The influence of reactor type and operating conditions on the molecular weight distribution in vinyl acetate polymerization

The vinyl acetate polymerization system was investigated with respect to the breadth of the molecular weight distribution (MWD) in batch, continuous segregated, and continuous micromixed reactors. Models were developed employing a complex kinetic scheme including polymer transfer and terminal double bond polymerization, without neglecting initiation and termination steps. Inclusion of a gel effect for terminal double bond polymerization gave better agreement with experimental molecular weight data in suspension polymerization. Simulation results showed the MWD order in the three reactor types is not fixed, but a function of reactant concentrations and the importance of chain branching. In some cases changing the initiator type and concentration will change the MWD order.     

Modeling of molecular weight and copolymer composition distributions for ethylene-propylene solution copolymerization

A comprehensive computational fluid dynamics (CFD) model was developed to investigate spatial distributions of molecular weight distribution (MWD) and copolymer composition distribution (CCD) for ethylene-propylene (EPM) copolymers in a bubble column reactor. The CFD approach incorporated Euler–Euler two-fluid model, copolymerization kinetics, and copolymer microstructural distribution model together by user-defined functions for ethylene-propylene heterogeneous copolymerization process. MWD and CCD distributions were calculated by introducing Flory's distribution and Stockmayer's distribution, respectively. CFD model results were validated with literature data. The multiphase hydrodynamics, interphase mass transfer, spatial–temporal variations of MWD and CCD distributions were analyzed. Both distributions are wider at the inlet of reactor for the inefficient mixing, but narrower at the outlet due to fully developed flow and polymerization. This model is beneficial to the improvement of polymer products and process control in industrial EPM reactor.     

An approach for complete molecular weight distribution calculation: Application in ethylene coordination polymerization

The objective of this article is to present an approach to ascertain the molecular weight distribution (MWD) of polymeric systems and its application to an industrial polyethylene reactor. Ascertaining the complete MWD can provide more reliable predictions of polymer end‐use properties, as some of them may depend on specific molecular weight ranges, instead of solely on the averages of the distribution. The proposed method is based on differentiation of the cumulative MWD, where the accumulated concentrations, evaluated at a finite number of chain lengths, are considered components in a reaction medium. Therefore, the dimension of the mathematical model may be suited to the desired level of detail on the MWD. The ethylene polymerization in solution with Ziegler–Natta catalyst is taken as a case study because of the lack of studies in this field. The reaction takes place in continuously stirred and tubular reactors. The results show the potential of the proposed approach and its usefulness in ascertaining the whole MWD, which in turn can be used to predict the polymer end‐use properties. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Continuous precipitation polymerization of vinylidene fluoride in supercritical carbon dioxide: A model for understanding the molecular-weight distribution

Poly(vinylidene fluoride) (PVDF) that is synthesized by precipitation polymerization in supercritical carbon dioxide (scCO₂) has a bimodal molecular weight distribution (MWD) and a very broad polydispersity index (PDI) under certain reaction conditions. Different models have been formulated to account for this behavior. This paper presents a homogenous model for a continuous stirred-tank reactor (CSTR) that includes the change of the termination reaction from kinetic control to diffusion control as the chain length of the polymeric radicals increases, and accounts for the change in the termination rate constant with macroradical chain length in the diffusion-controlled region. The model also includes the chain transfer to polymer reaction. Comparison of the model output with experimental data demonstrates that changes of the MWD, including the development of a bimodal distribution, with such reaction conditions as monomer concentration and average residence time are successfully predicted. In addition, the model can capture the occurrence of gelation, which appears to be responsible for a region of inoperability that was observed in the polymerization experiments. The success of this homogeneous model is consistent with recent research demonstrating that the CO₂-rich phase is the main locus of polymerization for the precipitation polymerization of vinylidene fluoride and vinylidene fluoride/hexafluoropropylene mixtures in scCO₂, at the conditions that have been studied to date.     

Modeling of branching density and branching distribution in low-density polyethylene polymerization

Low-density polyethylene (ldPE) is a general purpose polymer with various applications. By this reason, many publications can be found on the ldPE polymerization modeling. However, scission reaction and branching distribution are only recently considered in the modeling studies due to difficulties in measurement and computation of scission effect and branchings of polymer. Our previous papers [Kim, D.M., et al., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of CSTR. Chemical Engineering Science 59, 699-718; Kim, D.M., Iedema, P.D., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of a tubular reactor. Chemical Engineering Science, submitted for publication] are concerned with the scission reaction during ldPE polymerization and its effect on molecular weight distribution (MWD) of ldPE for various reactor types. Here we consider branching distributions as a function of chain length for CSTR and tubular reactor processes. To simultaneously deal with chain length and branching distributions, the concept of pseudo-distributions is used, meaning that branching distributions are described by their main moments. The computation results are compared with properties of ldPE samples from a CSTR and a tubular reactor. Number and weight average branchings and branching density increase as chain length increases until the longest chain length. The concentrations of long chain branching (LCB) are close to those of first branching moment in both CSTR and tubular reactor systems. The branching dispersity, a measure for the width of the branching distribution at a certain chain length, has the highest value at shorter chain length and then monotonously decreases approaching to 1.0 as chain length increases. Excellent agreements in branching dispersities between calculation with branching moments and prediction with assumption of binomial distribution for a tubular reactor and CSTR processes show that the branching distribution follows a binomial distribution for both processes.     

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     

A novel strategy for dynamic optimization of grade transition processes based on molecular weight distribution

To achieve different end‐use properties of polymers, an industrial plant must produce several grades of the product through the same process under different operating conditions. As molecular weight distribution (MWD) is a crucial quality index of polymers, grade transition based on MWD is of great importance. Dynamic optimization of the grade transition process using MWD is a challenging task because of its large‐scale nature. After analyzing the relationships among state variables during polymerization, a novel method is proposed to conduct the optimal grade transition using dynamic optimization with a small‐scale moment model, combined with a steady‐state calculation of the MWD. By avoiding expensive computation in dealing with dynamic MWD optimization, this technique greatly reduces the computational complexity of the process optimization. The theoretical equivalence of this simplification is also proved. Finally, an industrial high‐density polyethylene slurry process is presented to demonstrate the efficiency and accuracy of the proposed strategy. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2498–2512, 2014     

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.     

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     

Optimal process operation for the production of linear polyethylene resins with tailored molecular weight distribution

An optimization model is presented to determine optimal operating policies for tailoring high density polyethylene in a continuous polymerization process. Shaping the whole molecular weight distribution (MWD) by adopting an appropriate choice of operating conditions is of great interest when designing new polymers or when improving quality. The continuous tubular and stirred tank reactors are modeled in steady state by a set of differential‐algebraic equations with the spatial coordinate as independent variable. A novel formulation of the optimization problem is introduced. It comprises a multi‐stage optimization model with differential‐algebraic equality constraints along the process path and inequality end‐point constraints on product quality. The resulting optimal control problem is solved at high computational efficiency by means of a shooting method. The results show the efficiency of the proposed approach and the benefit of predicting and controlling the complete MWD as well as the interplay between operating conditions and polymer properties. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Optimal flowsheet configuration of a polymerization process with embedded molecular weight distributions

We consider the optimal reactor network synthesis of a polymerization process with detailed molecular weight distributions (MWDs). Based on an industrial high‐density polyethylene (HDPE) slurry process model including an embedded MWD, a fully connected process superstructure of continuous stirred tank reactors (CSTRs) is established through the introduction of splitters. Using this generalized superstructure as a basis, two nonlinear programming (NLP) problem formulations, which simultaneously maximize the monomer conversion and minimize the deviation between the calculated and target MWDs, are developed by applying multiobjective optimization (MO) methods. Different optimal flowsheet configurations are generated by systematically manipulating a set of continuous decision variables. Several case studies that consider different specifications on MWD are conducted to illustrate the effectiveness and efficiency of the proposed synthesis approach. Numerical results show that the optimal flowsheet configurations overcome the limitations of conventional reactor network structures and help to increase reactor productivity at the desired product quality. © 2015 American Institute of Chemical Engineers AIChE J, 62: 131–145, 2016     

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。     

Controlled free‐radical polymerization of vinyl chloride

Owing to the importance of poly(vinyl chloride) (PVC) as the second‐largest plastic in volume after the polyolefins and above styrene polymers, the control of the free‐radical polymerization of vinyl chloride (VC) is of high industrial and academic interest. But still the term “controlled” polymerization is not yet clearly defined. Often it is used for quasi‐living polymerizations with equilibrium reactions in the initiation and/or termination step or for the control of the molecular weight distribution (MWD), but it can also be applied to several structural aspects such as stereochemistry, branching, or special technical properties. In the present article, the control of chain growth and chain transfer is discussed. It has been well known for many years that the propagation step in the VC polymerization is terminated to a large degree by the rather frequent and temperature‐dependent chain transfer of the growing macromolecules to the monomer. Therefore, the degree of polymerization is strongly governed by the polymerization temperature. However, this transfer step does not result in a controlled or a narrow MWD. By means of free‐radical nitroxide‐mediated polymerization of VC in suspension, PVC with a narrower MWD can be obtained also at higher polymerization temperatures. The resulting PVC with nitroxide end groups can act as a macro‐initiator for various monomers, resulting in two‐block copolymers, which are, e.g., interesting compatibilizers in blends with PVC. J. VINYL ADDIT. TECHNOL., 11:86–90, 2005. © 2005 Society of Plastics Engineers     

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。     

An efficient algorithm of computation of molecular weight distributions and its moments for reversible step growth polymerization in homogeneous continuous flow stirred tank reactors

The reversible step growth polymerization in homogeneous continuous flow stirred tank reactors (HCSTRs), in which the condensation product (W) leaves the reactor through flashing, has been analyzed. The molecular weight distribution (MWD) of the polymer formed is governed by nonlinear coupled algebraic relations to be solved simultaneously. To find the MWD numerically a large number of these are normally solved simultaneously using a suitable iterative procedure. In this paper, these have been decoupled using the technique proposed in our earlier works (1, 2) and the MWD can now be obtained sequentially without any trial and error. This leads to considerable saving in computation time compared to methods currently used. To demonstrate the efficacy of the algorithm, the polycondensation step of the poly(ethylene terephthal-ate) (PET) formed in HCSTRs has been analyzed. The MWD, the average chain length and the polydispersity index of the polymer have been computed and it takes 0.1 CPU seconds on a DEC 1090 as opposed to the earlier method which would take seventy minutes for similar computations. The simple model of the HCSTR for the PET formation gives the effect of reactor temperature and pressure and the quantitative results have been presented in this paper.     

Control of molecular weight distribution (MWD) for polyethylene catalyzed over Ziegler-Natta/Metallocene hybrid catalysts

Two types of inorganic supports, MgCl₂ and SiO₂, for the impregnation of catalysts were prepared by the recrystallization and sol-gel methods, respectively. The Ziegler-Natta/Metallocene hybrid catalysts were prepared in order to control the molecular weight (Mw) and the molecular weight distribution (MWD) during ethylene polymerization. The polyethylene produced by the hybrid catalysts can control the Mw and the MWD of polymer, showing two melting temperatures and a bimodal MWD, corresponding to products arising from each of the individual catalysts. This suggests that these hybrid catalysts acted as individual active species and produced a blend of polymers. This paper was presented at the 8th APCChE (Asia Pacific Confederation of Chemical Engineering) Congress held at Seoul between August 16 and 19, 1999.     

Dynamic optimization for grade transition processes using orthogonal collocation on molecular weight distribution

To meet the demands of a competitive market, an industrial plant often produces several grades of polymer product through the same process in an economical way. As molecular weight distribution (MWD) is a crucial quality index of polymers, dynamic optimization for grade transition based on MWD is highly important, but challenging. This study considers the development of optimization models for MWD-based grade transition. An MWD reconstruction method using orthogonal collocation in two dimensions is developed to capture the dynamic feature of MWD in time and the distributive feature in chain length. The simultaneous collocation approach is adopted to discretize the model. Two optimization formulations are proposed to describe minimizing the transition time as well as off-spec production. Both formulations inherit the advantages of the simultaneous collocation approach. The numerical results show that the proposed methods can efficiently solve the grade transition problem with MWD specification, and obtain high performance control profiles to reduce the production cost. © 2019 American Institute of Chemical Engineers AIChE J, 65: 1198–1210, 2019     

Kinetics of high conversion polymerization of vinyl acetate. Effects of mixing and reactor type on polymer properties

In the present article the kinetics of polymerization of vinyl acetate in suspension up to high conversion was studied. The molecular weight distribution and the side chain branching of polyvinyl acetate produced were examined with respect to micro and macro mixing as well as to reactor type. The following results were achieved: the time–activity curves of the polymerization can be described up to high conversions considering the exponential increase in viscosity of the polymerizing system and combining the viscosity with rate constants of the polymerization. The change of volume of the polymerizing system has no significant influence on kinetics. The narrowest molecular weight distribution of the poly(vinyl acetate) produced was achieved when polymerizing in the homogeneous continuous stirred tank reactor while the broadest molecular weight distribution was observed in the segregated continuous stirred tank reactor. The batch reactor and the flow tube reactor produce polymers with molecular weight distributions lying in between. Considering the side chain branching, another order was found. The batch reactor and the tube reactor show the lowest side chain branching, the homogeneous continuous stirred tank reactor shows a larger one and the segregated continuous stirred tank reactor shows the largest. Possible reasons for the different behavior of the different reactors are discussed. The degree of segregation was determined by experiments.     

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.