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.     

A Detailed Polymerization Model for Cerenol® Polyols

Summary: A mathematical model of the acid catalyzed 1,3-propanediol polymerization has been developed. Two catalysts investigated include sulfuric acid and superacid (tetrafluoroethane sulfonic acid or triflic acid). Based on a detailed reaction mechanism, population and mass balance equations have been derived for small molecules as well as for polymeric species of numerous chain distributions, which are distinguishable in terms of protonation state and end group functionality. Due to the interaction of the sulfuric acid catalyst with the polymer ends, a novel, dual index polymer chain distribution was derived and implemented. The model has been validated with various sets of experimental data obtained in a lab-scale reactor setup. Dynamic model outputs such as monomer concentration, molecular weight averages, unsaturated and sulfate end groups, water evaporation rate and sulfate middle groups have been compared with experimental data of sulfuric and super acid catalyzed polymerization runs. Very good agreement between model predictions and experimental data has been obtained for both catalyst systems over an extended range of conditions using the same set of model parameter values. It is worth noting that the model is also capable of predicting polymerization equilibrium.     

Packed column reactor for continuous atom transfer radical polymerization: Methyl methacrylate polymerization using silica gel supported catalyst

A continuous column reactor packed with silica gel supported CuBr‐HMTETA catalyst has been successfully developed for ATRP of MMA. The reactor had a good catalytic stability up to 100 h. The MMA conversion decreased with an increasing feeding flow rate. The polymerization kinetics was first order with respect to the monomer. The molecular weight increased linearly with conversion, demonstrating the living character. Possible flow back‐mixing and polymer trapping in the pores of silica gel caused some broadening in the molecular weight distribution. This type of packed column reactor is believed to be a significant development for possible commercial exploitation of the ATRP process.     

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.     

Effects of Monomer Flow Rate,Flow Configuration,and Reactor Geometry on the Rate of Plasma Polymerization

The effects of flow rate on the plasma polymerization of ethylene in an rf discharge were investigated using both a tubular and a bell-jar-type of reactor. Both reactors contained parallel plate internal electrodes. Experiments with the tubular reactor showed that both the total thickness of the deposit and its distribution in the axial direction were strong functions of the flow rate. At low flow rates the polymer thickness decreased in the flow direction, while at high flow rates the polymer thickness increased. Each of these observations is explained by a simple model of plasma polymerization. Using the bell-jar reactor, different monomer flow distribution configurations were tested to determine their effect on the distribution of polymer thickness. It was found that distribution or diffusion of the monomer inflow provided a more uniform film.     

Structural analysis of polyethene prepared with rac‐dimethylsilylbis(indenyl)zirconium dichloride/methylaluminoxane in a high‐temperature,continuously stirred tank reactor

A study of ethene solution polymerization with the rac‐dimethylsilylbis(indenyl)‐zirconium dichloride/methylaluminoxane catalyst system in a high‐temperature (140 °C), continuously stirred tank reactor system was carried out. ¹³C NMR, gel permeation chromatography, Fourier transform infrared, and rheological measurements were used for polymer analyses. Polyethylenes with low molecular weights (weight‐average molecular weight ≈ 35–55 kg/mol) and small amounts of methyl, ethyl, and long‐chain branching were produced. ¹³C NMR measurements showed that the long‐chain and methyl branches increased and that the ethyl branch contents decreased with decreasing monomer concentrations. At high monomer concentrations, the chain transfer to the coordinated monomer was concluded to be the predominant chain termination mechanism, whereas the chain transfer to aluminum was dominant at low monomer concentrations, which was evidenced by the fact that the selectivity of end groups was reduced to about 50%. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3292–3301, 2002     

Simulation of free radical high-pressure copolymerization in a multi-zone autoclave reactor: compartment model investigation

A compartment model is used to describe the complex flow of a high-pressure ethylene copolymerization process in an industrial multi-feed multi-zone autoclave reactor at steady state operation conditions. To capture the imperfect mixing effects due to fresh initiator injection, each zone is considered as a set of three interconnected well mixed CSTRs with recycle streams. Volumes of the reactors and the recycle flow are adjusted to get the best fit with results of steady state well mixed analysis for each zone. Once the temperature and conversion as state variables in each reaction volume are known, the properties of polymer produced in each zone and those of final polymer can be determined. Using a realistic set of kinetic mechanisms, temperature, monomer conversion, molecular weights and short and long chain branching frequencies in each zone and at the exit point of the reactor are estimated. Some of the model results are compared with experimental data obtained for an industrial reactor.     

Model prediction of batch emulsion copolymerization as a function of conversion: A sensitivity analysis

Recently a model has been developed capable of predicting absolute monomer concentrations and their ratios in the polymer, aqueous, and monomer droplet phases as a function of conversion in batch emulsion copolymerizations without using any adjustable parameters. In this article the sensitivity of model predictions of composition drift toward deviations of 10% in all model parameters (maximum swellabilities of monomer in the polymer phase, water solubilities, reactivity ratios, and monomer and polymer densities) was estimated using the monomer combination methyl methacrylate-styrene as an example. From the sensitivity analysis it can be concluded that the reactivity ratios are the most important parameters affecting composition drift. The effects of deviations in maximum swellabilities and monomer and polymer densities on composition drift can be neglected, while the water solubility is important only in those cases where the amount of monomer in the aqueous phase cannot be neglected as compared with the total monomer amount. © 1994 John Wiley & Sons, Inc.     

Distribution of polymer deposition in plasma polymerization. I. Acetylene,ethylene, and the effect of carrier gas

Factors which influence the distribution of polymer deposition in an electrodeless glow-discharge system were investigated for acetylene and ethylene. Under the conditions in which “full glow” is maintained, the distribution of polymer deposition from pure monomer flow systems is nearly independent of flow rate of monomer or of the system pressure in discharge, but is largely determined by the characteristic (absolute) polymerization rates (not deposition rate) of the monomers. Acetylene has a high tendency to deposit polymer near the monomer inlet, whereas ethylene deposits polymer more uniformly in wider areas in the reactor. The addition of carrier gas such as argon or partially copolymerizing gas such as N₂, H₂, and CCl₂F₂ was found to narrow the distribution of polymer deposition. The distribution of polymer deposition is also influenced by a glow characteristic which is dependent on flow rate and discharge power.     

Kinetics of Living Polymerization with Propagation Rate Constants Depending on Degree of Polymerization

A study is presented on the kinetics of living polymerization in which the propagation rate constants decrease to zero at a certain degree of polymerization of the propagating chain. The general solution for the distribution function and the rate of polymerization is given and two special cases are discussed. When all the propagation rate constants are the same up to a critical degree of polymerization and null beyond it, the polymerization proceeds approximately as a normal living polymerization until the number-average degree of polymerization reach 85 to 90% of the critical value. When the propagation rate constants decrease linearly with the degree of polymerization, the distribution of living polymer is narrower than the usual Poisson distribution and the reaction order of the rate of polymerization with respect to monomer concentration is between first and second and is affected by the initial monomer and catalyst concentrations.     

Cationic polymerization of isoprene in the presence of the TiCl4-trichloroacetic acid catalyst system

Cationic polyisoprene characteristic of different molecular parameters can be obtained with high yields in the presence of the TiCl₄-trichloroacetic acid catalyst system. At low monomer concentrations, polyisoprene has a unimodal molecular-mass distribution. At elevated monomer concentrations, the polydispersity of polyisoprene increases significantly with conversion because of chain transfer to the polymer and branching. As the TiCl₄/trichloroacetic acid ratio in the catalyst and the total concentration of the catalytic complex increase, the average molecular masses of the produced cationic polyisoprene decrease as a result of chain transfer to trichloroacetic acid.     

Prediction of polymer composition in batch emulsion copolymerization

Monomer partitioning in emulsion copolymerization plays a key role in determining composition drift and polymerization rates. The combination of recently developed thermodynamically based monomer partitioning relationships with mass balance equations, makes predictions of monomer partitioning in emulsion copolymerizations possible in terms of monomer mole fractions and monomer concentrations in the particle and aqueous phases. Using this approach, the effects of monomer to water ratios and polymer volumes on the monomer mole fraction within the polymer particle phase in a nonpolymerizing system at thermodynamic equilibrium can be determined. Comparison of these monomer partitioning predictions with experiments for the monomer system methyl acrylate—vinyl acetate shows good agreement. Furthermore, composition drift occurring in a polymerizing system as a function of conversion can be predicted if the assumption is made that equilibrium is maintained during reaction. Comparison of predictions with experimental results for emulsion copolymerizations of the monomer systems methyl acrylate—vinyl acetate and methyl acrylate—indene shows good agreement. © 1994 John Wiley & Sons, Inc.     

Evaluation of mass transfer rate during Ziegler-Natta propylene polymerization

Mass transfer which affects the rate of propylene polymerization with titanium trichloride–triethylaluminum, has been evaluated by use of a new method developed for this heterogeneous reaction. The polymerization was carried out with the usual flask reactor equipped with a paddle stirrer; the rate of gas absorption into the polymerization slurry was proportional to stirring speed and the reciprocal of the total amount of polymers produced. It has been confirmed that the polymerization rate separated from the absorption rate is purely kinetic (propagation), and an effective physical process, such as monomer transfer through a polymer film covering the catalyst surface, no longer exists.     

Mathematical Modeling of the Long‐Chain Branch Structure of Polyolefins Made with Two Metallocene Catalysts: An Algebraic Solution

A mathematical model was developed to describe the populations of polymer chains containing different numbers of long‐chain branches (LCBs) made with a combination of two single‐site catalysts. One of the catalysts produces only linear chains (linear‐catalyst) and the other produces linear and long‐branched chains (LCB‐catalyst). The model shows that when the selectivity for macromer formation of the linear‐catalyst is the same as that of the LCB‐catalyst, it is not possible to maximize the number of LCB per chain, even though the number of LCB per 1 000 carbon atoms (C) can be maximized. On the other hand, if the selectivity for macromer formation of the linear‐catalyst is higher than that of the LCB‐catalyst, both LCB/1 000 C and LCB/chain pass through maxima when varying the fraction of the linear‐catalyst in the reactor. More importantly, polymer populations with different numbers of LCB per chain will reach their maximum values at different ratios of linear‐catalyst to LCB‐catalyst, thus permitting the maximization of individual polymer populations in the mixture.     

Stereoblock polymerization of methyl methacrylate with VOCl3?Al(C2H5)3 catalyst system

Kinetics of the polymerization of methyl methacrylate with the VOCl₃? AlEt₃ catalyst system at 40°C in n-hexane have been studied. A linear dependence of rate of polymerization on the monomer and catalyst concentrations as well as an overall activation energy of 5.87 kcal/mole were found. Characterization of the structure of the polymer by NMR spectra revealed the presence of stereoblock units. The mechanism of polymerization is discussed in relation to the kinetic data obtained.     

Stereospecific polymerization of methacrylonitrile. VI. Effect of esters as a complexing agent with diethylmagnesium catalyst

The stereospecific polymerizations of methacrylonitrile with diethylmagnesium were carefully studied by using various ethers as complexing agents. The complexed ethers exhibit a beneficial effect on the stereoregularity of the resulting polymer, namely, the crystallinity increased by using ethers as a complexing agent. The polymerization rate and the molecular weight of the polymer also increased by using ether-complexed catalysts. The polymerization behavior was studied with the dioxane–diethylmagnesium complex as a typical complexed catalyst. The behavior was mostly similar to that of the diethymagnesium alone, that is, the rate of the polymerization increased in proportion to monomer concentration, and the solubility index increased with increasing monomer concentration. Interestingly, the viscosity of the acetone-insoluble fraction increased with increasing monomer concentration, while that of the acetone-soluble fraction was independent of monomer concentration. This is explained by considering that the catalyst has at least two kinds of catalytic species, one being the species that produces the crystalline polymer by a coordinated anionic polymerization, another being the one from which an amorphous polymer is obtained by a conventional anionic mechanism. The fact that the viscosity of the polymer decreased with increasing the initiator concentration is explained in terms of chain trasfer to the initiator. In case of diethylmagnesium alone, the viscosity of the polymer is independent of the initiator concentration.     

An Improved Model for Polyether Production from 1,3‐Propanediol

A dynamic mathematical model is developed for production of Cerenol polyether from 1,3‐propanediol in a batch reactor system. The model accounts for polycondensation reactions and side reactions in the liquid phase and for mass transfer of volatile species to the vapor. Parameters are estimated using measured liquid‐phase concentrations of monomer, oligomers, water, and end groups as well as the mass and composition of condensate collected from the overhead condenser system. The proposed model uses novel probability factors to keep the model equations relatively simple while accounting for the complex influence of superacid catalyst on reaction rates. The model is a significant advance over previous Cerenol models because it better accounts for mass‐transfer rates and for the dynamic behavior of the condenser. In addition, the proposed model accounts for the inhibitory influence of water on polycondensation kinetics due to hydration of hydroxyl ends. The model equations and parameter estimates provide a substantial improvement in fit to the data, especially for long reaction times and high catalyst levels, resulting in a 97% reduction in the value of the weighted least squared objective function compared to equations and parameters from a previous model.     

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.     

Mathematical modeling of a slurry reactor for DME direct synthesis from syngas

In this paper,an axial dispersion mathematical model is developed to simulate a three-phase slurry bubble column reactor for direct synthesis of dimethyl ether(DME) from syngas.This large-scale reactor is modeled using mass and energy balances,catalyst sedimentation andsingle-bubble as well as two-bubbles class flow hydrodynamics.A comparison between the two hydrodynamic models through pilot plantexperimental data from the literature shows that heterogeneous two-bubbles flow model is in better agreement with the experimental data thanhomogeneous single-bubble gas flow model.Also,by investigating the heterogeneous gas flow and axial dispersion model for small bubblesas well as the large bubbles and slurry(i.e.including paraffins and the catalyst) phase,the temperature profile along the reactor is obtained.Acomparison between isothermal and non-isothermal reactors reveals no obvious performance difference between them.The optimum values ofreactor diameter and height were obtained at 7 m and 50 m,respectively.The effects of operating variables on the axial catalyst distribution,DME productivity and CO conversion are also investigated in this research.     

Propylene polymerization through supported metallocene/ MAO catalysts: Kinetic analysis and modelling

Several propylene polymerizations are carried out with supported metallocene catalyst, prepared by reaction of silica gel with methylaluminoxane and then with rac-dimethylsi-lanediylbis(indenyl)zirconiumdichloride. The rate–time curves obtained are analyzed to understand the influence of support and triisobutylaluminium on the reaction. As a first attempt to model this system we developed a partially new praticle growth model, based on a shell by shell fragmentation hypothesis (gradual break-up from the outside to the inside of the particle), and a final multigrain structure of the particle. A kinetic scheme including the TIBA interaction with the supported catalyst is also presented. The model prediction and the experimental data are compared for the rate–time curves and polymer properties. © 1995 John Wiley & Sons, Inc.