Evolution to similarity solutions for polymerization and depolymerization with microwave radiation

The kinetics of polymerization and depolymerization are critical in understanding the stability and characterization of polymers. The kinetics of simultaneous polymerization and degradation of poly(methyl methacrylate) have been investigated by varying the initiator concentration and monomer concentration under the influence of microwave energy. Microwave radiation initially polymerizes the monomer, then degrades the resulting polymer and the polymer attains an equilibrium molecular weight distribution with a polydispersity of two. To understand more fully the kinetics, the molecular weight distribution (MWD) is represented as a gamma distribution; the random degradation rate coefficient is assumed to vary linearly with molecular weight and the polymerization rate coefficient is assumed to be independent of molecular weight. The change of the MWD with time is studied by continuous distribution kinetics; the solutions obtained depict the change of the average molecular weight, polydispersity and the gamma distribution parameters with time. Experimental data indicate that reaction rates are enhanced by microwave radiation and the MWD approaches a similarity solution within 10 min for all the investigated cases. The model satisfactorily predicts the change of the MWD with time. © 2001 Society of Chemical Industry     

Copolymerization of ethylene with α-olefins over supported titanium–magnesium catalysts. II. Comonomer as a chain transfer agent

The data on the effect of comonomer (propylene and 1-hexene) on molecular weight (M_w), molecular weight distribution (MWD), and content of terminal double bonds were obtained for ethylene/α-olefin copolymers produced over a supported titanium–magnesium catalyst (TMC) upon polymerization in the absence of hydrogen. The experimental data on the effect of comonomer concentration on M_w of polymers were used to calculate the ratios between the effective rate constants of chain transfer with monomer and the propagation rate constant. It was shown that the effective rate constant of chain transfer with monomers increases in the row of monomers: ethylene < 1-hexene < propylene. Meanwhile, the data on the effect of copolymers on content of terminal double bonds of various types demonstrate that different reactions of chain transfer with comonomer may simultaneously occur during copolymerization. It results in simultaneous formation of terminal vinylidene and trans-vinylene bonds. Therefore, the calculated rate constants of chain transfer with comonomer are complex values, which include the rate constants of chain transfer with comonomer occurring via different mechanisms. The data on MWD, short chain branching (SCB) and terminal double bonds content of different types were obtained by molecular weight fractionation of copolymers followed by the analysis of narrow fractions. The analysis of the data on MWDs of SCB and terminal double bonds shows that active sites of the TMC are considerably heterogeneous with respect to the rates of different chain transfer reactions with monomers. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

A segment probability method for calculating the molecular weight distributions of linear polycondensates in a continuous reactor

The molecular weight distribution (MWD) of polymers is a target of the optimization and control of industrial polymerization processes, as it dictates the processability and properties of polymers. A method, named as segment probability method, is developed to calculate the MWD of polycondensates produced by monomers of types A₂ and B₂ in a continuous reactor. It considers a growing chain as being composed of A and B segments in the middle of the chain and two terminal segments at the chain ends. It calculates the propagation probabilities of these different types of segments upon taking into account both the polycondensation and side reaction kinetics as well as the residence time distribution of the continuous reactor. The method is validated by poly(butylene terephthalate) (PBT) obtained from an industrial polymerization process composed of a continuous esterification reactor. The MWDs of the PBT calculated by this method are in agreement with those measured by size exclusion chromatography with mean square errors less than 10%.     

Ethylene polymerization over supported titanium‐magnesium catalysts: Effect of polymerization parameters on the molecular weight distribution of polyethylene

The data on the effects of polymerization duration, cocatalyst, and monomer concentrations upon ethylene polymerization in the absence of hydrogen, and the effect of an additional chain transfer agent (hydrogen) on the molecular weight (MW), molecular weight distribution (MWD), and content of vinyl terminal groups for polyethylene (PE) produced over the supported titanium‐magnesium catalyst (TMC) are obtained. The effects of these parameters on nonuniformity of active sites for different chain transfer reactions are analyzed by deconvolution of the experimental MWD curves into Flory components. It has been shown that the polymer MW grows, the MWD becomes narrower and the content of vinyl terminal groups in PE increases with increasing polymerization duration. It is assumed to occur due to the reduction of the rate of chain transfer with AlEt₃ with increasing polymerization duration. The polydispersity of PE is found to rise with increasing AlEt₃ concentration and decreasing monomer concentration due to the emergence of additional low molecular weight Flory components. The ratios of the individual rate constants of chain transfer with AlEt₃, monomer and hydrogen to the propagation rate constant have been calculated. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

苯乙烯连续搅拌釜式本体聚合工业过程模拟

采用了机理分析建模法对苯乙烯工业本体预聚过程进行了模型化研究，并通过对流体在反应器中混合模式的分析，表明预聚釜可视作全混流（CSRT）反应器模型，此外对热聚合机理中的引发级数和终止反应进行了考察，利用预聚釜的工业数据确立了三分子引发，同时考虑偶合和歧化终止以及向溶剂链转移的反应机理模型，并选取了合适的动力学参数，然后利用工业装置采集的数据进行了模拟，从宏观转化率，平均分子量和微观分子量分布两个方面对模型进行了验证，模拟结果和工业数据符合得较好，该模型方程不仅能模拟稳态，非稳态预聚过程，同时也为装置开发新产品，改造扩建，优化操作方案等提供了理论基础。     

Modeling of molecular weight distribution of propylene slurry phase polymerization on supported metallocene catalysts

A mathematical model of the molecular weight distribution (MWD) based on a particle growth model and the kinetic scheme is developed to simulate the MWD of the slurry phase propylene polymerization on a silica-supported metallocene catalyst by means of the equations of moments. The model is used to predict molecular weight distribution, including the number-average molecular weight, the weight-average molecular weight, and the polydispersity index. The results show that the mass transfer has great influence on the polymerization reaction, and it can broaden the MWD especially; moreover, the MWD can be evaluated by simulation; the average molecular weight increases as pressure or temperature, and MWD shifts to long chain lengths as the effective diffusion coefficient increasing thought the influence is not remarkable; furthermore, the MWD's simulation results are calculated, which fit greatly with the experimental data.     

Molecular weight distribution of commercial emulsion grade PVC

At first glance the molecular weight distributions (MWDs) of suspension and emulsion grade PVC are very similar. However, studying the MWDs for both polymerization technologies in more detail reveals systematic differences that can be explained by the differences in the polymerization processes. The MWD of continuous emulsion PVC is broader than that of batch emulsion PVC, which, in turn, is broader than that of suspension PVC. When correlating molecular weight data to K values, it has to be considered that K values from resins including polymerization additives are different from the K value of the pure polymer. The knowledge of the differences in MWD may be helpful for estimating differences in other properties of the products.     

半间歇聚合反应分子量分布周期操作的迭代学习控制

通过对半间歇聚合反应的引发剂进料实施周期操作,研究了这类操作方式对聚合物分子量分布的影响。研究结果显示,周期操作能改善聚合反应过程,对分子量分布有明显的加宽作用。对性能指标进行改进,以引发剂周期进料的占空比为控制变量,采用基于粒子群优化的迭代学习算法,对分子量分布进行了优化控制。仿真分析表明,在实际对象和模型存在不匹配的情况下,运用迭代粒子群算法,控制输入随着批次学习的进行而逐渐趋于最优解,聚合反应的分子量分布则不断逼近希望的分子量分布。实验结果验证了以周期操作方式对半间歇聚合过程分子量分布进行迭代优化控制的可行性。     

Propene polymerization with MgCl2-supported TiCl4/dioctylphthalate catalyst. III. Effects of polymerization conditions on molecular weights and molecular weight distribution

In propene polymerization over the MgCl₂-supported TiCl₄/dioctylphthalate (DOP) catalyst, the weight- and number-average molecular weights and the molecular weight distribution (MWD) of polypropene products and of the isotactic and atactic polymer portions were studied. The average molecular weights and MWD were found to be independent of time. The isotactic polymer had higher molecular weight and broader distribution than the atactic portion by almost an order of magnitude. An increase in temperature and cocatalyst/catalyst ratio resulted in lowering molecular weight due to increasing transfer reaction. Alkyl aluminum was used as a cocatalyst, and the molecular weight did not vary significantly with different alkyl groups. Of the three external bases studied, 2,2,6,6-tetramethyl piperidine (TMPIP), dimethoxydiphenyl silane (DMDPS), and t-butylmethyl ether (TBME), the addition of a small amount of one of the first two bases caused a substantial increase in both molecular weight and polydispersity of the isotactic polymer. Those increases leveled off quickly with increasing amounts of the external base. On the other hand, both average molecular weights and polydispersity of the atactic polymer decreased with a net increase in the molecular weight of the whole polymer. TBME, however, has no significant effect on either molecular weight or MWD. These effects are discussed in the context of the roles of the external base in propene polymerization. © 1995 John Wiley & Sons, Inc.     

丁二烯气相聚合产物分子量分布和粒径分布模型研究

对非均相催化的丁二烯气相聚合,基于聚合物多层模型,考虑催化剂颗粒间活性位初始浓度和粒径分布对聚合物分子量分布和粒径分布的影响,建立了聚合物分子量分布和粒径分布的数学模型。模拟了反应温度、催化剂颗粒间活性位初始浓度和粒径分布等因素的影响,结果表明。随着温度升高,聚合物颗粒平均粒径变小,粒径分布变窄,聚合物分子量变小,分子量分布变宽;催化剂颗粒间的活性组分负载越均匀,聚合物分子量越大,分子量分布和粒径分布越窄;随着催化剂平均粒径变大,聚合物分子量变小,分子量分布变宽,不存在催化剂颗粒粒径分布和聚合物颗粒粒径分布间的复制现象。模型模拟结果与实验结果吻合较好,可用于预测丁二烯气相聚合产物的分子量、分子量分布和粒径分布。     

Modeling of molecular weight distribution of gas‐phase polymerization of butadiene

A mathematical model of the molecular weight distribution (MWD) based on a multilayer model and an improved intrinsic kinetics model was proposed to simulate the MWD of the gas‐phase polymerization of butadiene with a heterogeneous catalyst. Intrinsic kinetics and heat and mass‐transfer resistances based on the multilayer model of a polymeric particle were considered in the modeling of the MWD. The effects of the reaction conditions, catalyst particle size, mass‐transfer resistance, deactivation of active sites, and transfer of the polymer chain on the molecular weight and MWD were simulated. The results show that the effects of the deactivation of active sites and transfer of the polymer chain on the average molecular weight are significant and that the effect of the catalyst particle size on the MWD is not significant. The simulation results of the molecular weight and MWD are compared with the experimental results. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 88–103, 2003     

Molecular Weight Distribution of Polystyrene Produced in a Starved Feed Reactor

A starved feed reactor (SFR) is a semi-batch polymerization reactor where initiator and monomer are fed slowly into a fixed amount of solvent. The polymerization is carried out isothermally at elevated temperatures, The added initiator decomposes instantaneously and the added monomer polymerizes immediately. The molecular weight (MW) and molecular weight distribution (MWD) of the product polymer can be effectively controlled by the feed ratio of monomer to initiator. This paper preaeats a study on the MWD of styrene polymerization in a SFR. The MWD model parameters are regressed with experimeatvJ data. Although the solids fraction in the SFR is high (higher than 50%), vlscceity is not too high and the “gel effect“ is weak due to the low molecular weight of the products. It is found that the termination rate constant is a power function of molecular weight, radicals terminate via 100% combination,the thermal iuitiation can be neglrcted even at high reaction temperature studied. And calculated results indicate that in the SFR, the validity of the long chain assumptinn becomes doubted. It appears that other alterative assumption should be found for an improved model.     

Hydrogen effect on the molecular weight distribution of polymers obtained by polymerization of ethylene and α-olefins over supported titanium-magnesium catalysts

Comparative data on the molecular weight distribution of polymers obtained by polymerization of ethylene, propylene and 1-hexene, and copolymerization of ethylene with α-olefins over the titanium-magnesium catalysts (TMC) in the absence and presence of hydrogen are presented. In contrast to the ethylene polymerization, in the cases of propylene and 1-hexene polymerization and copolymerization of ethylene with α-olefins, the hydrogen addition is characterized by noticeable narrowing of the molecular weight distribution (MWD) due to lower contribution of the MWD component with high molecular weight. This result is an evidence of the increased reactivity of TMC active sites producing high molecular weight poly-α-olefins and copolymers of ethylene with α-olefins in the chain transfer reaction with hydrogen. It is suggested that the increased reactivity of these sites in the transfer reaction with hydrogen appears after the 2,1-addition of α-olefin to the growing polymer chain.     

Modeling and analysis of a slurry reactor system for heterogeneous olefin polymerization: The effects of hydrogen concentration and initial catalyst size

This article deals with the development of a model for the polymerization process using a Ziegler‐Natta catalyst in a slurry reactor system. Employed here is the hierarchical model describing the entire reactor system that is subcategoried by the gas bubble phase, the continuous gas phase, the liquid phase, the solid polymer particle, and the surface of catalyst where chemical reaction occurs. The concept of the multigrain model (MGM) is introduced to describe the growth of polymer particle from the original catalyst particle. We also adopt the concept of multiple active sites to elucidate the broad molecular weight distribution (MWD). The major concern here is the effects of the hydrogen concentration and the size of the initial catalyst on the performance of the polymerization reactor. It is demonstrated that the hydrogen gas can be used for the purpose of controlling not only the molecular weight but the molecular weight distribution (MWD) of the polymer. In addition, the relationship between the molecular weight and the concentration of hydrogen gas is investigated. The size of the initial catalyst is found to exercise a significant influence on the morphology of the resultant polymer particle. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2480–2493, 2001     

多段加氢聚合制备宽相对分子质量分布PP

采用球形TiCl4/MgCl2·内酯型高效催化剂,通过加氢与非加氢气相聚合间多段切换的方法合成了宽相对分子质量分布的聚丙烯(PP)。研究了加氢/非加氢切换频率和加氢量对PP相对分子质量及其分布和结晶形貌的影响。总聚合时间相同时,增加加氢/非加氢切换频率对聚合活性的影响较小,对相对分子质量及其分布的影响也不明显,但使PP球晶尺寸减小,球晶形貌不规整程度增大。增大加氢量使相对分子质量分布增至11．0以上,球晶尺寸减小。     

反应介质对催化链转移聚合反应的影响探究

采用催化链转移聚合法制备得到了端基带双键的聚甲基丙烯酸甲酯(PMMA)大分子单体,通过红外吸收光谱(FT-IR)、核磁共振氢谱(1HNMR)对大分子单体的结构进行了表征,并用凝胶渗透色谱法(GPC)测定了大分子单体的分子量及分子量分布;首次利用碘值法测定了大分子单体的双键含量。实验过程中考察了反应介质及其含量对大分子单体的分子量的影响,结果表明由于催化链转移剂与反应溶剂的络合作用,大分子单体的数均分子量随溶剂含量的增加而变大。     

Multiscale modeling of syndiospecific styrene polymerization

A detailed mathematical model for syndiospecific styrene polymerization based on combining features of the multigrain model (MGM) and the polymeric multigrain model (PMGM). This model has been established to predict the radial monomer concentration within the growing macro particles and the rate of polymerization. The latter, the parameters, have an effect on the molecular weight distribution (MWD). In this model, the effect of intraparticle diffusion resistance and the radius of catalyst particles on the rate of polymerization and MWD were studied. The model simulation showed the presence of a large distribution of monomer concentration across the radius of particles. It was further noticed that the diffusion resistance was most intense at the beginning of the polymerization process. For MWD, the model simulation showed that the existence of diffusion resistance led to have an increase in the molecular weight within a period of time similar to the one needed in the catalyst decay. Moreover, the validation of the model with experimental data given a good agreement results and show that the model is able to predict a correct monomer profile, polymerization rate, particle growth factor and MWD, an algorithm, which embeds physicochemical effects, has been developed to model the industrial reactors.     

Kinetic model for lonic polymerization initiated by difunctional initiator with monomer transfer

The kinetics of difunctional ionic polymerization with monomer transfer and without assumption of instantaneous initiation is studied theoretically. The set of kinetic differential equations is rigorously solved by way of graphical theory. Expressions for the molecular weight distribution (MWD) function, the number- and weight-average degrees of polymerization, and the distribution of functionality are obtained. A procedure is proposed for calculating the MWD curve and the values of other molecular parameters.     

Addition polymerization of norbornene, 5-vinyl-2-norbornene and 2-methoxycarbonyl-5-norbornene with a catalyst based on a palladium(0) precursor complex

Pd(dibenzylideneacetone)₂, when activated in situ with 1 equiv of [CPh₃][B(C₆F₅)₄] in the presence of 1 equiv of P(C₆H₁₁)₃, efficiently catalyzed the addition polymerization and copolymerization of norbornene and its derivatives. Homopolymerization of 5-vinyl-2-norbornene took place regio-selectively with the endo-cyclic double bond to give high-molecular weight polymers, while the exocyclic double bond remained intact so that the resulting polymer had pendent vinyl groups along the polymer chain. In the polymerization of a mixture of the endo-/exo- isomers of 2-methoxycarbonyl-5-norbornene, the endo-isomer was consumed prior to consumption of the exo-isomer, contrary to the well-known tendency in Pd(II)-based catalyst systems. Another notable feature of the present catalytic system was the strong dependency of the molecular weight on the reaction temperature, which was studied in detail for the copolymerization of 2-methoxycarbonyl-5-norbornene with norbornene: we could control the molecular weight without the use of a chain transfer agent. The extracted oligomeric fraction of poly(norbornene) showed the presence of a terminal CC double bond as well as a C₆F₅ unit that was bound to the first norbornane unit in the polymer chain.     

Radical polymerization of acrylamide initiated by ceric ammonium nitrate-methionine redox initiator system

The polymerization of acrylamide, initiated by a cerium (IV) [Ce(IV)] ammonium nitrate-methionine redox initiator system, was carried out in an aqueous solution at different reaction conditions. The dependence of molecular weight and polymerization yield on the concentration of Ce(IV), polymerization time, and temperature was determined. The molecular weight distributions (MWD) of the resulting polymers were examined using the HPLC method. Based on the HPLC results, optimum reaction conditions were determined that provided an opportunity to obtain a polymer that had a narrow MWD. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1643–1648, 1997