Modeling of molecular weight development in atom transfer radical polymerization

A kinetic model has been developed for atom transfer radical polymerization processes using the method of moments. This model predicts monomer conversion, number‐average molecular weight and polydispersity of molecular weight distribution. It takes into account the effects of side reactions including bimolecular radical termination and chain transfers. The determining parameters include the ratios of the initiator, catalyst and monomer concentrations, as well as the ratios of the rate constants of propagation, termination, transfer and the equilibrium constant between radicals and their dormant species. The effects of these parameters on polymer chain properties are systematically simulated. The results show that an ideal living radical polymerization exhibiting a linear relationship between number‐average molecular weight versus conversion and polydispersity approaching unity is only achievable under the limiting condition of slow monomer propagation and free of radical termination and transfers. Improving polymerization rate usually accompanies a loss of this linearity and small polydispersity. For polymerization systems having a slow initiation, the dormant species exercise a retention effect on chain growing and tend to narrow the molecular weight distribution. Increasing catalyst concentration accelerates the initiation rate and thus decreases the polydispersities. It is also shown that for a slow initiation system, delaying monomer addition helps to reduce the polydispersities. Radical termination and transfers not only slow down the monomer conversion rates but also broaden polymer molecular weight distributions. Under the limiting conditions of fast propagation and termination and slow initiation, the model predicts the conventional free radical polymerization behaviors.     

On the character of molecular weight distribution of polyethylene produced in the presence of the homogeneous catalytic system (C5H5)2TiCl2Al(C2H5)2Cl

Experimental results obtained when studying the kinetics of ethylene polymerization in toluene, as well as data on fractionating polyethylene, are analysed and compared with the results of theoretical consideration of molecular weight distribution on the basis of the proposed kinetic scheme.The constants of the reactions of propagation, initiation, transfer and termination of polymer chains are evaluated and compared with literature data.     

脉冲激光引发自由基聚合的动力学研究

处理了无链转移时脉冲激光引发自由基聚合中的动力学问题:推导出聚合产物数均和重均分子量的严格数学表达式,给出了链自由基、死聚物及总的聚合产物的归一化的分子量分布函数,计算结果表明:随着单体转化率的上升,各种分子参数,例如数均和重均分子量,以及多分散指数的数值周期性地振荡,且振幅逐渐下降,分子量分布曲线则包含一些特征峰,且随着每次脉冲激光产生的初级自由基浓度的降低,分布曲线峰的数目增加,另外,与歧化终止相比,偶合终止使产物的分子量分布略为变窄.     

甲基丙烯酸甲酯聚合动力学和分子量模型及仿真

考虑甲基丙烯酸甲酯聚合过程中体积收缩，反应物和生成物的浓度变化，以及由于凝胶、玻璃化和笼闭等效应对各速率常数和物性参数的影响，从基元反应和物料平衡出发，推导了半间歇，有链转移剂参与情况下的聚合动力学和分子量模型。用模型仿真计算了聚合温度、引发剂、溶剂和链转移剂的种类和浓度等对甲基丙烯酸甲酯聚合动力学和聚合过程中分子量变化的影响规律，并与实验和文献数据进行比较。     

Nonsteady-state kinetics for anionic polymerization of polar monomer initiated instantaneously by electron transfer

With the help of the nonsteady-state method, the kinetic differential equations for the anionic polymerization of polar monomer initiated instantaneously by electron transfer with monomer termination are treated rigorously. The expressions for the molecular weight distribution, the number-average and weight-average degrees of polymerization, and the functionality distribution are derived in closed form. A theoretical means is established by which all the molecular parameters of the polymer can be calculated from polymerization conditions, such as the reaction constants, the concentrations of initiator and monomer, and the monomer conversion.     

Kinetics of initiation, propagation, and termination for the [rac-(C(2)H(4)(1-indenyl)(2))ZrMe][MeB(C(6)F(5))(3)]-catalyzed polymerization of 1-hexene.

Metallocene-catalyzed polymerization of 1-alkenes offers fine control of critical polymer attributes such as molecular weight, polydispersity, tacticity, and comonomer incorporation. Enormous effort has been expended on the synthesis and discovery of new catalysts and activators, but elementary aspects of the catalytic processes remain unclear. For example, it is unclear how the catalyst is distributed among active and dormant sites and how this distribution influences the order in monomer for the propagation rates, for which widely varying values are reported. Similarly, although empirical relationships between average molecular weights and monomer have been established for many systems, the underlying mechanisms of chain termination are unclear. Another area of intense interest concerns the role of ion-pairing in controlling the activity and termination mechanisms of metallocene-catalyzed polymerizations. Herein we report the application of quenched-flow kinetics, active site counting, polymer microstructure analysis, and molecular weight distribution analysis to the determination of fundamental rate laws for initiation, propagation, and termination for the polymerization of 1-hexene in toluene solution as catalyzed by the contact ion-pair, [rac-(C(2)H(4)(1-indenyl)(2))ZrMe][MeB(C(6)F(5))(3)] (1) over the temperature range of -10 to 50 degrees C. Highly isotactic (>99% mmmm) poly-1-hexene is produced with no apparent enchained regioerrors. Initiation and propagation processes are first order in the concentrations of 1-hexene and 1 but independent of excess borane or the addition of the contact ion-pair [PhNMe(3)][MeB(C(6)F(5))(3)]. Active site counting and the reaction kinetics provide no evidence of catalyst accumulation in dormant or inactive sites. Initiation is slower than propagation by a factor of 70. The principal termination process is the formation of unsaturates of two types: vinylidene end groups that arise from termination after a 1,2 insertion and vinylene end groups that follow 2,1 insertions. The rate law for the former termination process is independent of the 1-hexene concentration, whereas the latter is first order. Analysis of (13)C-labeled polymer provides support for a mechanism of vinylene end group formation that is not chain transfer to monomer. Deterministic modeling of the molecular weight distributions using the fundamental rate laws and kinetic constants demonstrates the robustness of the kinetic analysis. Comparisons of insertion frequencies with estimated limits on the rates of ion-pair symmetrization obtained by NMR suggest that ion-pair separation prior to insertion is not required, but the analysis requires assumptions that cannot be validated.     

High-conversion polymerization. I. Theory and application to methyl methacrylate

The concept of polymer entanglements has been applied in conjunction with classical free-radical kinetics to describe vinyl polymerizations carried to high conversion. A kinetic model has been developed on the assumption that two populations of radicals exist in a high-conversion polymerization system: those radicals whose chain lengths are long enough to become entangled with neighboring molecules and have, therefore, a restricted mobility; and those shorter radicals whose mobilities are not strongly affected by diffusional effects. It has also been assumed that the kinetic rate constant for the termination step between entangled radicals is inversely proportional to the mean entanglement density. The model contains only two parameters in addition to the kinetic rate constants required to describe low-conversion polymerizations. One of these parameters can be determined, at least in principle, from measurements of solution properties of the polymer-monomer mixtures. The model so developed has been tested against experimental data obtained from the literature on the bulk polymerization of methyl methacrylate. The agreement between predicted and experimental monomer conversions and molecular weight averages is found to be satisfactory.     

SET‐LRP of methyl methacrylate initiated with sulfonyl halides

Single electron transfer‐living radical polymerization (SET‐LRP) represents a robust and versatile method for the rapid synthesis of macromolecules with defined architecture. The present article describes the polymerization of methyl methacrylate by SET‐LRP in protic solvent mixtures. Herein, the polymerization process was catalyzed by a straightforward Cu(0)wire/Me₆‐TREN catalyst while initiation was obtained by toluenesulfonyl chloride. All experiments were conducted at 50 °C and the living polymerization was demonstrated by kinetic evaluation of the SET‐LRP. The process follows first order kinetic until all monomer is consumed which was typically achieved within 4 h. The molecular weight increased linearly with conversion and the molecular weight distributions were very narrow with M_w/M_n ～ 1.1. Detailed investigations of the polymer samples by MALDI‐TOF confirmed that no termination took place and that the chain end functionality is retained throughout the polymerization process. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2236–2242, 2010     

Modeling the reversible addition–fragmentation transfer polymerization process

A kinetic model has been developed for reversible addition–fragmentation transfer (RAFT) polymerization with the method of moments. The model predicts the monomer conversion, number‐average molecular weight, and polydispersity of the molecular weight distribution. It also provides detailed information about the development of various types of chain species during polymerization, including propagating radical chains, adduct radical chains, dormant chains, and three types of dead chains. The effects of the RAFT agent concentration and the rate constants of the initiator decomposition, radical addition, fragmentation, disproportionation, and recombination termination of propagating radicals and cross‐termination between propagating and adduct radicals on the kinetics and polymer chain properties are examined with the model. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1553–1566, 2003     

Kinetics of polymerization reactions with reversible-chain termination

General kinetic features of radical and ionic polymerization processes accompanied by reversible chain termination reactions are considered. Special attention is paid to the conditions of applicability of the steady-state approximation usually employed to analyze the kinetics of radical polymerization. It is shown that the steady-state concentration of radicals is attained at practically the very beginning of the reaction, while the steady-state concentration of a reversible termination agent is reached with a certain delay. A kinetic explanation of the reversible termination reaction effect on the pattern of the molecular-mass distribution is suggested. Conditions providing the obtainment of a polymer with a narrow molecular-mass distribution in processes with reversible termination are formulated.     

Simulation model for the molecular weight distribution in emulsion polymerization

A Monte Carlo simulation model for the kinetics of emulsion polymerization is proposed. In the present model, the formation of each polymer molecule is simulated by the use of only a couple of probability functions; therefore, the calculation can be handled well even on personal computers. It is straightforward to account for virtually any kinetic event, such as the desorption of oligomeric radicals and chain length dependence of kinetic parameters, and as a consequence very detailed information such as the full distributions of the dead polymer molecular weights and the macroradicals among various polymer particles can be obtained. When bimolecular terminations are the dominant chain stoppage mechanism, the instantaneous molecular weight distribution (produced in a very small time interval) becomes broader than that for homogeneous polymerizations due to a higher possibility that short and long polymer radicals react with each other if bimolecular reactions are fast enough. The increase in the polydispersity of the MWD is fairly large, especially when bimolecular termination by disproportionation is significant; however, the gel permeation chromatography (GPC) may not be a suitable analytical technique to detect such broadening since oligomeric peaks may not be observed in the elution curve. The present simulation method provides greater insight into the complicated phenomena of emulsion polymerizations. © 1995 John Wiley & Sons, Inc.     

Reversible addition-fragmentation chain transfer polymerization in microemulsion

This tutorial review first details the uncontrolled microemulsion polymerization mechanism, and the RAFT polymerization mechanism to provide the necessary background for examining the RAFT microemulsion polymerization mechanism. The effect of the chain transfer agent per micelle ratio and the chain transfer agent aqueous solubility on the RAFT microemulsion polymerization kinetics, polymer molecular weight and polydispersity, and polymer nanoparticle size are discussed with a focus on oil-in-water microemulsions. Modeling of RAFT microemulsion polymerization kinetics and the resulting final polymer molecular weight are presented to assist with the analysis of observed experimental trends. Lastly, the current significance of RAFT microemulsion polymerization and the future directions are discussed.     

STUDIES ON TiCI4/Mg (OEt)_2/EB SUPPORTED CATALYSTS FOR PROPYLENE POLYMERIZATION

The supported catalysts for propylene polymerization were prepared by milling Mg (OEt)_2 with EB (ethylbenzoate) and treating with TiCl_4 solution. When TiCl_4/(Mg(OEt)_2/EB) (mol.) ratio was increased, decrease in contents of-OEt and Ti of the catalysts was observed, while the content of EB increased. It is proved by analyses of IR, X-ray and XPS that during co-milling Mg(OEt)_2 with EB no reactions have taken place. But after treatment with TiCl_4 solution, Mg(OEt)_2 converts into MgCl_2 and EB coordinates on the resulting MgCl_2 carrier, a surface complex forms.The activity of catalysts,isotacticity and vicosimetric molecular weight of polypropylene increase with the decrease of the content of ethoxyl group. The kinetic curves of propene polymerization obtained with present catalysts system display decay curves. It is found from the triad tacticity calculated from the expanded spectra of methyl carbon region that, ethoxyl group in catalyst has an effect on the configuration of polymer chain.     

Molecular weight distribution in emulsion polymerizations

A mathematical formulation is given which describes the evolution of the number distribution of the molecular weight (MWD) of linear polymer chains that grow in emulsion polymerization systems. The resulting set of coupled ordinary differential equations takes into account the microscopic events of free radical entry, exit, chain annihilation, bimolecular termination (by combination and disproportionation), and chain transfer in a mono- or polydisperse system. Simple analytic solutions are presented for systems in which the number of particles, as well as the average number of free radicals per particle, is constant and in which the rate coefficients are size independent. These solutions indicate that compartmentalization of the free radicals in the latex particles results in a significant increase in the polydispersity of the polymer produced by emulsion polymerization, compared with that in bulk systems. The theory shows that significant mechanistic information may be obtained from experimental MWDs and that, in principle, experimental conditions may be prescribed to grow a desired MWD. The MWDs are presented in a novel manner that facilitates the comparison of theory with experiment.     

Influence of catalyst depletion or deactivation on polymerization kinetics. III. Solution polymerization of acrylonitrile in N,N-dimethylformamide at −30°C.

The experimental results on homogeneous polymerization of acrylonitrile initiated with the sodium triethylthioisopropoxyaluminate, NaAlEt₃S(i-Pr), catalyst in DMF at ?30°C. are compared with the prediction of equations based on a postulated mechanism. The agreement between the calculated and observed number-average molecular weight combined with the kinetic data and the relationship between the conversion and the initial catalyst concentration provides a rigorous test concerning the validity of the equations and the mechanism of the polymerization. A plausible mechanism is postulated as follows: The initiation must be relatively fast in accordance with the rate equations and the growing polymer undergoes propagation, transfer (to monomer), and deactivation simultaneously. The infrared spectrum of the low molecular weight polymer prepared at a high catalyst concentration showed strong absorption at 2337, 2205, and 1620 cm.^?1 but no absorption at 900 cm.^?1, indicating that there are two nitriles in the polymer, one of which is conjugated. The possibility of having ? CH?CH₂ groups in the polymer is ruled out by the absence of the band at 900 cm.^?1. In view of these facts, it is concluded that the polymer has a ? CH?CHCN endgroup resulting from the transfer reaction.     

Polymerization of epoxidized vegetable oil derivatives: Ionic‐coordinative polymerization of methylepoxyoleate

Ring‐opening polymerization of epoxidized methyloleate (EMO) with various ionic‐coordinative initiators have been studied and compared with other internal epoxy monomers: benzyl 9,10‐epoxyoleoylether and cis‐4,5‐epoxyoctane. The structure and molecular weight of the resulting polymers have been studied by ¹H‐ and ¹³C‐NMR, MALDI‐TOF‐MS, and size exclusion chromatography analysis. Polymers with higher molecular weight than those obtained with conventional cationic catalyst are obtained. These materials have been found to consist of a complex mixture of cyclic and linear polymer chains with different chain ends that can be related to the catalyst nature and the occurrence of two main polymerization mechanisms, the cationic and the ionic‐coordinative. In the polymerization of EMO, transesterification by‐side reactions leading to ester linkages in the main chain have been identified. These undesired reactions have been suppressed by copolymerization with small amounts of tetrahydrofuran with no substantial decrease in the polymer yield and molecular weight. Finally, the polymerization of EMO has been tested in a larger scale to prepare a renewable resource‐based polyether as starting material to produce polyether polyols for polyurethane applications. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Molecular weight distributions in radiation-induced polymerization. IV. A comprehensive kinetic scheme for polymerization in the liquid state

A comprehensive kinetic scheme is proposed which takes into consideration γ-ray-initiated polymerization via free radical, cationic, or radical-cationic species, or their combinations, and the relative contribution of each depending upon experimental conditions. From this kinetic model, equations describing the kinetics of polymerization and the resulting molecular weight distributions have been derived. The resulting expressions are complex in nature, particularly for the case where a combination of mechanisms is involved. In view of this, a general approach to the problem of generating theoretical molecular weight distributions based on the application of high speed digital computers has been presented. The proposed technique is particularly powerful since no simplifying assumptions or mathematical approximations are required in order to obtain the molecular weight distribution.     

Influence of Termination and Transfer on Molecular Weight Distribution of Polymers. III. Spontaneous Termination

This article deals with the kinetics of ionic polymerization with instantaneous initiation and spontaneous termination. The set of kinetic differential equations was solved rigorously by means of nonsteady-state analysis. Even though the expressions of the molecular size distribution function and other molecular parameters include an exponential integral function, all the molecular parameters can easily be computed numerically. Thus, this work is significant for controlling and regulating the relevant polymerizations.     

Diffusion-controlled vinyl polymerization. I. The gel effect

It is well known that the reaction rate and molecular weight of vinyl polymers can change markedly during the course of polymerization and that these changes are due to the influence of diffusion on the termination reaction. The chain length dependence of the termination rate constant has been considered in this work and has resulted in a general method of treating the polymerization kinetics and molecular weight distribution. This method is independent of the form of the chain length dependency and is capable of dealing with both disproportionation and recombination modes of termination. A specific model for the termination rate constant with chain length dependence is proposed and is based on free volume theory and entanglement coupling. Master curves for the characteristics of the reaction rate and molecular weight distribution are presented with the application of this model.