Molecular weight distribution of emulsion-polymerized polyethylene

Emulsion polymerizations of ethylene were run using potassium persulfate as the initiator and either an anionic or a cationic surfactant, usually at five times the critical micellar concentration. The molecular weight distributions had at least two major peaks. The broadly distributed lower molecular weight component is formed in the early stages of polymerization. The higher molecular weight component has a narrow distribution characteristic of termination by the combination of chain radicals. The weight-average molecular weight of this component was about 400,000 when the surfactant was sodium laurate and 33,600,000 when the surfactant was dodecyl amine hydrochloride. © 1992 John Wiley & Sons, Inc.     

Unimodal molecular weight distribution of commercial polymers from viscoelastic data

This article presents a method that provides the molecular weight distribution (MWD) of polymeric material from rheological data. The technique has been developed to deal with linear polymers with a log‐normal molecular weight distribution. The rheological data must include the shear storage modulus, G′(ω), and the shear loss modulus, G″ (ω), ranging from the terminal zone to the rubberlike zone. It was not necessary to achieve the relaxation spectrums via the extremely unstable problem of inverting integral equations. The method has been tested with different polymers (polydimethylsiloxane, polyisoprene, random copolymer of ethylene and propylene, and polystyrene) and the calculated MWDs were in good agreement with experimental data. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1539–1546, 2000     

Investigating the impact of operating parameters on molecular weight distributions using functional regression

Molecular weight distributions (MWDs) are inherently functional observations in which differential weight fraction is expressed as a function of chain length. Conventional approaches for analyzing and predicting MWDs include discretization and treatment as multi-response estimation problems, characterization using moments, and detailed mechanistic modeling to predict fractions for each chain length. However, these approaches can be sensitive to loss of information, complexity and problem conditioning. An alternative is to treat the MWDs as functional observations, and to use techniques from Functional Data Analysis (FDA), notably functional regression. The objective of this paper is to develop and apply empirical modeling techniques based on functional regression for investigating the impact of operating parameters on MWDs.     

Controlling molecular weight distributions of polyethylene by combining soluble metallocene/MAO catalysts

A critical look at the possibility of controlling the molecular weight distribution (MWD) of polyolefins by combining metallocene/methylalumoxane (MAO) catalysts is offered. Catalysts investigated were bis(cyclopentadienyl)zirconium dichloride (Cp₂ZrCl₂), its titanium and hafnium analogues (Cp₂TiCl₂ and Cp₂HfCl₂), as well as rac-ethylenebis(indenyl)zirconium dichloride (Et(Ind)₂ZrCl₂). As observed by other researchers, the MWD of polyethylene can be manipulated by combining soluble catalysts, which on their own produce polymer with narrow MWD but with different average molecular weights. Combined in slurry polymerization reactors, the catalysts in consideration produce ethylene homopolymer just as they would independently. Unimodal or bimodal MWDs can be obtained. This effect can be mimicked by blending polymers produced by the individual catalysts. We demonstrate how a variability in catalyst activity translates into a variability in MWD when mixing soluble catalysts in polymerization. Such a variability in MWD must be considered when setting goals for MWD control. We introduce a more quantitative approach to controlling the MWD using this method. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 831–840, 1998     

凝胶色谱法测定顺丁橡胶平均分子量及其分布的研究

通过一系列的条件试验,包括样品浓度、样品量及流动相流速对柱效的影响,确定了最佳的凝胶色谱（ＧＰＣ）试验条件;采用普适校正法将聚苯乙烯（ＰＳ）标定曲线转换成顺丁橡胶（ＰＢ）标定曲线,并对Ｍａｒｋ－Ｈｏｕｗｉｎｋ方程式中Ｋ,α值的选择进行了讨论;采用４种分子量加宽方程对色谱柱加宽效应进行改正计算,通过比较,选定适合本试验系统的加宽效应的改正方法;用粘度法测得的顺丁橡胶特性粘度（η）吻合ＧＰＣ所测得特性粘度值,证明了方法的可靠性。     

Copolymerization of ethylene and α‐olefins with combined metallocene catalysts. I. A formal criterion for molecular weight bimodality

Metallocene and other single‐site catalysts can be combined to produce polyolefins with broadened distributions of molecular weight, chemical composition, and long‐chain branching. These resins are finding increasing applications because of their enhanced properties compared to ones made with conventional Ziegler–Natta catalysts. Resins with bimodal molecular weight distributions (MWDs) have especially attractive mechanical and rheological properties. Although the use of these resins is expected to increase, there are very few studies available to quantify MWD bimodality or to decide a priori which combinations of metallocene catalysts will lead to the formation of polyolefins with bimodal MWDs. In this article, a necessary condition for the production of polymer with bimodal MWD using two single‐site‐type catalysts is derived. Additionally, a bimodality index is defined to quantify MWD bimodality. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1408–1416, 2000     

用GPC研究壳聚糖氧化降解过程中的分子量及其分布

用凝胶渗透色谱法跟踪研究了过氧化氢对壳聚糖氧化降解过程中壳聚糖的分子量及其分布的影响,结果表明,反应温度、时间和过氧化氢用量对壳聚糖的降解程度及降解产品质量均有影响。     

Sulfonation of polystyrene: Toward the “ideal” polyelectrolyte

Sulfonation of narrow polydispersity polystyrene, PS, standards remains the method of choice for generating polystyrene sulfonate, PSS, samples with defined composition. Although a variety of sulfonation techniques have been described, relatively little is reported on the material obtained, which is used for so many studies on the fundamental behavior of polyelectrolytes. Here, we show that powdered polystyrene treated with concentrated sulfuric acid (96%) at 90 °C without catalyst yields fully sulfonated PSS. Extensive characterization with ¹H and ¹³C NMR as well as size exclusion chromatography coupled with static and dynamic light scattering shows no evidence of sulfone crosslinking or chain degradation under the conditions used. Though mono‐sulfonated as soon as it dissolves in the acid, the PSS contains about 6% meta substitution. Sulfonation kinetics for this heterogeneous reaction depend strongly on particle size, sulfuric acid content and temperature. For preparing perdeuterated PSS from the corresponding PS it is essential to employ D₂SO₄, as about half of the aromatic units undergo H/D exchange during sulfonation. The remaining ortho H/D may be exchanged with extended exposure to the concentrated sulfuric acid, but the meta site is deactivated. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2416–2624     

Determination of molecular weight distributions of novolac resins by gel permeation chromatography

The number- and weight-average molecular weights of several statistical and high ortho novolac resins were determined using gel permeation chromatography (GPC). The standards used were pure compounds having between 2 and 12 phenol units bridged via methylene linkages. Three series of compounds were studied: (i) those with methylene linkages substituted in only the ortho positions relative to the phenolic hydroxyl group; (ii) those in which all para positions, together with sufficient ortho positions, were used to synthesize the compounds; and (iii) those in which the methylene linkages were substituted at a mixture of ortho and para positions. Such compounds, having known molecular architecture and units similar to the segments of industrial novolac resins, provide for a more exact measurement of the molecular weight than do the commonly used poly(styrene) standards. Using these new standards the number average molecular weights of the resins determined by GPC were in good agreement with the average molecular weight obtained by ¹H-NMR spectra of the resins, particularly for low molecular weight resins. GPC analysis of higher molecular weight resins tends to underestimate the molecular weights because of complications introduced by hydrogen bonding. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 1399–1407, 1997     

Extent of branching from linear viscoelasticity of long‐chain‐branched polymers

We present new results and examine literature data concerning the linear viscoelastic behavior of polyethylene with sparse to intermediate levels of long‐chain branching (LCB). These branched polymers displayed a common rheological signature, namely, a region of frequency‐independent loss tangent along with the corequisite scaling of the storage and loss moduli to the same frequency exponent. This apparent power‐law response occurred within a finite frequency window and bore resemblance to the behavior of physical gels. The appearance of this region, however, was the consequence of the presence of two distinct, yet partially overlapping, terminal relaxation processes. After considering the analogous relaxation behavior of wholly linear polymers with bimodal molecular weight distributions, we considered the polymers with LCB as blends of linear and branched species to develop a simple method of quantifying the extent of LCB. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1671–1684, 2004     

复合茂钛催化剂制备宽分子量分布间规聚苯乙烯的研究

采用新型茂钛化合物Cp^*Ti(O-Ph-OCH3)3(A)／CpTi(O-Ph-OCH3)3(B)和Cp^*Ti(O-Ph-OCH3)3(A)／Cp^*Ti(O-Ph-F),(C)作为复合催化剂,在甲基铝氧烷(MAO)、三异丁基铝(TIBA)激活下进行苯乙烯间规聚合。采用A／B复合催化剂可通过调节两种茂钛催化剂的摩尔配比,得到宽分子量分布的间规聚苯乙烯(s-PS);而采用A／C复合催化剂得到的产物分子量分布基本不变。对不同聚合条件下得到的s-PS产物进行了GPC分析。     

Aminosilylene-bridged ansa-zirconocenes for branched polyethylenes with bimodal molecular weight distributions

Reactions of the dilithium salt of aminosilylene-bridged ligands with (Me₂N)₂ZrCl₂(THF)₂ followed by the treatment of Me₃SiCl are found to be an efficient synthetic route to aminosilylene-bridged ansa-zirconocenes, R₂N(Me)Si(η⁵-C₅H₄)₂ZrCl₂ (R = Me (1), Et (2)) and Me₂N(Me)Si(η⁵-C₅H₄)(η⁵-C₅Me₄)ZrCl₂ (3). Crystal structure of 3 determined by X-ray diffraction study reveals the presence of π-bonding interaction between N and Si atoms, which is further supported by DFT calculation results. These complexes are very active (>1 × 10³ Kg/(mol Cat.·atm·h)) for homopolymerization of ethylene in the presence of methylalumoxane (MAO) cocatalyst, generating polyethylenes that contain branches as well as bimodal molecular weight distribution (MWD). Methyl, ethyl, butyl, and other longer branches (n ≥ 6) are observed in the resulting polyethylenes. The polyethylenes from 1, 2 and 3/MAO show a broad MWD range (6.3-42.2, 3.5-4.0 and 2.6-3.4, respectively).     

Enthalpy distributions and densities of states in linear polymers

Using polypropylene as an example, we applied a method we have recently developed to calculate the probability distribution of enthalpy from the temperature dependence of the heat capacity. The method involves the use of local temperature expansions of the heat capacity to calculate a set of moments of the enthalpy distribution. Using the maximum‐entropy method, one can then construct the enthalpy distribution for the system. The method is completely model free. The enthalpy distribution so obtained is the analogue of the Maxwell–Boltzmann distribution of kinetic energies for a gas, and like that function, tells one the distribution of enthalpies that an average unit in the polymer chain can have, a quantity that is crucial to understanding the chemical and physical properties of a polymer. Given the enthalpy distribution, one can then calculate the Gibbs free energy and the density of states that correspond to a particular value of enthalpy, thus giving one an expanded thermodynamics of the system in addition to the usual average quantities. We illustrate the fact that the Gibbs free‐energy distribution for this system scales as a simple function of temperature and that the density‐of ‐states function yields a simple empirical partition function for the system giving both the average thermodynamics and the distribution functions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1513–1518, 2001     

Characterization of the molecular weight distribution of isotactic polypropylene by turbidity at the lower critical solution temperature (LCST)

The molecular weight distribution (MWD) of high-molecular-weight isotactic polypropylene is measured by a new method developed for polyethylene (PE) using the turbidity at the lower critical solution temperature (LCST). The attenuation of transmitted light h_i is measured at T_i as each fraction i is separated from the solution during a temperature increase ΔT_i. From the thermogram, the set of h_i (T_i), the MWD can be calculated through a relation M_i = f(T_i). The solvent chosen, a mixture of butane and 2-methylbutane, optimizes resolution and relatively rapid dissolution. Homogenization and absence of degradation are verified by different methods including calorimetry in solution. © 1992 John Wiley & Sons, Inc.     

A Monte Carlo Method to Quantify the Effect of Reactor Residence Time Distribution on Polyolefins Made with Heterogeneous Catalysts: Part I—Catalyst/Polymer Particle Size Distribution Effects

Polyolefins are commercially produced in continuous reactors that have a broad residence time distribution (RTD). Most of these polymers are made with heterogeneous catalysts that also have a particle size distribution (PSD). These are totally segregated systems, in which the catalyst/polymer particle can be seen as a microreactor operated in semibatch mode, where the reagents (olefins, hydrogen, etc.) are fed continuously to the catalyst/polymer particle, but no polymer particle can leave. The reactor RTD has a large influence on the PSD of the polymer particles leaving the reactor, as well as in polymer microstructure and properties, polymerization yield, and composition of reactor blends. This article proposes a Monte Carlo model that can describe how particle RTD in a single or a series of reactors can affect the PSD of polymer particles made under a variety of operation conditions. It is believed that this is the most flexible model ever proposed to model this phenomenon, and can be easily modified to track all properties of interest during polyolefin production in continuous reactors with heterogeneous catalysts.