Non-steady-state model for kinetics of free radical polymerization, 4. Direct thermal initiation

This paper deals with the non-steady-state kinetics of direct thermal initiated polymerization. The initiation is assumed to be a bimolecular reaction of the monomer. The relationship between the radical concentration and the monomer conversion is rigorously derived. In further treatment a few very close approximations are introduced based on the fact that the number of monomer molecules reacting in the initiation step is much less than that consumed in the propagation step for a process producing high polymer, and the value of the rate constant for propagation or chain transfer is much lower than that for chain termination. Expressions for various molecular parameters, such as molecular weight distribution, number-average and weight-average degrees of polymerization, and dispersity, are given. Several numerical examples are provided.     

Calculation method of molecular weight averages in polymerization with chain-length-dependent termination

A systematic method for calculating the molecular weight distribution moments in free radical polymerization where termination rate depends on the size of the participating radicals, is presented. The central part of the method is the evaluation of the distribution of termination rates in the balance equations. From an adopted functional form of the termination rate constant, the moment equations are derived. For evaluating the moments of the termination rate distribution an approximate reconstruction of the radical chain length distribution using Laguerre polynomials is proposed. The calculation method can handle termination by disproportionation and combination simultaneously and allows easily to take into account diffusioncontrolled initiation, propagation and chain transfer reactions. The usefulness of the method is illustrated by simulating the bulk polymerization of methyl methacrylate and styrene. The calculated results of conversion, molecular weight averages (M _n,M _w,M _z and M _z+1) and polydispersity are in good agreement with the reported experimental data.     

水性体系用颜料分散剂的分子量及分子量分布的控制

采用自由基聚合和稳定自由基聚合,可合成水性体系用的颜料分散剂。介绍了低聚合度、窄分子量分布的聚合物分散剂的控制方法。引发剂、链转移剂、单体的浓度、溶剂种类、反应方式、温度等诸因素对分散剂的分子量和分子量分布有很大影响。讨论了诸因素对分散剂分散性的影响。     

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%.     

Calculating molecular weight distributions in emulsion polymerization under conditions of diffusion limited chain transfer

When highly reactive chain transfer agents with low water solubilities (e.g., long chain thiols) are used in emulsion polymerizations, transport of the chain transfer agent (CTA) from the monomer droplets to the polymer particles can become diffusion limited. Consequently, the concentration of CTA in the particles is lower than expected, resulting in apparent transfer constants that can be much lower than the actual transfer constants obtained from studies with homogeneous systems such as bulk or solution. Furthermore, molecular weights will be greater than those obtained in homogeneous systems with the same overall concentration of CTA. There are currently no techniques or methodologies available for predicting molecular weight distributions when the transport of CTA is diffusion limited. Apparent transfer constants may be used but they are typically restricted to a given system and operating conditions. In this work, we describe how the actual CTA concentration in the polymer particles can be estimated through analysis of instantaneous molecular weight distributions. This information is then used to calculate the cumulative molecular weight distribution during the polymerization. Comparisons with experimental molecular weight distributions validate the essential correctness of the approach, but also highlight potential problems. The extension of the approach to online applications is discussed. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 217–227, 2000     

Evolution of molecular weight and molecular weight distribution in ab initio styrene emulsion polymerizations using series of rigid rodlike cationic amphiphiles as surfactants

The emulsion polymerization of styrene is carried out using a series of unconventional rigid rodlike cationic surfactants (1‐[ω‐(4′‐methoxy‐4‐biphenylyloxy)alkyl]pyridinium bromides, PCX) of different lengths. The evolution of the molecular weight (M) and molecular weight distribution of the polymers is analyzed to obtain information about the chain stopping mechanism. Our results indicate that the M is strongly dependent on the initial surfactant concentration and is not dependent on the alkyl chain length. The Clay and Gilbert model [ln P(M) versus M plots] yields a concave‐up region at low molecular weights and a linear region that extends to high values. The slope of the linear region, which is related to the rate coefficient of the chain transfer to the monomer versus the propagation rate coefficient ratio, decreases as the PCX concentration increases. This behavior indicates that as the PCX concentration increases the chain transfer to monomer becomes the dominant chain stopping mechanism. On the other hand, the ln P(M) versus M plots of polymer samples taken at low and high conversions show differences in slope, particularly at low PCX concentration. It is likely that at low conversion the chain transfer to monomer competes with other chain stopping mechanisms that could be associated with a coagulative nucleation process. The formation of a high molecular weight fraction at low conversion supports this explanation. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 1513–1523, 2002; DOI 10.1002/app.10489     

Non-steady-state model for kinetics of free radical polymerization, 2. Redox initiation

This work deals with the non-steady-state kinetics of free radical polymerization with redox initiation. Rigorous expressions for the radical concentration, monomer conversion, molecular size distribution function, and number-average and weight-average molecular weights, etc., were derived. The molecular parameters of the resulting polymer were evaluated in relation to the polymerization conditions.     

Effect of an added base on (4-cyanopentanoic acid)-4-dithiobenzoate mediated RAFT polymerization in water

The effect of an added base on the aqueous reversible addition-fragmentation chain transfer polymerization of a methacrylic glycomonomer with (4-cyanopentanoic acid)-4-dithiobenzoate was investigated. When sodium carbonate or sodium bicarbonate were used to dissolve the RAFT agent in aqueous solution at room temperature, an inhibition period of 60-90 min was observed at the beginning of the polymerization together with a marked decrease in the overall polymerization rate. Also, experimental M_n values were much higher than the calculated ones in both cases. When sodium carbonate was used, control over the polymerization process was lost within 43% conversion. Better results were obtained with sodium bicarbonate, in which case the molecular weight distribution remained narrow and unimodal up to 81% conversion. At that point, a higher molecular weight shoulder developed that kept growing in intensity at the proceeding of the reaction. Dramatically improved results were obtained by adding circa 10% ethanol to the polymerization mixture to facilitate the dissolution of (4-cyanopentanoic acid)-4-dithiobenzoate. Following this protocol, narrow polydispersity poly(methyl 6-O-methacryloyl-α-d-glucoside) was obtained possessing a molecular weight close to the predicted value.     

Polymerization of conjugated dienes initiated by soluble organosodium compounds in hydrocarbon solvents

Polymerization of butadiene and isoprene in hydrocarbon solvents initiated by unsolvated organosodium compounds was studied. It was found that the polymer molecular weight and the MWD are determined mainly by chain transfer to solvent and polymer, and no chain transfer to monomer was observed even in the case of isoprene. The overall polymerization rate is proportional to the concentrations of the monomer and the initiator. Apparent chain propagation rate constants were found to be 0.11 litre mol^?1 s^?1 for butadiene and 0.065 litre mol^?1 s^?1 for isoprene polymerization in heptane at 30°C. It is suggested that associated (dimeric) forms of polydienylsodium active centres play an important role in chain propagation, being responsible for a stronger chain transfer and a greater 1,2-butadiene, or 3,4-isoprene, unit content than in polymerization with other alkali metals.     

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     

Modeling of semibatch styrene suspension polymerization processes

We developed a mathematical model to describe the behavior of semibatch styrene suspension polymerization processes, where the constituents of a typical emulsion polymerization process are added into the reaction vessel during the course of a typical suspension reaction. This technique was recently described for the production of core–shell polymer particles. The model assumes that the nucleated emulsion particles can agglomerate with the sticky and much bigger suspension particles and that the agglomeration rate constant is a function of the internal states of the suspended droplets. The proposed model presented good agreement with experimental conversion, average molecular weight, and molecular weight distribution data. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 1950–1967, 2005     

A novel polymer chain growing mode and styrene copolymer prepared with low molecular weight copolymer of α‐methylstyrene and styrene as macroinitiator

A new polymer chain growth mode, having multiple potential chain propagation sites, initiated by oligomer of α‐methylstyrene (AMS) and styrene (St) (PAS) is presented in this article. The effects of PAS content, AMS fraction in PAS and reaction temperature on bulk polymerization of St have been investigated. It is demonstrated that the PAS performed as macroinitiator in the polymerization of St. The average molecular weights of products increase significantly with the evolution of the polymerization, which is different from conventional free radical polymerization. With 20 wt % macroinitiator, the molecular weights increase from 1.21 × 10⁵ to 3.00 × 10⁵ with the monomer conversion increasing from 15.3 to 83.0%. This unique feature is tentatively attributed to both the reversible polymerization–depolymerization of AMS segments at high temperature which could generate more than one propagation sites in a polymer chain and the combination termination of St free radical polymerization. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41460.     

苯乙烯可逆加成-断裂链转移聚合动力学

为了实现可逆加成-断裂链转移(RAFT)聚合过程中,苯乙烯均聚、高分子量聚苯乙烯的合成及苯乙烯与其他单体共聚时,对苯乙烯转化率、共聚时组成和分子量大小的控制,进行了二硫代苯乙酸-1-苯基乙酯(PEPDTA)调控苯乙烯本体和细乳液聚合动力学分析。在本体聚合中,反应速率慢,链增长自由基与"中间态"自由基的终止反应对聚合速率影响较小,很难合成窄分布、高转化率、高分子量的聚苯乙烯;在细乳液聚合中,反应速率快、转化率高,随着PEPDTA含量增加,乳胶粒数量减少、粒径分布变宽,诱导期和缓聚现象明显;聚合物的数均分子量随转化率线性增长,RAFT试剂浓度越高,分子量分布越窄,反应时间越长,分布越宽。以Smith-Ewart方程为基础,建立了苯乙烯RAFT细乳液聚合动力学模型,模型动力学曲线与实验数据相符合,能较好地预测实验过程。     

Synthesis of emulsion styrene butadiene rubber by reversible addition–fragmentation chain transfer polymerization and its properties

Emulsion polymerization is generally used to synthesize styrene butadiene rubber (SBR), and the molecular weight of this rubber can be easily increased. However, the broad molecular weight distribution (MWD) of SBR increases energy loss and adversely affects the dynamic viscoelastic properties. To overcome this disadvantage, reversible addition–fragmentation chain transfer (RAFT) polymerization, which is a type of living polymerization, is applied to emulsion polymerization for preparing RAFT emulsion SBR (ESBR). The molecular weight and microstructure of RAFT ESBR are compared to those of commercially available ESBR 1502 by gel permeation chromatography and proton nuclear magnetic resonance spectroscopy. The aforementioned two polymers are used to prepare unfilled ESBR compounds, which are compared in terms of key physical properties (abrasion resistance, mechanical properties, and dynamic viscoelastic properties). It is confirmed that various physical properties of RAFT ESBR are improved due to its narrow MWD. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47069.     

Mechanistic study of boron trifluoride catalyzed ε‐caprolactone polymerization in the presence of glycerol

Boron trifluoride catalyzed ε‐caprolactone polymerization in the presence of glycerol can produce poly(ε‐caprolactone) with a high weight‐average molecular weight and a broad molecular weight distribution. This article reports an investigation of the polymerization mechanism to determine the formation of these molecular weight features through a study of the polymerization kinetics and the molecular structure with NMR. The polymerization proceeds via an activated monomer mechanism, resulting in polymer molecules with hydroxyl chain ends. The broad molecular weight distribution can be attributed to the etherification reactions between hydroxyl chain ends. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3900–3906, 2006     

Living cationic polymerization of isobutyl vinyl ether (II): Photoinduced living cationic polymerization in a mixed solvent of toluene and diethyl ether

A new method of preparation of living cationic polymer of isobutyl vinyl ether via photoinduced polymerization in the presence of diphenyliodonium iodide (DPII, initiator) and zinc iodide in a mixed solvent of toluene/diethyl ether, which was irradiated at ?78°C for short period, was completed within 15 min. The reaction was allowed for further reaction in the dark until monomer was fully consumed. It was found that increase in the conversion of monomer to polymer during the irradiation is very limited. Confirmation of the linear dependence of number‐average molar mass of resulting polymer on % conversion together with the fact that polymerization proceeds until monomer consumption, and controllability of number‐average molar mass of resulting polymer, depending on the molar ratio of monomer and initiator, strongly suggests the living nature of this polymerization, unless reaction temperature becomes higher than 0°C, i.e., the absence of chain breaking process. The narrow molar mass distribution, whose polydispersity index values are less than 1.2, reveals that the rate of initiation where irradiation is usually completed within 15 min is much faster than that of propagation in cationic nature in this system. Effect of some major factors, such as solvent polarity and temperature, on the living nature of the polymerization was also investigated. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 3581–3586, 2006     

Radical styrene polymerization in the presence of trace levels of sulfonic acids

The bulk polymerization of styrene in the presence of the vinyl functional sulfonic acid 2‐sulfoethylmethacrylate (SEM) was found to have utility for making polystyrenes with narrow polydispersity, bimodal polydispersity, and ultrahigh molecular weight at fast polymerization rates. Narrow polydispersity polymers were made by the addition of SEM to nitroxide‐mediated polymerizations. Bimodal polydispersity polymers were made by the ultrahigh molecular weight component being made in the presence of SEM in the absence of an initiator and the low molecular weight component being made in the presence of an initiator and/or chain‐transfer agent. Ultrahigh molecular weight monomodal polystyrenes were prepared at much faster polymerization rates than possible via spontaneous polymerization in the absence of SEM. SEM was found to be more effective, by an order of magnitude, than camphor sulfonic acid on a weight basis and, because it is copolymerized into the polymer chain, should not lead to corrosion problems during fabrication of the polymer. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 869–875, 2003     

基于聚合物分子量分布的乙烯淤浆聚合工艺优化

分子量及分布是聚合物生产过程中极其重要的质量指标,但目前的技术水平并不能实现分子量及其分布的实时测量,基于反应机理的动态建模是实现其软测量的重要方法。以乙烯淤浆聚合工艺为研究对象,基于聚合机理,分别以聚合物的平均分子量和分子量分布为目标,以循环气中氢气乙烯比为决定变量,采用稳态优化方法求取聚合物生产的工艺条件。结果表明:以平均分子量为优化目标所得的结果与分析值的偏差较大,虽然聚合物的平均分子量符合要求,但聚合物的分子量分布曲线与所需产品的分子量分布曲线之间的最大误差可达0.092;而以分子量分布曲线为目标所得的最大误差只有0.069。因此,以分子量分布曲线作为目标的优化方法明显比常规的以平均分子量为目标的优化方法优越。     

Control of molecular weight distribution and tensile strength in a free radical styrene polymerization process

A new method is presented for modeling and controlling polymer molecular weight distribution (MWD) and tensile strength in a batch suspension polymerization of styrene. The molecular weight distribution is modeled by computing the weight fraction of the polymer in different chain length intervals. Tensile strength is then related to the modeled molecular weight distribution using a correlation available in the literature and based on the concept of a threshold molecular weight. This method enables the design of operating conditions for a batch suspension polymerization reactor, which will theoretically yield amorphous polystyrene with a desired tensile strength. Two numerical examples are presented to illustrate the feasibility of the proposed method. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 1017–1026, 1998     

Kinetic and molecular weight control for methyl methacrylate semi‐batch polymerization. I. Modelling

There are gel, glass, and cage effects in the methyl methacrylate (MMA) bulk polymerization. These effects will cause the propagation and termination rate constants and initiator efficiency change during the polymerization process, and make the kinetics and molecular weight more complex. A violent increase of conversion will bring a large amount of reaction heat evolved in a short time, and will promote temperature increase if the heat cannot be removed in time. Molecular weight of polymer will raise ten times at the same time. So, the temperature of polymerization system, kinetics of polymerization, and molecular weight and its distribution of polymer cannot be controlled. To control and unify them, the semibatch polymerization method is preferably selected. Furthermore, the kinetic and molecular weight models for MMA semibatch polymerization with the participation of chain transfer agent and new materials addition flow rate are presented. Using the presented models, the effects of temperature, initiator concentration and type, monomer or solvent concentration, and chain transfer agent concentration and type on the kinetics, and molecular weight and its distribution are simulated in this article. Experimental data of kinetics and molecular weight obtained from the published literature are compared with the simulation results to examine the presented models. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2838–2846, 2006