samples were characterized by gel permeation chromatography, ¹H and ¹³C NMR, and differential scanning calorimetry. The hyperbranched PE chains had narrow molecular weight distribution and contained a single terminal benzyl chloride per chain. Both hyperbranched PE and linear PS or PMMA blocks had well‐controlled molecular weights. Slow initiation was observed in ATRP because of steric effect of hyperbranched structures, resulting in slightly broad polydispersity index in the block copolymers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3024–3032, 2010     

Determination of polymer branching with gel-permeation chromatography. II. Experimental results for polyethylene

The recently developed methods of characterizing branching in polymers from gelpermeation chromatography and intrinsic viscosity data are verified experimentally. An iterative computer program was written to calculate the degree of branching in whole polymers. Long-chain branching in several low-density polyethylene samples was determined by both the fraction and whole polymer methods. The two methods gave consistent ranking of the branching in the samples although absolute branching indices differed. Effects of various experimental errors and the particular model used for branching were investigated. For polyethylene, the data show that the effect of branching on intrinsic viscosity is best described by the relation 〈g₃〉_W^1/2 = [η]_br/[η]₁ where 〈g₃〉_w is the weight-average ratio of mean-square molecular radii of gyration of linear and trifunctionally branched polymers of the same weight-average molecular weight.     

Synthesis and solution properties of star‐shaped poly(tert‐butyl acrylate)

A series of star polymers consisting of poly(tert‐butyl acrylate) arms and an ethyleneglycol dimethacrylate (EGDMA) microgel core were synthesized using anionic polymerization. The effect of various parameters (precursor length, ratio [[EGDMA]/[Initiator], reaction time, and overall concentrations) on the average number of arms was investigated. Molecular weights were determined using GPC coupled with an online viscometer and MALLS. The exponents for the relation between intrinsic viscosity or radius of gyration and molecular weight, respectively, are extremely low, indicating that the dimensions of the star polymers only slightly increase with the number of arms. After a certain number of arms is reached the intrinsic viscosity even decreases with molecular weight. Computer simulations for star polymers were carried out where the radius of gyration was calculated as a function of the number of arms. The results are in good agreement with the experimental data.     

Simulation of gel permeation chromatography measurement for long chain branched metallocene polyethylene

The research about the polymerization reaction mechanism of long chain branched polymer provides a method to simulate the generation of LCB mPE (long chain branched metallocene polyethylene).^[1-3] In this work, after simulating the generation of one million LCB mPE molecules, we calculate the sizes (i.e. radii of gyration) of molecules in good solvents to obtain the molecular size distributions. Then we simulate the fractionation in GPC (gel permeation chromatography) measurement and the different GPC detector responses to obtain simulated GPC MWDs (molecular weight distributions). The simulated MWDs are compared to the real GPC results provided by the Dow Chemical Company.     

高度支化共聚物的均方回转半径和支化度的关系

对于聚合物的均方回转半径和支化度的关系, 过去鲜有定量研究, 这是由于具有不同支化度的系列同种聚合物样品较难合成之故. 1982年, Kricheldorf等[1]报道了AB2和AB型单体的共缩聚反应, 这种反应可以方便地通过调节AB2和AB型单体的比例来控制产物的支化度.