Modelling free-radical copolymerization kinetics, 3. Molecular weight calculations for copolymers with crosslinking

A comprehensive model for molecular weight calculations of free-radical crosslinking copolymerizations was developed using the pseudo-kinetic rate constants and the method of moments. The moments of copolymer chain distributions are defined in such a way so that the molecular weight averages of crosslinking copolymers can be calculated using the moments. The present model is based on a general crosslinking copolymerization scheme, accounting for chain transfer to small molecules and polymer, bimolecular termination, and crosslinking reactions. The influence of crosslinking reactions on molecular weight development is discussed. The effects of the reactivity of pendant double bonds on the moments development were further demonstrated using model simulations. The simulations results suggest that the higher-order molecular weight averages are very sensitive to the reactivity of pendant double bonds. It was found that chain transfer to polymer affects the gelation point significantly. The radical fractions must be calculated accounting for chain transfer reactions in addition to propagations in order to properly evaluate pseudo-kinetic rate constants. The present model was used to predict kinetic behavior and molecular weight development of styrene/m-divinylbenzene and styrene/ethylene dimethacrylate free-radical crosslinking copolymerizations in benzene solution at 60°C. It was found that the present model is in excellent agreement with the experimental data published in the literature. Model predictions and experimental data show that the reactivity of pendant double bonds is much lower than that of vinyl and divinyl monomers. The simulation results suggest that the assumption of the same reactivity of functional groups is likely not valid for many free-radical crosslinking copolymerizations. The present model based on a kinetics approach can be used to predict molecular weight development for vinyl/divinyl free-radical crosslinking copolymerizations and to estimate kinetic parameters in the pre-gelation period.     

Kinetics of long-chain branching in emulsion polymerization

A kinetic model suitable to deal with the case of branched polymers produced in emulsion both in the case of chain transfer to polymer and propagation to terminal double bond is briefly presented and numerically solved through the method of the moments. Thanks to the “numerical fractionation” approach, the whole molecular weight distribution of the polymer is evaluated while accounting for the compartmentalized nature of the system. The results of some illustrative calculations concerning the effects upon the molecular properties of the final polymer of starved semibatch monomer feed policies, addition of a chain transfer agent and propagation to terminal double bond are discussed.     

Monte carlo simulation of copolymerization by ester interchange reaction in miscible polyester blends

The effects of reaction variables on the degree of randomness in copolymers formed by ester interchange reaction in miscible polyester melt blends were systematically investigated using a Monte Carlo method. Three reaction variables such as the molecular weight difference between two component polymers, the blend ratio, and the reaction ratio of end attack to bond flip, were particularly considered on the cubic lattice model. Ester interchange reactions were assumed to take place during reptational chain motions. It was found that the copolymerization was dependent upon the molecular weight difference and reaction ratio: As the molecular weight difference becomes smaller and when both end attack and bond flip reactions are involved simultaneously, the copolymerization is accelerated. However, the blend ratio does not affect the copolymerization process. This result is discussed in relation to the polymer chain conformation for the ester interchange reaction. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1637–1645, 1998     

Gel formation in free radical polymerization via chain transfer and terminal branching

Gel formation in free-radical polymerization via chain transfer to polymer, recombination termination, and terminal branching due to either chain transfer to monomer or disproportionation termination is investigated using the method of moments. It is found that no gel can possibly form in the systems consisting of initiation, propagation, and one of the above reactions. However, systems with the following combination of reactions are found to be capable of gelling. They are: chain transfer to polymer + recombination termination; chain transfer to polymer + terminal branching due to disproportionation termination; and terminal branching due to transfer to monomer + recombination termination. Systems with the following combination of reactions are incapable of gelling; transfer to polymer + terminal branching due to transfer to monomer; and terminal branching due to disproportionation termination + recombination termination. An examination of the gelation mechanisms reveals that the formation of multivinyl macromonomers during the course of polymerization is the reason that systems involving terminal branching gel. Sol/gel diagrams are generated to give critical kinetic parameters required for gelation. It is found that terminal branching does not always promote gelation due to the adverse effect on chain length through chain transfer to monomer and termination by disproportionation, reactions which generate terminal double bonds. © 1994 John Wiley & Sons, Inc.     

Theoretical study of chain transfer in anionic polymerization. Transfer by the mechanism of side-group substitution

A new theoretical consideration of chain transfer to monomer in the anionic polymerization of hydrocarbon monomers is presented. It is shown that the kinetic scheme used in theoretical studies reported previously contradicts the widespread views on the chemical mechanism of carbanionic reactions. It is suggested that the most probable path of the transfer reaction is the proton abstraction from the side group of the monomer; the terminal double bond of the monomer molecule remains unchanged, and therefore the intermediate species can participate in succeeding reactions as a macromonomer. The molecular characteristics of polymer formed in processes with monomer transfer by side-group substitution are determined. At high conversion, the polymer formed in such a process is shown to possess a number-average degree of polymerization, P̄_n, approaching the theoretical value for living polymers, and a P̄_w exceeding it the more the higher the intensity of transfer. Furthermore, it shows a broad molecular weight distribution and a fairly noticeable degree of branching. These results considerably differ from those previously reported.     

Modelling free-radical copolymerization kinetics—evaluation of the pseudo-kinetic rate constant method, 2. Molecular weight calculations for copolymers with long chain branching

The full moment equations and equations using pseudo-kinetic rate constants for binary copolymerization with chain transfer to polymer in the context of the terminal model have been developed and solved numerically for a batch reactor operating over a wide range of conditions. Calculated number- and weight-average molecular weights (M̄_n and M̄_w) were compared with those found using the pseudo-kinetic rate constant method (PKRCM). The results show that the weight-average molecular weights calculated using PKRCM are in agreement with those found using the method of full moments for binary copolymerization when polymeric radical fractions φ₁^˙ and φ₂^˙ of type 1 and 2 (radical centers are on monomer types 1 and 2 for a binary copolymerization) are calculated accounting for chain transfer to small molecules and polymer reactions in addition to propagation reactions. Errors in calculating M̄_w using PKRCM are not always negligible when polymer radical fractions are calculated neglecting chain transfer to small molecules and polymer. In this case, the relative error in M̄_w by PKRCM increases with increase in monomer conversion, extent of copolymer compositional drift and chain transfer to polymer rates. The errors in calculating M̄_w, however, vanish over the entire monomer conversion range for all polymerization conditions when chain transfer reactions are properly taken into account. It is theoretically proven that the pseudo-kinetic rate constant for chain transfer to polymer is valid for copolymerizations. One can therefore conclude that the pseudo-kinetic rate constant method is a valid method for molecular weight modelling for binary and multicomponent polymerizations.     

Modeling and Experimentation of RAFT Solution Copolymerization of Styrene and Butyl Acrylate,Effect of Chain Transfer Reactions on Polymer Molecular Weight Distribution

Chain transfer reactions widely exist in the free radical polymerization and controlled radical polymerization, which can significantly influence polymer molecular weight and molecular weight distribution. In this work, the chain transfer reactions in modeling the reversible addition–fragmentation transfer (RAFT) solution copolymerization are included and the effects of chain transfer rate constant, monomer concentration, and comonomer ratio on the polymerization kinetics and polymer molecular weight development are investigated. The model is verified with the experimental RAFT solution copolymerization of styrene and butyl acrylate, with good agreements achieved. This work has demonstrated that the chain transfer reactions to monomer and solvent can have significant impacts on the number‐average molecular weight (M_n) and dispersity (Ð).     

Molecular weight distribution formed through chain-length-dependent crosslinking reactions

The molecular weight distribution formed through chain-length-dependent crosslinking reactions in free-radical vinyl/divinyl copolymerization is investigated by using Monte Carlo simulations. When the crosslinking reaction rates for larger polymer molecules are reduced, the high molecular weight tails cannot extend smoothly, resulting in distorted, sometimes bimodal distribution profiles, which exhibit qualitative similarity with those reported experimentally. Although the reduced crosslinking reaction rates between larger polymer molecules may not affect the average crosslinking density levels significantly, they can delay the developments of the weight-average molecular weight significantly. Because the wastage of pendant double bonds through cyclization would result in a similar tendency, one cannot distinguish these two types of nonidealities through the measurements of the pendant double bond consumption and the average molecular weight development.     

Reaction mechanism and rheological properties of polypropylene irradiated under various atmospheres

It is well-known that the melt-strength properties of a polymer increases with molecular weight and with long chain branching due to the increase in the entanglement level. This study is a contribution for the understanding of the following points: — the role of branching, crosslinking and degradation on melt strength properties; — the mechanism and the kinetics of PP irradiation with time of irradiation and the importance of double bond formation.

The results showed that degradation was the major reaction in the initial step of irradiation no matter the atmosphere and or antioxidant. However, double bond formation increased the production of branching and crosslinking reactions. Double bond formation had no effect on the crystallization kinetics, on the other hand, long chain branching had a marked effect on the crystallization temperature.     

凝胶点前氯乙烯－邻苯二甲酸二烯丙基酯共聚物表征，支化度模型及悬挂双键活性

根据单烯－二烯自由基共聚合反应特点，提出一种新的支化点对分子量的分布模型，讨论了用凝胶色谱－特性粘数法表征文化聚合物时，文化点对分子量分布和式［η］０，ｂ／［η］０．１＝ｇ０中的指数ｃ对结果的影响．建立了氯乙烯－二烯类单体悬浮聚合凝胶点前的平均支化度模型．用凝胶点前平均文化度和平均分子量模型拟合实验结果发现：ａ．新的支化分布模型更合理，且ｃ＝０．７２；ｂ．悬挂双键活性下降一个数量级；ｃ．对本文样品，特性粘数和分了量仍符合Ｍａｒｋ－Ｈｏｕｗｉｎｋ方程，［η］＝０．２３５７Ｍ￣０．５２７．     

Mechanistic investigation and reaction kinetics of the low-pressure copolymerization of cyclohexene oxide and carbon dioxide catalyzed by a dizinc complex

The reaction kinetics of the copolymerization of carbon dioxide and cyclohexene oxide to produce poly(cyclohexene carbonate), catalyzed by a dizinc acetate complex, is studied by in situ attenuated total reflectance infrared (ATR-IR) and proton nuclear magnetic resonance ((1)H NMR) spectroscopy. A parameter study, including reactant and catalyst concentration and carbon dioxide pressure, reveals zero reaction order in carbon dioxide concentration, for pressures between 1 and 40 bar and temperatures up to 80 °C, and a first-order dependence on catalyst concentration and concentration of cyclohexene oxide. The activation energies for the formation of poly(cyclohexene carbonate) and the cyclic side product cyclohexene carbonate are calculated, by determining the rate coefficients over a temperature range between 65 and 90 °C and using Arrhenius plots, to be 96.8 ± 1.6 kJ mol(-1) (23.1 kcal mol(-1)) and 137.5 ± 6.4 kJ mol(-1) (32.9 kcal mol(-1)), respectively. Gel permeation chromatography (GPC), (1)H NMR spectroscopy, and matrix-assisted laser desorption/ionization time-of-flight (MALDI-ToF) mass spectrometry are employed to study the poly(cyclohexene carbonate) produced, and reveal bimodal molecular weight distributions, with narrow polydispersity indices (≤1.2). In all cases, two molecular weight distributions are observed, the higher value being approximately double the molecular weight of the lower value; this finding is seemingly independent of copolymerization conversion or reaction parameters. The copolymer characterization data and additional experiments in which chain transfer agents are added to copolymerization experiments indicate that rapid chain transfer reactions occur and allow an explanation for the observed bimodal molecular weight distributions. The spectroscopic and kinetic analyses enable a mechanism to be proposed for both the copolymerization reaction and possible side reactions; a dinuclear copolymerization active site is implicated.     

Molecular weight distribution in free radical polymerization with long-chain branching

A new theory to predict the molecular weight distribution in free radical polymerization that includes chain transfer to polymer is proposed. This theory is based on the branching density distribution of the primary polymer molecules. The branching density distribution provides the information on how each chain is connected to other chains, and therefore, a full molecular weight distribution can be calculated by application of the Monte Carlo simulation. The present theory accounts for the history of the generated branched structure and can be applied to various reaction systems that involve branching and crosslinking regardless of the reactor types used. The present simulation confirmed the validity of the method of moments in a batch polymerization proposed earlier. It was shown clearly why gelation never occurs by chain transfer to polymer without the assistance of other interlinking reaction such as bimolecular termination by combination. © 1993 John Wiley & Sons, Inc.     

A simulation model for long-chain branching in vinyl acetate polymerization: 1. Batch polymerization

A new simulation model for the kinetics of long-chain branching formed via chain transfer to polymer and terminal double-bond polymerization is proposed. This model is based on the branching density distribution of the primary polymer molecules. The theory of branching density distribution is that each primary polymer molecule experiences a different history of branching and provides information on how each primary polymer molecule is connected with other chains that are formed at different conversions, therefore making possible a detailed analysis on the kinetics of the branched structure formation. This model is solved by applying the Monte Carlo method and a computer-generated simulated algorithm is proposed. The present model is applied to a batch polymerization of vinyl acetate, and various interesting structural changes occurring during polymerization (i.e., molecular weight distribution, distribution of branch points, and branching density of the largest polymer molecule) are calculated. The present method gives a direct solution for the Bethe lattice formed under nonequilibrium conditions; therefore, it can be used to examine earlier theories of the branched structure formation. It was found that the method of moments that has been applied successfully to predict various average properties would be considered a good approximation at least for the calculation of not greater than the second-order moment in a batch polymerization. © 1994 John Wiley & Sons, Inc.     

Reduced‐order model for monitoring spectroscopic and chromatographic polymer properties

A reduced‐order mechanistic polymerization model and its application in the design of a low‐dimension multi‐rate state estimator (soft sensor) for monitoring spectroscopic and chromatographic polymer properties are presented. A model reduction approach is used to simplify a method‐of‐moments mechanistic model. Using this approach, the order (number of the state variables) of the model is reduced from 20 to 7. The soft sensor estimates spectroscopic and chromatographic polymer properties from (a) frequent measurements of the reactor temperature and the flow rates of monomer (n‐butyl acrylate), initiator (t‐butyl peroxy acetate) solution and solvent (xylene) feed streams, and (b) infrequent and delayed measurements of polymer number‐ and weight‐average molecular weights and the concentrations of terminal solvent groups, terminal double bonds and short chain branches. The benefits of using the infrequent measurements in the estimation are shown. The soft sensor is implemented in real‐time, and the calculated continuous estimates of polymer number‐ and weight‐average molecular weights and the concentrations of solvent, terminal double bonds and short chain branches are compared to the corresponding chromatographic and spectroscopic measurements. Copyright © 2007 John Wiley & Sons, Ltd.     

不饱和环缩醛与苯乙烯的原子转移自由基共聚合反应

不饱和环状单体与烯类单体共聚所得的共聚物 ,已经或正在开发成一系列新的产品 .例如 ,水解后得到末端带有—OH,— SH,—COOH等官能团的聚苯乙烯、聚乙烯、聚甲基丙烯酸甲酯等的低聚物[1] ,用于制备新型聚酯和聚氨酯 ;与乙烯的共聚物可在细菌作用下彻底分解成脂肪酸或醇 ,可赋予聚合物生物降解活性 ;与双甲基丙烯酸酯等的共混物 ,可用于制作高强度补牙材料[2 ] 等 .以前报道的不饱和环状单体与烯类单体的共聚反应 ,均为无规共聚 ,而且是普通自由基引发聚合 ,不能控制分子量 ,分子量分布很宽 .原子转移自由基聚合是近几年发展起来的实现…     

丙烯酰胺-二氰二胺大单体及其与苯乙烯共聚物的研究(Ⅰ)——大单体及其共聚物的合成和表征

通过丙烯酰胺、二氰二胺、甲醛及氯化铵的缩合反应,合成了分子链端含C=C双键的大单体,缩合过程用高压液相色谱考察,以AIBN为引发剂,二甲基亚砜为溶剂,使大单体与苯乙烯共聚,得到主链具有疏水性、侧链具有亲水性的共聚物,用GPC、IR光谱及溶解性对共聚物进行鉴定,苯乙烯含量较低时,共聚物溶于水,共聚物在MeOH/H₂O混合溶剂中的粘性行为表明它是带有疏水基团的聚电解质。     

Synthesis of polyester having sequentially ordered two orthogonal reactive groups by anionic alternating copolymerization of epoxide and bislactone

This article presents a route to a novel polyester having sequentially ordered two orthogonal reactive groups. The polyester was given by the imidazole‐initiated alternating copolymerization of allyl glycidyl ether (AGE) and a bislactone 1 . This copolymerization system is characterized by the following three reaction behaviors: (1) the selective participation of only one of the two lactone moieties of 1 to the copolymerization to give a linear polyester, and the consequent introduction of the second lactone into the side chain of the polyester, (2) the participation of the epoxy moiety in AGE to the copolymerization, and the consequent introduction of the carbon–carbon double bond into the side chain of the polyester, and (3) arrangement of the sequentially ordered two orthogonal reactive groups according to the alternating manner. The introduction of the two reactive groups to the side chain of the alternating copolymer allowed two routes of sequential chemoselective reactions: (A) The ring‐opening reaction of the lactone moiety with n‐propylamine and the following Pt‐catalyzed hydrosilylation of the carbon–carbon double bond with dimethylphenylsilane and (B) the sequential reactions of the reverse order. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009     

The Formation of Terminal Double Bonds in Vinyl Chloride Polymerization

The determination of double bonds in PVC is achieved with an increased accuracy in comparison with earlier methods by the addition of iodine monochloride (Wijs reaction) to PVC coupled with x-ray fluorescence analysis to determine the iodine content of the polymer. The number of double bonds per unit weight of polymer increases on increasing the polymerization temperature and is proportional to the number of polymer molecules. It is not affected, however, by the presence of the chain transfer agent tetrahydrofuran (THF). At the technically important polymerization temperatures of 30 to 80°C and in the absence of the chain transfer agent, 0.9 double bonds per polymer molecule are found. The number of double bonds per polymer molecule is lowered using the chain transfer agent THF. These results support the theory that the chain transfer to monomer and possibly the termination reaction are coupled with the formation of terminal double bonds. Contributions by internal double bonds formed by dehydrochlorination of the polymer during polymerization are excluded by investigating the Cl^θ content of the water phase in the oxygen-free VC suspension polymerization. No hydrogen chloride is formed. In IR spectra of PVC, the stretching vibration of the double bonds is detected at 1667 cm^?1 by the correlation of the double bond contents and the intensities of the absorption bands. The stretching vibration at 1667 cm^?1is in accordance with those of model compounds with a 1-chloro-2-alkene structure.