Mathematical modeling of seeded miniemulsion copolymerization for oil-soluble initiator

A mathematical model of seeded miniemulsion copolymerization of styrene-methyl methacrylate for oil-soluble initiator is presented. The mathematical model includes the mass transfer, from the miniemulsion droplets to the polymer particles, by both molecular diffusion and collision between miniemulsion droplets and the polymer particles. The mathematical model also includes the calculation of both the distribution of partices with i radicals and the average number of radicals per particle in the miniemulsion copolymerization using oil-soluble initator. Studies were carried out on the mass transfer coefficients of monomers across the interface between the miniemulsion droplet and the aqueous phase, hexadecane concentration in the miniemulsion droplets, the miniemulsion droplet sizes, and the collision between miniemulsion droplets. The results indicated that the copolymerization of styrene-methyl methacrylate was not a mass transfer controlled process. The mass transfer by collision between miniemulsion droplets and polymer particles plays an important role and was included in the model in order to predict the experimental data of seeded miniemulsion copolymerization.     

Miniemulsion copolymerization of vinyl acetate and butyl acrylate. II. Mathematical model for the monomer transport

A mathematical model is presented to describe the monomer transport between monomer droplets, aqueous phase, and polymer particles during the course of an emulsion polymerization. The model was used to investigate the role of the cosurfactant (hexadecane) in the miniemulsion copolymerization of 50:50 molar ratio vinyl acetate-butyl acrylate monomer mixture, as well as the effect of the different components and process variables on the rate of copolymerization, monomer distribution between phases, and composition of the copolymer.     

Fundamental studies of grafting reactions in free radical copolymerization. II. Grafting of styrene,acrylate, and methacrylate monomers onto cis-polybutadiene using AIBN initiator in solution polymerization

Grafting can be initiated by primary and/ or polymer radical attack on the backbone polymer and it is well known that AIBN does not readily promote grafting, even when using poly-butadiene. We have studied the grafting of several different monomers onto cis-polybuta-diene using AIBN initiator and find dramatically different results among the monomers. As expected, styrene grafts at very low levels due to the inactivity of the initiator radicals and the polystyryl radicals. Methacrylate monomer grafts at a slightly higher level due to its more reactive polymer radical, while acrylate monomer readily grafts onto the poly-butadiene because polyacrylate radicals are quite reactive. The use of a kinetic model allowed the evaluation of rate coefficients for graft site initiation to be in the relative order of 0.1 : 1.0 : 10.0 (L/mol/s) for styrene:methacrylate:acrylate monomers. The model also pro-vided successful interpretations of the grafting data and its dependence upon the concen-trations of monomer, initiator, and backbone polymer. Due to the relatively higher reactivity of the polyacrylate radicals, the benzene solvent acted as a chain transfer agent in this system. This affected the molecular weight of both free and grafted acrylate polymer and also surpressed the graft level. Polyacrylate radicals attack the cis-polybutadiene backbone by abstracting an allylic hydrogen and also adding across the residual double bond. The latter mechanism is responsible for the majority of the grafting; the hydrogen abstraction leads to relatively inactive radicals which cause a retardation in the overall reaction rate. © 1995 John Wiley & Sons, Inc.     

Free-radical multicomponent polymerization reactors and chemical composition distribution

Formulae to calculate the statistically caused instantaneous copolymer composition distribution as well as the chemical distribution of accumulated macromolecules, which is due to polymerization statistics and shifts in mean polymer composition during the reaction process, are derived on the basis of a universal model for free-radical solution polymerization with any number of monomers proceeding in a batch, semi-batch or continuous, ideally mixed vessel. The influence of the reactor type on chemical composition distributions is investigated for a copolymerization of different reactive components (methyl methacrylate/styrene/maleic anhydride), a system with nearly equal reactive monomers (methyl methacrylate/styrene), and the ternary polymerization of methyl methacrylate/styrene/maleic anhydride. Though products of constant mean composition are obtainable in a semi-batch or steady-state continuous reactors, considerable statistical dispersion cannot be removed in any case.     

Simulation of Molecular Weight Distributions Obtained by Pulsed Laser Polymerization (PLP): New Analytical Expressions Including Intramolecular Chain Transfer to the Polymer

A new approach for the simulation of PLP (pulsed laser polymerization) is presented. This approach allows one to obtain new analytical solutions for different polymerization schemes, including either chain transfer to the monomer or intramolecular chain transfer to the polymer. The first results of the simulation of PLP experiments on n‐butyl acrylate at 20 °C and ambient pressure are presented.

MWDs simulated for PLP of n‐butyl acrylate, in bulk at 20 °C and ambient pressure using three models: the model with intramolecular chain transfer to the polymer (solid line), the model with chain transfer to monomer (dashed line), and the classical model (dotted line).     

乳液聚合共聚物玻璃化转变温度及其理论计算

从共聚单体的竞聚率、油相水相分布系数出发,通过动力学模拟计算了丙烯酸丁酯与醋酸乙烯酯乳液共聚物的链结构,并用Johnson公式对其玻璃化转变温度(T_g)进行了理论计算,给出了共聚物T_g及其对应聚合物的重量分布图。发现半连续共聚物有1个T_g,其值随共聚物组成而变化;但一步法共聚物有两个T_g:低温区T_g代表富丙烯酸丁酯共聚物,高温区T_g则代表PVA均聚物。计算结果与实验十分吻合。     

Characterization of polymer-silica nanocomposite particles with core-shell morphologies using Monte Carlo simulations and small angle X-ray scattering

A two-population model based on standard small-angle X-ray scattering (SAXS) equations is verified for the analysis of core-shell structures comprising spherical colloidal particles with particulate shells. First, Monte Carlo simulations of core-shell structures are performed to demonstrate the applicability of the model. Three possible shell packings are considered: ordered silica shells due to either charge-dependent repulsive or size-dependent Lennard-Jones interactions or randomly arranged silica particles. In most cases, the two-population model produces an excellent fit to calculated SAXS patterns for the simulated core-shell structures, together with a good correlation between the fitting parameters and structural parameters used for the simulation. The limits of application are discussed, and then, this two-population model is applied to the analysis of well-defined core-shell vinyl polymer/silica nanocomposite particles, where the shell comprises a monolayer of spherical silica nanoparticles. Comprehensive SAXS analysis of a series of poly(styrene-co-n-butyl acrylate)/silica colloidal nanocomposite particles (prepared by the in situ emulsion copolymerization of styrene and n-butyl acrylate in the presence of a glycerol-functionalized silica sol) allows the overall core-shell particle diameter, the copolymer latex core diameter and polydispersity, the mean silica shell thickness, the mean silica diameter and polydispersity, the volume fractions of the two components, the silica packing density, and the silica shell structure to be obtained. These experimental SAXS results are consistent with electron microscopy, dynamic light scattering, thermogravimetry, helium pycnometry, and BET surface area studies. The high electron density contrast between the (co)polymer and the silica components, together with the relatively low polydispersity of these core-shell nanocomposite particles, makes SAXS ideally suited for the characterization of this system. Moreover, these results can be generalized for other types of core-shell colloidal particles.     

Dipalladium Catalyst for Olefin Polymerization: Introduction of Acrylate Units into the Main Chain of Branched Polyethylene

A dipalladium complex with a double‐decker structure catalyzes ethylene–acrylate copolymerization to produce the branched polymer containing the acrylate units in the polymer chain, not at the branch terminus. The cooperation of the two palladium centers, which are fixed in a rigid framework of the macrocyclic ligand, is proposed to have a significant dinuclear effect on the copolymerization.     

The significance of transfer reactions in pulsed laser polymerization experiments

In this work simulation calculations are presented, which carefully analyze pulse initiated polymerization experiments of butyl acrylate in bulk in an extended temperature range published in the recent literature. Taking into account entire data sets of experimental results, a model has been developed which describes the experiments using a single parameter set. Especially the inadequacies in experiments are also captured by the model, that occur evaluating propagation rate coefficients using the pulsed laser polymerization technique at low laser repetition rates and elevated temperatures. Enhanced chain transfer to small species is identified to be responsible for these effects and transfer rate constants are derived from the simulations. The model is then used to test experimental strategies in order to expand the k_p determination towards temperatures higher than 35°C, the maximum temperature for which k_p values of butyl acrylate are available so far. Performing pulsed laser experiments at high laser repetition rates (200 Hz) and initial radical concentrations (1 · 10⁻⁴ mol/L) should prevent the formation of the characteristic structure in the molecular weight distribution to be suppressed by this competing process.     

High Temperature Semibatch Free Radical Copolymerization of Styrene and Butyl Acrylate

Summary: High temperature semibatch free radical solution copolymerizations of n-butyl acrylate (BA) and styrene (ST) were carried out over a range of copolymer composition. The significant increase in experimental polymer weight-average molecular weight with time, as well as the shift in the entire polymer molecular weight distribution, is explained by assuming fast β-scission of BA midchain radicals with an adjacent styrene unit, followed by subsequent addition of the resultant macromonomer to growing radicals. A mechanistic model including backbiting and β-scission, macronomer incorporation, long-chain branching, and propagation and termination penultimate effects was constructed in Predici; the model provides a good representation of the experimental data using rate coefficients taken from literature.     

Semicontinuous seeded emulsion copolymerization of vinyl acetate and methyl acrylate

The semicontinuous seeded emulsion copolymerization of vinyl acetate and methyl acrylate was investigated. The effect of type of process (starved process versus semi-starved process), type of feed (neat monomer addition versus monomer emulsion addition), amount of seed initially charged in the reactor, and feed rate on the time evolution of the overall conversion, copolymer composition, and polymer particle size was analyzed. It was found that, in the case of the starved process, both monomers, but mainly vinyl acetate, accumulated in the reactor. The preferential accumulation of vinyle acetate resulted in a drift of the copolymer composition. Both monomers accumulation and copolymer composition drift were reduced by increasing the amount of seed initially charged in the reactor and by decreasing the feed rate. For the semi-starved process, it was found that a vinyl aceatate rich copolymer was formed when a low methyl acrylate feed was used, whereas a methyl acrylate rich copolymer was obtained at high methyl acrylate feed rates. For both starved process and semi-starved process, the total number of polymer particles, after an initial increase, reached a plateau value which was the same in all of the experiments carried out. These results were analyzed by means of a mathematical model developed for this system.     

Simulation of the latex particle morphology

A model is presented for the simulation of the structuration of polymer particles under conditions in which the new polymer chains are compatible with the polymer previously formed. The model involves the calculation of the monomer concentration gradients within the particles due to discrepancies in thermodynamic interactions between the monomer and the different polymers present in each part of the polymer particle. In addition, the distribution of free radicals in the latex particle is taken into account. This distribution results from the anchoring of the hydrophilic end-group of the growing polymer chain on the surface of the particle. The model was applied to the simulation of the polymerization of vinyl acetate on a butyl acrylate–vinyl acetate copolymer seed. It was found that the development of the particle morphology was mainly due to the profile of concentration of radicals in the particle. On the other hand, the effect of the monomer–polymer thermodynamic interactions on the particle morphology was found to be negligible. However, it has to be pointed out that this is because, for the system studied, the interaction parameters of vinyl acetate with polyvinyl acetate and polybutyl acrylate are nearly identical.     

Grafting onto Wool. XXVII. Graft Copolymerization of MixeD Vinyl Monomers by Use of Ceric Ammonium Nitrate as Redox Initiator

In order to ascertain the effect of a donor monomer, vinyl acetate (VAc), on the graft copolymerization of acceptor monomers, ethyl acrylate (EA) and butyl acrylate (BA), grafting of mixed vinyl monomers (EA + VAc) and (BA + VAc) was carried out on Himachali wool in aqueous medium using ceric ammonium nitrate (CAN) as a redox initiator. Graft copolymerization was carried out at different temperatures for various reaction periods. Percent grafting and percent efficiency were determined as functions of 1) concentration of mixed vinyl monomers, 2) concentration of CAN, 3) concentration of HNO₃ 4) temperature, and 5) reaction time. VAc, the donor monomer, was found to decrease percent grafting of EA and BA onto wool.     

Termination Rates in Free Radical Copolymerizations

The rates of free radical copolymerizations at given rates of initiation can be analyzed ideally in terms of monomer feed concentrations and reactivity ratios, propagation rate constants for homopolymerizations of the particular monomers, and an overall rate constant for termination during copolymerization. This model, which is due to Atherton and North, can account for the effects of initiator concentration and viscosity of the polymerization medium on copolymerization rates.

This article reports an empirical formulation for the overall termination rate constant in terms of monomer concentrations and reactivity ratios and a cross-termination factor. The new model accounts for experimental data in the styrene-methyl methacrylate system in which polarity differences between unlike radicals may result in enhanced termination rates. It also predicts observed copolymerization rates of methyl methacrylate-vinyl acetate and styrene-α-methylstyrene mixtures in which polarity effects are absent. The cross-termination factor may be approximated from reactivity ratio data for predictive purposes.     

Perspective on metal-mediated polar monomer/alkene copolymerization

A major unsolved problem in polymer synthesis is the design of efficient metal-mediated systems for the copolymerization of alkenes with polar vinyl monomers, such as acrylates and methacrylates. There are several reasons for the absence of efficient transition metal-based insertion copolymerization catalysts. First, following insertion, the ester group of the acrylate coordinates to the metal thereby hindering subsequent monomer coordination. A second reason stems from the preferred 2,1-insertion of acrylates into metal-carbon bonds resulting in the placement of the ester group on the α-carbon. This makes the metal-alkyl species particularly prone to homolysis because of the enhanced stability of the resultant alkyl radical, one that is essentially the same as the propagating species in radical-initiated acrylate polymerization. In this perspective we focus on this issue of facile metal-carbon bond homolysis, especially following acrylate insertion, using examples from our own work. We suggest ways to circumvent these issues, for example forcing 1,2-insertion by imposing steric crowding at the metal. Finally, we discuss the danger of relying on radical traps as probes for polymerization mechanism. Radical traps can react with metal-hydrides and attenuate metal-centered nonradical reactions. However, even when radical traps fail to stop an observed polymerization, it may be wrong to conclude that a nonradical mechanism is at work since the traps can be destroyed under certain reaction conditions.     

Controlled free-radical azeotropic copolymerization of styrene and n-butyl acrylate in the presence of tert-butyl dithiobenzoate

The free-radical azeotropic bulk copolymerization of styrene and n-butyl acrylate at 90°C mediated by tert-butyl dithiobenzoate and copoly(strene—n-butyl acrylate) dithiobenzoate as reversible chain-transfer agents has been studied. It has been shown that low-and high-molecular mass chain-transfer agents allow one to efficiently control the molecular-mass characteristics of the copolymers. For all studied systems, the molecular mass linearly increases with conversion, and the copolymers are characterized by low polydispersity indexes. When polystyryl dithiobenzoate and poly(butyl acrylate) dithiobenzoate are used as polymer reversible chain-transfer agents in the azeotropic copolymerization of styrene and n-butyl acrylate, the diblock copolymers with the controlled block lengths are prepared. As evidenced by ESR studies, radical intermediates are formed in the course of the azeotropic copolymerization of styrene and n-butyl acrylate mediated by tert-butyl dithiobenzoate and the copolymer reversible chain-transfer agent; the kinetics of formation of these intermediates has been investigated. It has been demonstrated that the rate of the azeotropic copolymerization mediated by low-and high-molecular-mass reversible chain-transfer agents decreases with an increase in their concentration. The possible causes of this phenomenon are discussed.     

Sequence selection during copolymerization

We analyze a simple model for the copolymerization of two chemically distinct monomers that displays a wide variety of product sequence compositions depending on the rate coefficients for the stepwise addition of each monomer to a growing polymer chain. We show that in certain regions of parameter space the copolymer sequence composition depends sensitively on these parameter values, and we compute the information content of the resultant sequences. Finally, we show how the model may be used to interpret experimental data on copolymerization reactions.     

Semibatch Atom Transfer Radical Copolymerization of Styrene and Butyl Acrylate

Summary: Batch and semibatch butyl acrylate (BA) polymerizations are carried out using a heterogeneous atom transfer radical polymerization (ATRP) catalyst system, with excellent molecular weight (MW) control maintained at temperatures below 80 °C. A kinetic model, using rate coefficients from literature and catalyst solubility data from this study, provides a good representation of the experimental results, after modifying the model to account for the decrease in rate caused by intramolecular chain transfer. It is also demonstrated experimentally that well-defined random, gradient, and block styrene/BA copolymers can be synthesized by manipulating monomer feed profiles in the ATRP semibatch process.     

Effect of a bi-unsaturated monomer on the emulsion polymerization of ethyl acrylate

The emulsion polymerization and copolymerization of ethyl acrylate with a bi-unsaturated comonomer (divinylbenzene, 1,6-hexamethylene diacrylate), present in small proportions, in the presence of anionic emulsifier sodium dodecyl sulfate have been kinetically investigated at 60°C under batch conditions by gas chromatograhy and gravimetric methods. The rate of polymerization in interval 2 was found to be proportional to the 0,37, 0,23, and 0,5 power of the emulsifier concentration for the system A (ethyl acrylate), the system B (ethyl acrylatedivinylbenzene), and the system C (ethyl acrylate/1,6-hexamethylene diacrylate). Divinylbenzene was found to decrease both the rate of polymerization and the polymer particle size. Addition of 1,6-hexamethylene diacrylate slightly increases both the rate of polymerization and the polymer particle size.