In this study a framework consisting of a computational fluid dynamics simulation coupled to a population balance model for the modeling of emulsion polymerizations is proposed. The combined approach is used to understand the impact of changing length and time scales, as well as mixing conditions on the particle size distribution (PSD) of a polymer latex under different conditions. It is shown that the effect of agitation rate can have a profound impact on the distribution of ionic species in the reactor, and thus on the evolution of the PSD.
A model is developed for hydrolytic copolymerization of caprolactam with hexamethylene diamine (HMD) and adipic acid (ADA) in a batch reactor to produce nylon 6/6,6 copolymer. The reaction mechanism includes hydrolysis of caprolactam and cyclic dimer, polycondensation, polyaddition, transamidation, and ring formation via end biting and back biting. The catalyzing effect of carboxyl groups is accounted for using kinetic parameters from the literature. Model predictions are compared with low‐temperature literature data before simulating reactor conditions of industrial interest. The model predicts a higher degree of polymerization (DP) for nylon 6/6,6 copolymer compared to nylon 6 and 6,6 homopolymers produced using the same reactor conditions. Dynamic changes in concentrations of water, caprolactam, HMD, ADA, and end groups are tracked and used to explain the positive influence of comonomers on reaction rates and DP. Insights gained from this model will form a useful basis to build future models of continuous industrial reactors.
Chain‐shuttling polymerization with dual catalysts has introduced a new class of polyolefins called olefin block copolymers (OBCs). A dynamic Monte Carlo model to describe the kinetics of chain‐shuttling copolymerization in a semi‐batch reactor is developed, and used it to study how the microstructure of OBCs with different numbers of blocks per chain evolves during polymerization. The model also describes how chain‐shuttling rate constants and concentration of chain‐shuttling agent affect populations of OBCs with different numbers of blocks per chain. These model predictions are useful to make OBCs with precisely designed microstructures.
The preparation of forced gradient polymers has received considerable attention using batch reactors, while the preparation of usable quantities of forced gradient copolymers using continuous flow reactors has been hampered by the need to vary the composition of the monomer feedstock continuously during the reaction. A reactor that allows for addition of a monomer feedstock continuously at all points along the length of the reactor tubing allows for the preparation of forced gradient copolymers in continuous flow reactors, allowing for the scale‐up and bulk preparation of these polymers. This study reports here the initial investigation of preparing forced gradient copolymers using the reversible addition–fragmentation chain transfer methodology in tube‐in‐tube continuous flow reactors.
The authors apply the method of moments to the study of network formation in continuous flow stirred reactors when chain transfer to polymer and coupling are present in the reaction scheme. This approach leads to analytical solutions for the various moments involved. The authors start by assuming that the rate of coupling is proportional to the length of dead chains, which allow them to review and extend previous work in this area. This is followed by similar derivations when a coupling agent is present and the rate of coupling is proportional to the number of coupling groups that such agent leaves in dead polymer molecules, demonstrating that higher values of second order moments can be reached at lower levels of unreacted coupling agent.
Significant progress has been made over the past 20–30 years in terms of the ability to develop and solve mechanistic models of emulsion polymerization processes, and in particular models for prediction of the particle size distribution. However, this does not imply that modeling of these economically important processes is by any means a “solved problem,” or that it is no longer necessary to perform fundamental research in this area. There are a number of areas where strong scientific work would increase the understanding of the process, including events in the aqueous phase, radical entry into growing particles, monomer partitioning, and especially the mechanisms and modeling of particle coagulation.
The effect of prepolymerization on ethylene homopolymerization and ethylene/1‐hexene copolymerization with a commercial TiCl4/MgCl2 catalyst was investigated and the apparent homo‐ and copolymerization rate constants were estimated by varying polymerization temperature, pressure, time, and 1‐hexene/ethylene molar ratio during the prepolymerization. The apparent rate constants for activation, propagation, and deactivation depend on the prepolymerization conditions, showing that the prepolymerization stage strongly regulates the behavior of the catalyst in the main polymerization. Interestingly, the surface morphology of the prepolymer particles correlates to and explains these changes in polymerization kinetics behavior.
Polymer microgels with sizes of some tens to hundreds of micrometers can be formed with exquisite control by droplet‐based microfluidic templating. This study presents a systematic assessment of the effect of the premicrogel droplet size on the ability of production of such microgels. The focus is on two popular acrylamide‐derivatives at a fixed monomer concentration and external polymerization temperature. An exponential dependence of the success of droplet gelation on the droplet size is found, which can be rationalized in view of the balance between production and transfer of heat within and from the droplets on basis of a simple Arrhenius argument.
The present article reveals important roles of metal alkyl activators in tuning the performance of the Phillips catalyst in ethylene polymerization. The addition of aluminum alkyl aids the activation of the catalyst, while excess addition leads to the loss of the activity. The balance between the activation and deactivation depends on the type of employed aluminum alkyl, and tri‐n‐octylaluminum offers the most efficient catalyst usage by preferentially suppressing the deactivation. The passivation of aluminum trialkyl with a hindered phenol mildens not only the deactivation but also chain transfer reactions, leading to an increment of high molecular weight fractions.
Strategies have been successfully developed for the monitoring of the homo and copolymerization of styrene and butyl acrylate in a miniemulsion system using near‐infrared (NIR) spectroscopy. Different concentrations of costabilizer, stearyl methacrylate, are tested to obtain the best stabilization condition. The spectral data are associated with the properties of the reaction medium, such as particle average diameter, conversion, number, and surface area of particles, through linear regression based on partial least squares. It is observed that the NIR spectrophotometer is sensitive to the dynamics of miniemulsion polymerization reactions, thus confirming the promising aspect of NIR technology for monitoring the latex properties.
The homopolymerization of the water‐insoluble N‐(isobutoxymethyl)acrylamide (IBMA) is investigated for the first time by nitroxide‐mediated polymerization. The homopolymerization is characterized by a linear increase in number average molecular weight (Mn) versus conversion (X) to X > 0.80 while maintaining dispersities of Mw/Mn < 1.30. A strong Arrhenius relationship correlates the apparent rate constants and the homopolymerization temperatures between 105 and 120 °C. All poly(IBMA) homopolymers are then successfully chain‐extended with styrene (S) to form well‐defined block copolymers of poly(IBMA)‐b‐poly(S) suggesting a high degree of livingness of the poly(IBMA) macroinitiators. Thermogravimetric analysis and differential scanning calorimetry are both used to characterize the thermal properties of the homopolymers and block copolymers and identify possible unique degradation of the poly(IBMA) block through imide formation at elevated temperatures.
The present work describes a kinetic approach which is able to predict how the internal surface area of polymer particles evolve during suspension copolymerization in the presence of porogen. For such a purpose, the concept of elementary gel structures has been introduced by modeling their surface area through the numerical fractionation technique. Thus, variables such as diluents composition, divinyl monomer concentration, and dilution degree could be assessed in the simulations. The present mathematical model is validated by using different experimental data from literature and a fair agreement is reached. Furthermore, the developed model is also capable of predicting the most significant copolymerization variables, e.g., conversion rate, concentration of species, and average molecular weights.
Computational fluid dynamics (CFD) is used to study the gas–particle heat transfer in gas‐phase olefin polymerizations. Particularly, the effects of particle rotation on the gas–particle heat transfer coefficient and internal particle temperatures are evaluated, showing that particle rotation can exert a significant impact on observed temperature profiles, so that this effect should not be neglected during detailed CFD process simulations. As a consequence, particle rotation can lead to particle cooling and development of spherical gradient symmetry, validating the use of simpler modeling schemes that are based on reaction–diffusion in symmetrical spherical geometry.
This work aims at deriving analytical solutions for the molecular architecture of multi‐block polymer synthesized in a dual‐catalyst single CSTR. While the relevant equations are developed for homopolymerization, they can easily be extended to copolymerization. Special emphasis is placed on the quantities associated with each catalyst rather than the overall ones. However, if all rate parameters are available, the expressions can be used to calculate the properties of the material made by each catalyst as well as the overall ones under various process conditions. Given the reasonable assumption of large residence time, the solutions are simplified to elucidate the kinetics of chain‐shuttling involving two catalysts. It is shown that systems with low chain‐shuttling ability, if DPPn,0 ≠ DPQn,0, may exhibit significant deviation from Flory's most probable distribution. Furthermore, systems with high chain‐shuttling ability produce macromolecules with more uniform architecture and polydispersity index close to 2.
The reactivity ratios for the bulk free‐radical copolymerization of n‐butyl acrylate (BA)/n‐butyl methacrylate (BMA) are estimated at 80 °C. By performing a series of low conversion runs including replicate runs, the reactivity ratios are estimated as rBA = 0.460 and rBMA = 2.008. Runs to high conversions are then conducted at three different feed compositions (fBMA = 0.2, 0.5, and 0.8) to validate the reactivity ratios. The composition data from the high conversion experiments show good agreement with the estimated reactivity ratios in the integrated form of the Mayo–Lewis model. The molecular weight, gel content, and glass transition temperature of BA/BMA copolymers are also determined.
A vertically stirred tubular reactor is designed and studied in this work to perform the styrene batch suspension polymerization. Computational fluid dynamic techniques are applied to acquire information regarding the heat transfer and fluid flow behavior along the reactor. The simulated findings are used to support the experimental results (particle size distribution—PSD) obtained by varying the stirring system configuration, stabilizing agent concentration, and system holdup (styrene/water ratio v/v). According to the results, an efficient temperature control is attained due to the tubular geometry of the equipment. In addition, the PSD broadens by increasing the size of the shaft and the number of impellers installed along the reactor. An evaluation of the particle sedimentation throughout the reaction demonstrates that the PSD and the stirring rate play an important role in the sedimentation kinetics. Such findings demonstrate the potential of the proposed reactor to be explored in order to perform suspension polymerizations semicontinuously or continuously by applying suitable operation strategies.
The synthesis of poly(acrylic acid) (PAA) of low molar mass under safe conditions is difficult due to the high polymerization rate of acrylic acid (AA) and the fast heat generation. The aqueous‐solution “semibatch” polymerization of non‐ionized AA in almost starved conditions involves high initiator loads when low molar masses are required. This article proposes the simultaneous feeding of AA and nonconventional chain transfer agents (CTA) as a strategy aimed at controlling both the molar masses and the generated heat rate. Three CTAs are investigated: 2‐mercaptoethanol, thioglycolic acid, and isopropyl alcohol. Even when PAA of relatively low molar mass can be produced by adequately selecting the flow rates and concentrations of both AA and CTA, it is found that the nature of CTA can have a significant effect on the polymerizations kinetics. The mechanisms responsible for these effects are discussed with the help of a representative mathematical model.
ArF candidate photoresist polymers have been synthesized by nitroxide mediated polymerization (NMP). Statistical copolymerizations of α‐gamma butyrolactone methacrylate, 3‐hydroxy‐1‐adamantyl methacrylate, and 2‐methyl 2‐adamantyl methacrylate with 5–10 mol% of controlling comonomers (i.e., styrene, p‐acetoxystyrene, 2‐vinyl naphthalene, acrylonitrile, and pentafluorostyrene), which are necessary for controlled polymerization of methacrylates by NMP with the unimolecular alkoxyamine initiator BlocBuilder, have been used. As little as 5 mol% controlling comonomer in the feed is demonstrated to be sufficient to produce linear evolution of number average molecular weight against conversion (X) up to X = 0.7 for relatively low target degrees of polymerization. All of the resulting copolymers have relatively low dispersities and show relatively low absorbance at 193 nm, comparable to other 193 nm candidate photoresists reported previously, with the exception of VN‐containing copolymer.
Various MgCl2‐supported Ziegler–Natta (ZN) catalysts are synthesized with the intention to influence polymerization performance and 1‐butene incorporation in an ethylene copolymer. Modifications are introduced during different steps in the synthesis process, namely support preparation, titanation, and catalyst workup. While multiple different effects are observed upon modification, heat treatment during titanation shows the greatest impact. Increasing the heat‐treatment temperature increases polymerization activity. More importantly, the 1‐butene distribution can be shifted toward a more homogeneous profile. The amount of 1‐butene incorporated is similar to both for short‐ and for very long‐chain molecules. This behavior has so far been known only from metallocene‐based polyethylene and suggests that active sites are distributed more homogeneously in the ZN catalyst.
In this article a systematic method is proposed to deconvolute the time‐dependent molecular weight distributions (MWD) and average comonomer fraction profiles of ethylene/1‐olefin copolymers made with heterogeneous Ziegler–Natta catalysts. These distributions with a high‐temperature gel permeation chromatography equipped with an infrared detector at four different polymerization times have been measured and used this information to infer how the fractions of polymer made on each site type varied with polymerization time. The model estimates here the minimum number of active site types needed to describe these copolymers, the MWD of polymer populations made on each site type, and their average comonomer fractions. This method is useful to quantify the microstructure of olefin copolymers made with multiple site type catalysts using the least number of adjustable parameters.
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