Evaluation of rate constants from experimental batch reactor data for anionic polymerization of poly(methyl methacrylate) at high temperatures

At high temperatures, in anionic polymerization, depolymerization and autocyclization reactions cannot be ignored and the molecular weight distribution (MWD) results based on irreversible polymerization give erroneous results. In this article, we have developed a semianalytical solution for the MWD of the polymer for a general complex mechanism. We then show that the various rate constants can be directly determined from the experimental data on MWD. After evaluating these, it is possible to model the anionic polymerization more rationally, as we have demonstrated using the experimental data from the literature. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65:845–859, 1997     

Polymerization mechanisms and molecular weight distribution. II. AIBN-initiated polymerization of styrene at 60°C

An experimental study was carried out on the AIBN-initiated polymerization of styrene at 60°C. The kinetic rate constants were determined by the method of moments and the MWD method, which was proposed in a previous paper. The results compared favorably with the data in the literature and the MWD method was noted to yield more consistent results than the method of moments, which indicates the importance of considering the whole molecular weight distribution. The theoretical MWD was found to approximate the experimental MWD well. The chain-transfer constant to AIBN was found to be between 0.09 and 0.14.     

Modeling of the bulk free radical polymerization up to high conversion—three stage polymerization model I. Model examination and apparent reaction rate constants

In this paper, a simple and useful model, the three stage polymerization model (TSPM) is proposed on the basis of recent experimental evidence and our preliminary treatment of the experimental kinetic results found in the literature. The model accounts for gel effect and glass effect in bulk free-radical polymerization. Equations for calculating the conversion of the polymerization reaction are derived based on TSPM. Using experimental kinetic data available in the literature, general expressions for apparent reaction rate constants in three stages for methylmethacrylate (MMA) and styrene (St) are obtained. In general, the experimental kinetic data can be treated very well with the TSPM from the low conversion stage to high conversion, except for some experimental data near the transition points. However, the deviation for this data may be reasonably explained by the non-isothermal effects that occur in this regime of experiments. This deviation is smaller for a smaller ampoule reactor used in polymerization experiments because of its better heat transfer ability. In order to establish that there is no glass effect stage when the reaction temperature is greater than the glass transition temperature for a polymerization process, some experimental data for ethylmethacrylate (EMA) bulk polymerization at a reaction temperature higher than its glass transition temperature were checked with TSPM. The plots show that the model is also suitable for EMA bulk polymerization.     

Polymerization mechanisms and molecular weight distributions. III. Gamma-radiation-initiated polymerization of methyl methacrylate

The termination mechanism in gamma-radiation-initiated polymerization of methyl methacrylate was investigated. The termination mechanism and the associated rate constants were determined by comparing the theoretical molecular weight distribution (MWD) and the experimental MWD, which was determined by gel permeation chromatography. Disproportionation occurs 1.2 times as frequently as combination at 30°C and 0.5 times as frequently at 0°C. The activation energy for disproportionation is 5.5 kcal/mole greater than that for combination. The rates of initiation were determined by a new method and were found to compare well with those reported in the literature. It is also suggested that it is necessary for the theoretical MWD to have the same shape as the experimental MWD before a mechanism can be authenticated.     

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     

Polymerization of butadiene in toluene with nickel(II) stearate–diethyl aluminum chloride catalyst. II. Kinetic study

Based on the polymerization data presented in part I of this series, a kinetic mechanism for the polymerization of butadiene in toluene initiated with nickel(II) stearate–diethyl aluminum chloride was proposed. Expressions for the conversion, the degree of polymerization, and the cis content were derived. Those models were then used to correlate the experimental data from which the rate constants were estimated. A quantitative discussion of various aspects of the polymerization is also presented.     

Rate and molecular weight distribution modeling of syndiospecific styrene polymerization over silica-supported metallocene catalyst

The kinetics of syndiospecific polymerization of styrene over silica-supported Cp^∗Ti(OCH₃)₃/MAO catalyst has been investigated through experimentation and theoretical modeling. At low monomer concentrations, the polymerization rate increases almost linearly with monomer conversion, but the reaction rate becomes independent of monomer concentration at high bulk phase monomer concentrations. A kinetic model that incorporates the monomer partition effect between the solid and the liquid phases has been proposed. The model simulations show that the observed non-linear kinetics can be adequately modeled by the monomer partition model. The polymer molecular weight has also been found to increase with the monomer concentration and the polymer molecular weight distribution (MWD) is quite broad, suggesting that the catalytic behavior deviates from the single site catalytic polymerization model. The MWD broadening is modeled by a two-site kinetic model and a good agreement between the model and the experimental data has been obtained.     

Pseudokinetics for the copolymerization of butadiene and styrene produced using n-butyl lithium and N,N,N′,N′-tetramethylethylenediamine,considering different reactivities of the structural units

The anionic solution copolymerization of butadiene and styrene prepared by anionic living polymerization using an initiator composed of n-butyl lithium, and N,N,N′,N′-tetramethylethylenediamine as active center modifier was modeled as a tetrapolymerization. The kinetic model proposed considering that the reactivity of the active sites is different because of varying configurations cis, trans, vinyl, and styryl. From the reaction scheme expressions to rate of monomers consumption, microstructure and dyad formation were obtained. With the first-order Markov model, the expressions for the fraction of active sites and dyad distribution as a function of the conditional probabilities were obtained. Therefore, the model proposed is different to kinetic models previously reported, because it allows obtaining the parameters kinetic in order to know the distribution of the isomeric species presents in the copolymerization of butadiene and styrene, and the intrinsic reactivity of configurational active sites. The rate constants were determined by fitting to the conversion and dyad experimental data using the nonlinear least square method. The experimental data reported in the literature, monomer conversion and microstructure, in addition to dyad sequence distribution were correctly predicted.     

Polymer chain extension in semibatch emulsion polymerization with RAFT‐based transfer agent: The influence of reaction conditions on polymerization rate and product properties

A mathematical model was developed for batch and semiemulsion polymerizations of styrene in the presence of a xanthate‐based RAFT agent. Zero–one kinetics was employed along with population balance equations to predict monomer conversion, molecular weight (MWD), and particle size (PSD) distributions in the presence of xanthate‐based RAFT agents. The effects of the transfer agent (AR), surfactant, initiator, and temperature were investigated. Monomer conversion, MWD, and PSD were found to be strongly affected by monomer feed rate. The polymerization rate (Rp), number average molecular weight (Mn) and particle size (r) decreased with increasing AR. With increases in surfactant and initiator concentrations Rp increased, whereas with increase in temperature Mn decreased, Rp increased and r increased. In semibatch mode, Mn and r increased with increase in monomer flow rate. By feeding the RAFT agent along with the monomer (F_M/F_AR = N_Mo/N_ARo = 100), Mn attained a constant value proportional to monomer/RAFT molar ratio. The observed retardation in polymerization and growth rates is due to the exit and re‐entry of small radicals. Thus, chain extension was successfully achieved in semibatch mode. The simulations compared well with our experimental data, and the model was able to accurately predict monomer conversion, Mn, MWD, and PSD of polymer products. Our simulations and experimental results show that monomer feed rate is suitable for controlling the PSD, and the initial concentration and the feed rate of AR for controlling the MWD and PSD. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Emulsion polymerization kinetics and its reactor design. II. The MWD behavior in isothermal batch operation

The emulsion polymerization of styrene in an isothermal batch operation can be divided into three stages, and the corresponding kinetic rate equations are obtained from the experimental conversion-reaction time curve. The course of polymerization between the beginning of the reaction and any subsequent time is successfully computed for the reaction rate, the MWD, and the average degree of polymerization using the intergrals of these rate equations, which could readily explain the behavior of the emulsion polymerization. A comparison is made between the theoretical results and the experimental data. Both the theoretical treatment and the experimental data predict that the MWD for a typical emulsion polymerization is characterized by the rapid decrease in M _w/M _w ratio at the entrance of the zero-order stage and a gradual increase in the first-order stage regardless of an autoacceleration effect. An autoacceleration effect in the first-order stage is, however, evidence for a typical emulsion polymerization.     

Simulation of reversible nylon-66 polymerization in homogeneous continuous-flow stirred tank reactors

Experimental data of Ogata¹ has been curve-fitted to obtain the forward and reverse rate constants for nylon-66 polymerization. Its molecular weight distribution (MWD) has been simulated in homogeneous continuous-flow stirred tank reactors (HCSTR) for 11 h of residence time when the reaction mass is very close to equilibrium. The set of algebraic equations have been solved using Brown's algorithm,² which was found to be more efficient compared to the Gauss-Jordon techniques of solution. The MWD thus obtained is compared with our earlier simulation of the molecular weight distribution from batch reactors³ and was found to differ significantly. In HCSTR, the weight fraction distribution does not undergo a maximum and the polydispersity index ρ of the polymer formed is much higher than that obtained from batch reactors. The number and weight average of the polymer formed in HCSTR is found to be significantly lower.     

Continuous free-radical polymerization of styrene in the stirred tank reactor. Effect of inhibitors

The influence of inhibitors (p-benzoquinone) on the conversion and the molecular weight distribution (MWD) during free radical polymerization (AIBN) of styrene was examined. A continuous stirred tank reactor (CSTR) was used for the experiments. The concentration of the inhibitor and initiator, the mean residence time and the reaction temperature were modified. The measurement of the residence time distribution (macroscopic mixing) and the estimation of the segregation number showed an ideal mixing behaviour (HCSTR). The conversion and the MWD were calculated. As the results show, it is possible to calculate the reaction in a HCSTR by only using the kinetic constants measured in discontinuous runs.     

Algorithms for Using Some Models of Gel and Glass Effects in Free-Radical Polymerization of Methyl Methacrylate

The aim of this article is the modeling and simulation of the batch bulk polymerization of methyl methacrylate (MMA). Simple dependencies between the propagation and termination rate constants and monomer conversion for the gel and glass effects are proposed. The empirical parameters in these relations are determined from conversion and molecular-weight experimental data obtained under various reaction conditions (initiator concentration and temperature). Sometimes, different relations were necessary to express the variation of the kinetic constants on conversion subintervals. Thus, these models have been used continuously or discontinuously, as a function of their results. An algorithm for using this model was also established.

The analysis of this model has two aims: (1) to get a good agreement between simulation and experiment; (2) to provide a simple model to be used under different reactor conditions (batch, semibatch, or continuous) or which can be easily handled in polymer engineering studies, such as sensitivity analysis, optimal control, and so forth.     

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     

Dynamic prediction of the bivariate molecular weight-copolymer composition distribution using sectional-grid and stochastic numerical methods

In the present study, a two-dimensional fixed pivot technique (2-D FPT) and an efficient Monte Carlo (MC) algorithm are described for the calculation of the bivariate molecular weight-copolymer composition (MW-CC) distribution in batch free-radical copolymerization reactors. A comprehensive free-volume model is employed to describe the variation of termination and propagation rate constants as well as the variation of the initiator efficiency with respect to the monomer conversion. Simulations are carried out, under different reactor conditions, to calculate the individual monomer conversions, the leading moments of the ‘live’ and ‘dead’ polymer chain length distributions as well as the dynamic evolution of the distributed molecular properties (i.e., molecular weight distribution (MWD), copolymer composition distribution (CCD) and joint MW-CC distribution). The validity of the numerical calculations is examined via a direct comparison of the simulation results, obtained by the two numerical methods, with experimental data on the styrene-methyl methacrylate batch free-radical copolymerization. Additional comparisons between the 2-D FPT and the MC methods are carried out for different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular and copolymer properties, with high accuracy, up to very high monomer conversions. It is also shown that the proposed dynamic MC algorithm is less computationally demanding than the 2-D FPT.     

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.     

Application of statistical experimental design in Ziegler–Natta polymerization of butadiene

The results of butadiene polymerization initiated with CoCl₂ · 4Py/Et₂AlCl/H₂O are presented. The effectiveness of statistical experimental design techniques is demonstrated in identifying the individual and joint effects of polymerization variables on rate constants, molecular weights, and polydispersity. The proposed conversion model, representing polymerization with instantaneous initiation and bimolecular termination, was found to provide an adequate representation of experimental conversion data. Evidence indicates that water is not only directly involved in the initiation reaction but also plays an important role in the chain transfer reaction.     

丁二烯/苯乙烯阴离子连续溶液共聚反应模型化研究

针对n_BuLi引发剂引发的丁二烯／苯乙烯阴离子连续溶液共聚反应,结合共聚机理与反应器操作模式,建立了完全混合全混流模式下共聚单体转化率及分子量分布模型,并借助共聚单体转化率实验结果,对共聚单体转化率模型进行参数估计,求得了4个链增长速率常数。在此基础上,进行了分子量分布模型的模拟计算,并将模拟结果与共聚物分子量分布的实测结果进行了比较。研究结果表明,建立的模型能较为满意地描述丁二烯／苯乙烯阴离子连续溶液共聚反应的单体转化率和分子量分布。     

Propylene polymerization in a semibatch slurry reactor over supported TiCl4/MgCl2/ethyl benzoate/triethyl aluminum catalyst. II. A kinetic study based on a multisite model

In propylene polymerization over TiCl₄/MgCl₂/ethyl benzoate (EB)/triethyl aluminum (TEA) catalysts, experimental evidence strongly suggests that active sites have differing propagation and termination rate constants. Although the chemical structure of these sites may be quite similar, their location on the support may affect their polymerization activity, and this results in a distribution of the propagation and deactivation rate constants. To model this type of system, we developed a kinetic model accounting for multiple active sites. The model was fitted to simulated polymerization data to investigate the validity of mathematical approximations used in the derivation of the model equation. Using experimental data, the adequacy of the model was tested, and the statistical inference of parameter estimation was also discussed. The effects of experimental operating variables and additives on the kinetic model parameters revealed an important insight into the fundamentals of this system. The optimum productivity commonly observed has been shown to be the result of differing rates of increase of both propagation and termination rates with Al/Ti ratio and temperature. Kinetic evidence also suggests that the additive selectively poisons atactic-specific sites.     

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.