Optimal operation of ethylene polymerization reactors for tailored molecular weight distribution

This work presents a comprehensive steady‐state model of the high‐pressure ethylene polymerization in a tubular reactor able to calculate the complete molecular weight distribution (MWD). For this purpose, the probability generating function technique is employed. The model is included in an optimization framework, which is used to determine optimal reactor designs and operating conditions for producing a polymer with tailored MWD. Two application examples are presented. The first one involves maximization of conversion to obtain a given MWD, typical of industrial operation. Excellent agreement between the resulting MWD and the target one is achieved with a conversion about 5% higher than the ones commonly reported for this type of reactor. The second example consists in finding the design and operating conditions necessary to produce a polymer with a bimodal MWD. The optimal design for this case involves a split of the initiator, monomer, and modifier feeds between the main stream and two lateral injections. To the best of our knowledge, this is the first work dealing with the optimization of this process in which a tailored shape for the MWD is included. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

关于聚苯乙烯的摩尔质量分布与性能

对国内外聚苯乙烯瓣摩尔质量分布的渗透色谱法测定结果,结合有关性能进行了分析和讨论,表明了熔融指数不仅随重均摩尔质量的增高而变小,而且和摩尔质量分布有关。国内某些厂（批）的聚苯乙烯性脆问题与低聚物含量较多有关。     

Supported titanium–magnesium catalysts with different titanium content: Kinetic peculiarities at ethylene homopolymerization and copolymerization and molecular weight characteristics of polyethylene

The effect of Ti content on the activity of titanium–magnesium catalysts (TMC) and molecular weight distribution (MWD) of polyethylene (PE) produced has been studied. It was found that the activity enhances sharply as Ti content decreases from 0.6 to 0.07 wt %, and shows no significant changes in the Ti content range of 0.6–5.0 wt %. The maximum activity (36 kg PE/mmol Ti × h × bar C₂H₄) was observed for TMC with the lowest Ti content. The catalyst with low titanium content (～ 0.1 wt % of Ti) produced PE with narrower MWD (M_w/M_n = 3.1–3.5) as compared to catalysts with higher titanium content (3–5 wt % of Ti; M_w/M_n = 4.8–5.0). New data on the effect of hydrogen on MWD of PE have been found. Increasing hydrogen concentration results in broadening the MWD of PE, especially in the case of TMC with high titanium content. The data presented indicate the heterogeneity of active centers of TMC in the reaction of chain transfer with hydrogen. The data on the ethylene–hexene‐1 copolymerization over TMC with different titanium content are presented. Comonomer reactivity ratios were shown to be independent of the Ti content in TMC. Presumably the difference in activity of these catalysts is mainly caused by the difference in the number of active centers. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102:5436–5442, 2006     

Modeling of a multizone gas‐phase polyethylene reactor with a cluster‐based approach

A circulating fluidized reactor of polyethylene was modeled with the proper hydrodynamics for a riser and downer and combined with a kinetic model based on the moment equations. The hydrodynamic model was able to predict the profiles of the following parameters through the riser and downer: cluster velocity, bed porosity, concentration of potential active sites, active sites, gas‐phase components, molecular weights, and reactor temperature. It was shown that one could control the monomer consumption and molecular weight, which are crucial in the reactor behavior and production properties, respectively, by setting different operating hydrodynamic conditions, such as the gas velocity in the riser and the solid circulation rate. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Simultaneous determination of molecular weight and crystallinity of recycled HDPE by infrared spectroscopy and multivariate calibration

An attempt of correlating molecular weight (M_n) of recycled high‐density polyethylene (HDPE) as measured by size‐exclusion chromatography (SEC) with diffuse reflectance near and mid‐infrared spectroscopy (NIR/MIR) was made by means of multivariate calibration. The spectral data obtained was also used to extract information about the degree of crystallinity of the recycled resin. Differential scanning calorimetry (DSC) was used as the reference method. Partial least‐squares (PLS) calibration was performed on the MIR and NIR spectral data for prediction of M_n. Four PC factors described fully the PLS models. The root‐mean‐square error of prediction (RMSEP) obtained with MIR data was 360, whereas a RMSEP of 470 was achieved when calibration was carried out on the diffuse reflectance NIR data. A PLS calibration for prediction of degree of crystallinity was performed on the NIR data in the 1100–1900‐nm region, but the ability of prediction of this model was poor. However a PLS calibration in the region 2000–2500 nm yield better results. Four PC factors explained the most of the variance in the spectra and the RMSEP was 0.4 wt %. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 321–327, 2002     

Effect of molecular weight and branch content on the creep behavior of oriented polyethylene

Creep studies were carried out on a range of homopolymers and copolymers of polyethylene with well‐defined molecular weight and branch content. The creep data were analyzed in terms of two thermally activated processes acting in parallel and the effects of molecular weight and branch content are discussed. It is shown that increasing either the number‐average molecular weight or the weight‐average molecular weight gives improved creep behavior at all stress levels. The introduction of butyl branches leads to lower creep at low‐stress levels but can give rise to higher creep at high stress. Plots of the equilibrium log₁₀(strain rate) versus stress at fixed draw ratio (strain) can be used to define sections through a unique true stress/true strain/strain rate surface for each material. These creep results have an additional value in terms of the link between slow crack propagation (SCG) in polyethylene and fibril creep, confirming the proposal made elsewhere that SCG can be quantified in terms of creep to failure across the true stress/true strain/strain rate surface. © 2003 Wiley Periodicals, J Appl Polym Sci 89: 1663–1670, 2003     

Modeling the solubility of ternary mixtures of ethylene,iso‐pentane,n‐hexane in semicrystalline polyethylene

The coabsorptions of ethylene and iso‐pentane, and ethylene and n‐hexane were measured by the use of a pressure decay method. The solubility data of ethylene‐iso‐pentane and ethylene‐n‐hexane in semicrystalline polyethylene (PE) of crystallinity of 48.6% were obtained at temperatures 70, 80, and 90 °C, and the total pressure 2 MPa, iso‐pentane partial pressure 80–190 KPa, n‐hexane partial pressure 20–90 KPa. The presence of iso‐pentane or n‐hexane in the corresponding ternary system leads to increase the solubility of ethylene, while the solubility of iso‐pentane or n‐hexane remains unchanged with an increase of the ethylene partial pressure, even slightly decreases. Assumed that the presence of iso‐pentane or n‐hexane decreases the crystallinity of the polymer sample, a coabsorption model was built to model the solubility of each gas in the ternary systems. The relative root mean square errors of the coabsorption model for ethylene‐iso‐pentane‐PE system and ethylene‐n‐hexane‐PE system are 5.13% and 4.64%, respectively. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 3654–3662, 2007     

Scale‐Free Power‐Law Distribution of Emulsion‐Polymerized Branched Polymers: Power Exponent of the Molecular Weight Distribution

Summary: The molecular weight distribution (MWD), formed in emulsion polymerization that involves the polymer transfer reaction during Interval II, may approach the power‐law distribution as polymerization proceeds. The power exponent, α, of the weight fraction distribution W(M) = M^?α conforms to the relationship, α = 1/P_b, where P_b is the probability that the chain end is connected to a backbone chain. The MWD of emulsion‐polymerized polyethylene reported in literature agrees reasonably well with the relationship, W(M) = M^?α with α = 1/P_b. This simple relationship could be used to estimate the P_b value from the MWD data, possibly leading to determining the polymer transfer constant under well‐designed experimental conditions. Because α > 1, the number‐average MW always approaches a finite value, but the weight‐ and higher order‐averages of MWD may continue to increase as the particle grows without limit depending on the magnitude of P_b. The power‐law distributions are self‐similar, possessing the nature of fractals and lacking a characteristic scale. The i‐th moment of the MWD for the present reaction system continues to increase without limit during Interval II for P_b ≥ 1/i.

Molecular weight distribution of the emulsion‐polymerized polyethylene.     

农膜用聚乙烯树脂分子结构与耐老化性能的关系

通过对低密度聚乙烯（PE_LD）、线形低密度聚乙烯（PE-LLD）、茂金属线形低密度聚乙烯（m-PE—LLD）、乙烯-乙酸乙烯酯共聚物（EVA）等原料直接吹塑农用棚膜进行农田扣棚试验和力学性能测试，分析了各种树脂对生产PE功能性农用棚膜的适用性，并尝试从各种树脂基础分子结构角度对农膜的耐老化性能进行解释。试验结果表明：m—PE-LLD附脂的力学性能明显优于PE-LD和EVA树脂，EVA树脂在透明性方面占有优势；在耐老化性能方面，m-PE-LLD和EVA树脂无论扣棚时间还是测试数据均比PE-LD要好，从连续取样测试数据看出PE-LD断裂伸长保留率下降趋势明显，而m-PE-LLD和EVA树脂则是拉伸强度保留率下降趋势明显。     

Ethylene polymerization by phenylenedimethylene‐bridged homobinuclear zirconocene/methylaluminoxane systems

In the presence of methylaluminoxane (MAO), ethylene polymerization was successfully performed with homobinuclear zirconocene complexes {[(C₅H₅)ZrCl₂](C₅H₄CH₂ C₆H₄CH₂C₅H₄)[(C₅H₅)ZrCl₂]; 3o , 4m , and 5p }, which were prepared conveniently by the reaction of disodium(phenylenedimethylene)dicyclopentadienide [C₆H₄(CH₂C₅H₄Na)₂] with 2 equiv of (N⁵‐Cyclopentadienyl)trichlorozirconium dimethoxyethane (CpZrCl₃(DME)) in tetrahydrofuran and characterized by ¹H‐NMR and elemental analysis. The effects of the polymerization parameters, such as the temperature, time, concentration of the catalyst, MAO/catalyst molar ratio, and isomeric difference of the homobinuclear metallocene complexes 3o , 4m , and 5p were studied in detail. The results showed that all three catalytic systems had moderate activities in ethylene polymerization and afforded polyethylene with relatively broad polydispersities. The catalytic activity of 4m was somewhat higher than that of 3o and 5p but lower than that of 4,4′‐bis(methylene)biphenylene‐bridged zirconocene catalysts; this indicated that the distance between the two metal centers was too short in comparison with a 4,4′‐bis(methylene)biphenylene bridge to increase the catalytic activity. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci, 2006     

Experimental validation of the optimal trajectory of initiator concentration in a batch MMA polymerization reactor

This article presents a method to determine the trajectory of initiator concentration that will produce polymer with desired number‐ and weight‐average molecular weights at a prespecified level of monomer conversion. The optimal control theory is applied to the mathematical model for a batch methymethacrylate (MMA) solution polymerization reactor system. By imposing the constraint that initiator concentration should decrease within the range of self‐consumption by the initiation reaction, one can obtain the initiator concentration trajectory that can be tracked by feeding the initiator alone. A control scheme is constructed with a cascade proportional‐integral‐derivative (PID) control algorithm for temperature control and a micropump is installed to manipulate the initiator feed rate. The experimental results show satisfactory tracking control performance despite the nonlinear features of the polymerization reactor system. Also, the monomer conversion and the average molecular weights measured are found to be in fairly good agreement with those of model prediction, respectively. In conclusion, the polymer having desired molecular weight distribution can be produced by operating the batch reactor with the initiator supplement policy calculated from the model. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1256–1266, 2000     

Modeling the oxidative degradation of ultra‐high‐molecular‐weight polyethylene

Understanding the sequence of reactions that occur in ultra‐high‐molecular‐weight polyethylene (UHMWPE) following ⁶⁰Co γ irradiation has been the focus of numerous experimental studies. In the study reported here, we have incorporated recent experimental findings into a mathematical model for UHMWPE oxidation. Simulation results for shelf aging and accelerated aging are presented. It is shown that very reasonable simulations of shelf‐aging and accelerated‐aging data can be obtained. It is also shown that simulations of shelf aging in reduced oxygen environments predict that the subsurface peaks of ketones will be shifted to the exterior surface. In vivo aging can be simulated if we assume that the oxygen level in the synovial fluid is about one‐eighth that of atmospheric levels. Some reduced irradiation doses are predicted to significantly reduce the ketone formation for shelf‐aging periods of up to 10 years. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 814–826, 2003     

Rheological behavior and mechanical properties of high‐density polyethylene blends with different molecular weights

The dynamic rheological and mechanical properties of the binary blends of two conventional high‐density polyethylenes [HDPEs; low molecular weight (LMW) and high molecular weight (HMW)] with distinct different weight‐average molecular weights were studied. The rheological results show that the rheological behavior of the blends departed from classical linear viscoelastic theory because of the polydispersity of the HDPEs that we used. Plots of the logarithm of the zero shear viscosity fitted by the Cross model versus the blend composition, Cole–Cole plots, Han curves, and master curves of the storage and loss moduli indicated the LMW/HMW blends of different compositions were miscible in the melt state. The tensile yield strength of the blends generally followed the linear additivity rule, whereas the elongation at break and impact strength were lower than those predicted by linear additivity; this suggested the incompatibility of the blends in solid state. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Determination of the molecular characteristics of commercial polyethylenes with different architectures and the relation with the melt flow index

The molecular weight distribution curves of several commercial polyethylene samples were evaluated by high‐temperature gel permeation chromatography with two detectors (a refractive‐index detector and a viscometer) to determine the molecular sizes and architectures (branching). The polymer samples included high‐ and low‐density polyethylenes with different molecular weight distributions (wide, medium, unimodal, and bimodal) from nine producers. The results were tested against the melt flow index and zero‐shear melt viscosity to find correlations. The data for high‐density polyethylene correlated well with the molecular weight, whereas the data for low‐density polyethylene did not correlate. However, when the weight‐average molecular weight was corrected by the branching parameter and a factor form, all the polyethylene samples fit a single equation. These results indicate that the melt flow index is dependent not only on the molecular weight but also on the molecular shape, including branching. The relation accounted for samples of different resin producers, molecular weights (65,000–638,000), and polydispersities (2.9–20). The use of the branching parameter for the correction of the molecular weight allowed the correlation of these parameters despite differences in the technologies, molecular weights, and molecular architectures. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1572–1578, 2007     

Experimental study on the effect of molecular weight and chemical composition distribution on the mechanical response of high-density polyethylene

This article aims to appraise the effect of microstructure comprising molecular weight distribution and chemical composition distribution on the mechanical properties of high-density polyethylene (HDPE). HDPE resins were synthesized using several titanium–magnesium-supported Ziegler–Natta catalysts in the industrial gas phase reactor under the same polymerization condition. Gel permeation chromatography and crystallization elution fractionation (CEF) were conducted on the resins to characterize the molecular weight and comonomer distribution. Crystallization, thermal and rheological behavior were evaluated following differential scanning calorimetry, polarization light microscopy, and rheometric mechanical spectrometry. The resins with higher soluble fraction in trichlorobenzene below 80°C (highly branched low molecular weight chains) exhibited longer crystallization time based on the crystallization kinetic obtained from the Avrami model. Rheological determination of the molecular weight between entanglements (M_e) and the average lamella thickness based on the Gibbs–Thomson equation revealed that the entanglement density and impact strength decreased, and the average lamella thickness increased with an increase in the ratio of CEF eluted fraction below 80°C to the crystallizable fraction in the range of 80–90°C.     

聚合物生产分子量分布建模与控制研究

分子量分布是关系聚合物性质的重要性能指标 ,针对聚合过程分子量分布的建模和控制关键技术进行了分析和综述 ,指出各自的优缺点 ,给出了这一领域今后的研究方向     

Influence of Aluminium Alkyl Compounds on the High‐Pressure Polymerization of Ethylene with Ternary Metallocene‐Based Catalysts. Investigation of Chain Transfer to the Aluminium

The influence of aluminium alkyl compounds on metallocene‐catalyzed high pressure polymerizations of ethylene has been investigated at 150 MPa and 180°C in a continuously operated autoclave. The catalysts were based on the metallocenes bis(cyclopentadienyl)zirconium dichloride (Cp₂ZrCl₂) and diphenylmethylene (cyclopentadienylfluorenyl)zirconium dichloride (Ph₂C‐(CpFlu)ZrCl₂), which were preactivated outside the reactor with triisobutylaluminium (TiBA) and N,N‐dimethylanilinium tetrakis(pentafluorophenyl)borate (DMAP, [PhNHMe₂][B(C₆F₅)₄]). The concentrations of triisobutylaluminium (TiBA) and triethylaluminium (TEA) in the reactor were varied over a wide range, using a separate dosing for these two aluminium alkyl compounds. Productivity and polymer properties strongly depended on the type and the concentration of the aluminium alkyl compound used. Highest productivities and molecular weights were obtained with low concentrations of TiBA in the reactor. Up to a concentration of 30 molppm Al in the reactor, unimodal polymers were formed with M̄_w/M̄_n between 2 and 3. With higher aluminium concentrations the products formed contained small amounts of waxes, due to oligomerization catalyzed by the aluminium alkyl compounds. The molecular weight distributions (MWDs) of these products could be described as a superimposition of two Schulz‐Zimm distributions. All MWDs were analyzed with regard to the amount of waxes produced by ethylene oligomerization and with regard to the influence of chain transfer reactions to the aluminium. The rate constants of chain transfer to aluminium, in relation to the rate constants of insertion of ethylene, were estimated.     

Modeling solubility of gases in semicrystalline polyethylene

An absorption model of gases in semicrystalline polymer was built that was based on the activity coefficient theory in polymer solution and associated with crystallinity dependent on temperature. The solubility of ethylene, isopentane, and n‐hexane in three types of polyethylene (PE) were obtained by the use of a pressure‐decay method at temperatures of 333–363 K and pressures of up to 2 MPa, 80–300 KPa, and 19–100 KPa, respectively. Experimental data from three gases in each PE sample were used for the single‐parameter fitting, and fitting error was within about 12%. It was found that a single parameter was merely dependent on the properties of PE used. It was shown that, unlike with the Flory–Huggins model and the UNIFAC–M‐H method, correlation between the crystallinity of the semicrystalline polymer and temperature had to be taken into account in order for the solubility data of alkane, olefin, and aromatic hydrocarbons in polyethylene to fit well, especially in the temperature range near the melting point of the polymer. The four free‐energy contributions to the total gas activity were experimentally determined to be about 47%–60% combined, the free‐volume contribution about 12%–25%, and the elastic effect about 22%–35%, but the interactional contribution was zero. The contributions changed with the size of the gas molecules. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1737–1744, 2007     

Heterogeneity of active sites of Ziegler‐Natta catalysts: The effect of catalyst composition on the MWD of polyethylene

Experimental data on the molecular weight distribution (MWD) of polyethylene (PE) produced over a broad number of Ziegler‐Natta catalysts differing in composition and preparation procedure are presented. These catalysts include nonsupported TiCl₃ catalyst, four types of supported titanium‐magnesium catalysts (TMC) differing in the content of titanium and the presence of various modifiers in the composition of the support, and a supported catalyst containing VCl₄ as an active component instead of TiCl₄. The studied catalysts produce PE with different molecular weights within a broad range of polydispersity (M_w/M_n = 2.8–16) under the same polymerization conditions. The heterogeneity of active sites of these catalysts was studied by deconvolution of experimental MWD curves into Flory components assuming a correlation between the number of Flory components and the number of active site types. Five Flory components were found for PE produced over nonsupported TiCl₃ catalysts (M_w/M_n = 6.8), and three–four Flory components were found for PE produced over TMC of different composition. A minimal number of Flory components (three) was found for PE samples (M_w/M_n values from 2.8 to 3.3) produced over TMC with a very low titanium content (0.07 wt %) and TMC modified with dibutylphtalate. It was shown that five Flory components are sufficient to fit the experimental MWD curve for bimodal PE (M_w/M_n = 16) produced over VMC. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Poly(ethylene‐co‐methacrylic acid)–lithium ionomer as a compatibilizer for poly(ethylene terephthalate)/linear low‐density polyethylene blends

Poly(ethylene terephthalate) (PET)/linear low‐density polyethylene (LLDPE) blends (75/25), with contents of poly(ethylene‐co‐methacrylic acid) partially neutralized with lithium (PEMA–Li) that were systematically changed from 0 to 45% relative to the LLDPE, were obtained by direct injection molding in an attempt to (1) ameliorate the performance of the binary blend and (2) find the best compatibilizer content. PEMA–Li did not modify the PET or LLDPE amorphous‐phase compositions or the crystalline content of PET. However, PEMA–Li did lead to a nucleation effect and to the presence of a second smaller and less perfect crystalline structure. PET induced a fractional crystallization in LLDPE that remained in the presence of PEMA–Li and reduced the crystallinity of LLDPE. The ternary blends showed two similar dispersed LLDPE and PEMA–Li phases with small subparticles, probably PET, inside. The compatibilizing effect of PEMA–Li was clearly shown by the impressive increase in the break strain, along with only small decreases in the modulus of elasticity and in the tensile strength. With respect to the recycling possibilities of LLDPE, a ternary blend with the addition of 22.5% PEMA–Li, which led to very slight modulus and yield stress decreases with respect to the binary blend and a break strain increase of 480%, appeared to be the most attractive. However, the highest property improvement appeared with the addition of 37.5% PEMA–Li, which led to elasticity modulus and tensile strength decreases of only 9%, along with a very high break strain increase (760%). © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1322–1328, 2003