The effect of Co(II)‐mediated catalytic chain transfer on the emulsion polymerization kinetics of methyl methacrylate

The effect the catalytic chain transfer agent, bis[(difluoroboryl) dimethylglyoximato] cobalt(II) (COBF), on the course of the ab initio emulsion polymerization of methyl methacrylate, and the product properties in terms of the molecular weight distribution were investigated. The emulsion polymerization kinetics have been studied with varying surfactant, initiator, and COBF concentrations. The experimentally determined average number of radicals per particle strongly depends on the concentration of COBF and proves to be in good agreement with the results of model calculations. The apparent chain transfer constant, determined up to high conversion, is in excellent agreement with the predicted value based on a mathematical model based on COBF partitioning and the Mayo equation. The results of this work enhance the fundamental understanding of the influence a catalytic chain transfer agent has on the course of the emulsion polymerization and the control of the molecular weight distribution. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5078–5089, 2009     

Trimethylsilyl triflate as an initiator for cationic polymerization: Improved initiation through the use of promoters

Trimethylsilyl triflate (TMSOTf) can be used as an initiator for the cationic polymerization of alkenes and heterocycles. However, TMSOTf without additives and promoters acts inefficiently. Initiation in the cationic polymerization of tetrahydrofuran is slow because of unfavorable charge distribution in the trimethylsilyltetrahydrofuranium cation—a product of the reaction of monomer with TMSOTf. Acetone, 1,3-dioxolane, and 1,2-propylene oxide have been used as promoters to react with TMSOTf to create more reactive initiating species and to improve efficiency of initiation. Of these promoters, 1,2-propylene oxide has been the most successful. When TMSOTf has been used to initiate the polymerization of 2-methyl-2-oxazoline, unfavorable charge distribution in the N-trimethylsilyl-2-methyl-2-oxiranium cation has produced an unreactive imine dimeric cation which extends the time required for polymerization to several weeks. 1,2-Propylene oxide has been utilized to prevent formation of the imine dimeric cation by producing a more reactive initiating species. In the polymerization of isobutyl vinyl ether initiated by TMSOTf, 1,2-propylene oxide has been shown to be ineffective as a promoter, but acetone can be used successfully. © 1995 John Wiley & Sons, Inc.     

Phosphate‐Loaded Hydrogel Nanoparticles for Sepsis Prevention Prepared via Inverse Miniemulsion Polymerization

Local depletion of intestinal phosphate triggers changes in bacterial phenotypes that adversely affect the health of the host. This article describes a process for encapsulating phosphates in crosslinked poly(ethylene glycol) diacrylate (PEGDA) nanoparticles using inverse miniemulsion polymerization as a drug delivery approach for sustained release of phosphates to the intestinal epithelium. The effects of crosslinker, PEGDA co‐monomer, N‐vinyl pyrrolidone, (NVP) and surfactant concentrations on the nanoparticle size distribution, swelling ratio and monomer conversion are investigated. Increased surfactant and PEGDA concentrations result in smaller particle size and swelling ratio. A copolymerization model of crosslinking is used to predict conversion and gelation dynamics as a function of polymerization conditions. The model assumes that bulk polymerization can be used to approximate inverse miniemulsion polymerization with an aqueous‐phase initiator. The initiator efficiency is used as an adjustable parameter to simulate the conversion dynamics, thus accounting for radical confinement effects and interaction with emulsifier molecules.     

Molecular‐Weight‐Distribution Modelling of Radical Polymerization in Batch and Continuous Reactors with Transfer to Polymer Leading to Gel Formation

Full chain‐length distribution (CLD) modelling applying the Galerkin finite‐element method^[1] (FEM) to polymerization reactors featuring a certain degree of gel formation is confronted with extremely long computation times. The paper describes a new method to predict CLDs for systems where gel formation may occur. The new concept is to model a part of the CLD up to a cut‐off length L, while satisfying the full set of population balances. With transfer to polymer as the mechanism responsible for gelation, this gives rise to a closure problem, which has been solved by assuming the dead CLD beyond L to be represented by a part of a Flory distribution. The method could be proved to work by performing simulations and comparing cut‐off CLDs to full CLDs for non‐gelling systems and comparing results for different L for systems with gelation. The model is demonstrated for polymerization reactors, the batch reactor and the continuous stirred‐tank reactor (CSTR), with either disproportionation or recombination termination. Reliable results are obtained for systems with moderate gel formation. Comparing these results to those from moment models including balance equations up to the fourth moment, a number of interesting differences have been found.     

Molecular Weight Development in Free‐Radical Polymerization with Polyfunctional Chain‐Transfer Agents, 1. Equal Reactivity Model

The analytic expression for the weight‐average molecular weight development in free‐radical polymerization that involves a polyfunctional chain‐transfer agent is proposed. Free‐radical polymerization is kinetically controlled; therefore, the probability of chain connection with a polyfunctional chain‐transfer agent as well as the primary chain‐length distribution changes during the course of polymerization. We consider the primary chains formed at different times as different types of chains, and the heterochain branching model is used to obtain the weight‐average chain length at a given conversion level in a matrix formula, described as P_w = W { D _w + ( I + T ) SP ( I – TSP )^–1 D_f }. Because the primary chains are formed consecutively, the number of chain types N is extrapolated to infinity, but such extrapolation can be conducted with the calculated values for only three different N values. The criterion for the onset of gelation is simply described as a point at which the largest eigenvalue of the product of matrixes, TSP reaches unity, i. e., det  ( I – TSP ) = 0. The present model can readily be extended for the star‐shaped polyfunctional initiators, and the relationships between the model parameters and kinetic rate expression for such reaction systems are also shown.     

Direct Transformation of N,N′‐Methylene Bisacrylamide Self‐Assembled Fibers Into Polymer Microtubes via RAFT Polymerization

A novel fabrication method of polymer tubes with simple operation process and high yield is presented. N,N′‐methylene bisacrylamide (MBA) polymer microtubes are fabricated via reversible addition–fragmentation chain transfer (RAFT) polymerization using MBA self‐assembled fibers as both the template and monomer source. The resulting products are characterized by SEM, TEM, FTIR, and element analysis. The mechanical properties of the gel‐like product and the MBA organogel are measured by rheometer. The morphology of the polymer tubes obtained via RAFT polymerization is compared with the sample obtained via conventional radical polymerization. Based on the current investigations, the fabrication mechanism of this method is initially proposed.     

Atom transfer radical polymerization of methyl methacrylate catalyzed by ion exchange resin immobilized Co(II) hybrid catalyst

Ion exchange resin immobilized Co(II) catalyst with a small amount of soluble CuCl₂/Me₆TREN catalyst was successfully applied to atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) in DMF. Using this catalyst, a high conversion of MMA (>90%) was achieved. And poly(methyl methacrylate) (PMMA) with predicted molecular weight and narrow molecular weight distribution (M_w/M_n = 1.09–1.42) was obtained. The immobilized catalyst can be easily separated from the polymerization system by simple centrifugation after polymerization, resulting in the concentration of transition metal residues in polymer product was as low as 10 ppm. Both main catalytic activity and good controllability over the polymerization were retained by the recycled catalyst without any regeneration process. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1416–1426, 2008     

Multivariate Composition Distribution in Free‐Radical Multicomponent Polymerization, 1

Statistical multicomponent polymerization is a typical example of a Markovian process for which the generating function approach can be applied. Up to the present, generating functions have been used mainly to obtain analytical solutions. However, recent advances of computer software capable of handling symbolic calculations can throw new light on the old mathematical technique. After formulating the equations representing the instantaneous composition distribution of polymers for a given chain length, r, the illustrative numerical calculations are conducted by using the symbolic calculator. For a multicomponent polymerization consisting of more than two components, the second component distribution is dependent on the composition of the first component (F₁), which is represented by the conditional probability given r and F₁, . It is found that is well approximated by the Gaussian distribution with the variance following the relationship, , as in the case of the first component distribution , where A and B are the constants. With the knowledge of chain length distribution, it is now possible to conduct the full analysis of multivariate distribution of chain length and compositions for multicomponent free‐radical polymerization.

Bivariate distribution of composition F₁ and F₂ for chain length r = 100 in a three‐component system.     

A simulation model for long-chain branching in vinyl acetate polymerization: 1. Batch polymerization

A new simulation model for the kinetics of long-chain branching formed via chain transfer to polymer and terminal double-bond polymerization is proposed. This model is based on the branching density distribution of the primary polymer molecules. The theory of branching density distribution is that each primary polymer molecule experiences a different history of branching and provides information on how each primary polymer molecule is connected with other chains that are formed at different conversions, therefore making possible a detailed analysis on the kinetics of the branched structure formation. This model is solved by applying the Monte Carlo method and a computer-generated simulated algorithm is proposed. The present model is applied to a batch polymerization of vinyl acetate, and various interesting structural changes occurring during polymerization (i.e., molecular weight distribution, distribution of branch points, and branching density of the largest polymer molecule) are calculated. The present method gives a direct solution for the Bethe lattice formed under nonequilibrium conditions; therefore, it can be used to examine earlier theories of the branched structure formation. It was found that the method of moments that has been applied successfully to predict various average properties would be considered a good approximation at least for the calculation of not greater than the second-order moment in a batch polymerization. © 1994 John Wiley & Sons, Inc.     

Modeling Nd-Catalyzed Butadiene Rubber Production

Summary: A simulation tool was developed for the industrial solution polymerization of 1,3-butadiene with a Nd-based homogeneous Ziegler-Natta catalyst system. Insight into underlying reaction mechanisms was gained from laboratory experiments. Besides the chain growth reaction, the following steps were identified: catalyst formation, deactivation reactions, and molecular weight control reactions. A kinetic model based on this reaction scheme was developed to quantitatively describe butadiene conversion and product molecular weight distribution. By including process characteristics, the laboratory (batch) model was transferred to the industrial production process. A correlation function relates product molecular weight to the relevant product property Mooney viscosity. This polymerization model was successfully applied, e.g. to optimize product grade transitions and to maintain high product quality by predicting the influence of process changes.     

Evaluation of the Chain Length Distribution in Free‐Radical Polymerization, 1. Bulk Polymerization

A method for the direct computation of the chain length distribution in a bulk polymerization is developed, based on the discretization procedure introduced by Kumar and Ramkrishna (Chem. Eng. Sci. 1996 , 51, 1311) in the context of particle size distribution. The overall distribution of chain lengths is partitioned into a finite number of classes which are supposed to be concentrated at some appropriate pivotal chain lengths. Several of the involved reactions lead to the formation of chain whose length differs from the pivotal values. Rules have been introduced in order to share chains between two contiguous classes, which have been designed so as to preserve two well‐defined properties of the distribution, such as, for example, two of its moments. The method has been applied to a polymerization system including propagation, bimolecular terminations and two different chain branching mechanisms: chain transfer to polymer and crosslinking. In addition, complex systems such as one with chain length‐dependent kinetic constants or a two‐dimensional distribution of chain length and number of branches have been considered.     

Elementary reaction and anionic polymerization of isopropenly t-butyl ketone

Isopropenyl t-butyl ketone (IPTBK) does not undergo radical homopolymerization and its anionic polymerization is a slow equilibrium process with a low ceiling temperature, which is due to its limited conjugation imposed by steric hindrance. Equimolar reactions of IPTBK with several anionic initiators were carried out, products isolated and identified by ¹H-and ¹³C-NMR, and product distributions determined by GC. While n-butyllithium and phenyllithium preferentially produce allyl alcohols, Grignard reagents predominantly undergo β-addition to produce mono-adducts, and a significant amount of dimers. t-Butyllithium and t-butylmagnesium chloride provide the cleanest β-addition with minimal dimer formation and no carbonyl addition. However, Grignard reagent do not yield a polymer. The 1:1 reaction mixture of IPTBK with t-butyllithium is very stable at 0°C, providing a methyl-terminated mono-adduct quantitatively when quenched with methyl iodide after 29 h. Addition of a second IPTBK to the mono-adduct anion appears to be affected by the low ceiling temperature. Although t-butyllithium can efficiently reduce as well as add to di-t-butyl ketone, such reactions are minor in the presence of IPTBK. Anionic polymerization of IPTBK with t-butyllithium was carried out under several conditions. The 1:1 model reactions and the lack of acidic hydrogens in its structure suggest that anionic polymerization of IPTBK with t-butyllithium may be “living.” The molecular weight distribution of the polymers ranged from 1.1 to 1.6 with the number-average molecular weight varying from 2,800 to 233,500. Group transfer polymerization of IPTBK produced only a six-membered lactone.     

Theory and simulation of polymerization‐induced phase separation in polymeric media

A rigorous model of polymerization‐induced phase separation (PIPS), based on the non‐linear Cahn‐Hilliard (C‐H) and Flory‐Huggins (F‐H) theories combined with a second‐order polymerization reaction equation, has been formulated and its solutions characterized. The model describes phase separation in system consisting of a non‐reactive polymer and a monomer that undergoes condensation polymerization. The model consists of a balance equation for the low molecular weight polymerization regime and another balance equation for the high molecular weight entangled regime. The model equations are solved, and the solutions are characterized to identify the dynamical and morphological phenomena of the PIPS process. The extent of phase separation increases significantly with time during the early stage of phase separation, and slows down in the intermediate stage. The various types of phase‐separated morphologies are fully characterized using a novel morphological characterization techniques, known as the intensity and scale of segregation. Both the dynamical and morphological features of the PIPS method are sensitive to the magnitudes of the dimensionless diffusion coefficient D* and the dimensionless reaction rate constant K*. The scale of segregation and the droplet size decreases as D* and K* increase. On the other hand, the intensity of segregation increases with K*, but decreases with D*. The present results extend the present knowledge of the PIPS process by taking into account the effects arising from the presence of a non‐reactive polymer.     

The effect of different catalytic chain transfer agents on particle nucleation and the course of the polymerization in ab initio batch emulsion polymerization of methyl methacrylate

The effect a Co(II) based catalytic chain transfer agent (CCTA) has on the course of the polymerization and the product properties of an emulsion polymerization is governed by the intrinsic activity and the partitioning behavior of the catalyst. The effect on the conversion time history, the molecular weight distribution and the particle size distribution is evaluated in batch emulsion polymerization of methyl methacrylate for three different CCTAs, which cover a range of intrinsic activities and partitioning behaviors. It was demonstrated that radical desorption from the particle phase to the aqueous phase preceded by chain transfer is the main kinetic event controlling the course of the polymerization and the product properties in terms of the particle size distribution. The experimental results show that the aqueous phase solubility of the CCTA is the key parameter controlling the course of the polymerization and the particle size distribution. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1038–1048, 2010     

Development of a methodology to predict material properties from environmental exposure. I. Kinetic treatment

This study focuses on bisphenol A polycarbonate and tracks changes in the properties of this material as a function of the degree of degradation, τ, induced by a hostile environment. Among many possible environmental effects, we have limited this investigation to those associated with elevated temperature, although the methodology is general. This τ parameter is a product of the kinetic rate constant, k, found from isothermal kinetics, and the time of degradation, t. The elucidation of τ has been linked to the measurement of the molecular weight distribution, which, in turn, can be related to various properties to yield valuable predictive relationships. Only the thermal history of the polymer and its initial properties are required for the model. This technique is not limited to a specific polymer or even to thermal degradation. As long as the kinetics of the process can be mathematically modeled, this approach should apply to a host of other situations, providing property prediction simply from knowledge of the material history. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 794–801, 2002     

Solid-state polymerization of long-chain vinyl compounds. VI. In-source polymerization of octadecyl acrylate by γ-ray irradiation

The in-source polymerization of octadecyl acrylate in the lamellar crystal (hexagonal packing) by γ-ray irradiation has been investigated, as compared with the two-step and one-step postpolymerizations. The viscosity-average molecular weight is very high even in the initial stage and is practically saturated after 3–5 hr, although the conversion increases successively with time. The molecular weight distribution of poly(octadecyl acrylate) obtained by in-source polymerization is very wide (M _w/M _n = 13.1, at 20°C). The results of in-source polymerization of the long-chain vinyl compounds can be interpreted using the cone model for polymerization probability, similar to those of one-step and two-step postpolymerizations.     

Steady State and Equilibrium in Reversible Copolymerization at Constant Comonomer Concentrations

Selected aspects of copolymerization processes carried on at constant comonomer concentrations are analyzed theoretically and modeled by Monte Carlo method. It is confirmed that some combinations of initial parameters lead to stationary conditions of copolymer formation for both irreversible and reversible systems which can be regarded as the first‐order Markov chain process. However, this study shows that for many copolymerization systems the stationary conditions are attained only at high number‐average degree of polymerization DP _n, and for some reversible copolymerizations, attaining equilibrium, stationary conditions are not observed at all. The analysis shows that the chain length distribution (CLD) for copolymerization carried out under steady state conditions at constant comonomer concentrations, equal to equilibrium concentrations for infinitely high DP _n, is approximately described by the modified Bessel and exponential functions. This type of CLD is analytically proved and confirmed by the Monte Carlo simulations for the analogous homopolymerization process.     

Modeling three-dimensional network formation with an atomic lattice model: application to silicic acid polymerization

We present an atomic lattice model for studying the polymerization of silicic acid in sol-gel and related processes for synthesizing silica materials. Our model is based on Si and O atoms occupying the sites of a body-centered-cubic lattice, with all atoms arranged in SiO(4) tetrahedra. This is the simplest model that allows for variation in the Si-O-Si angle, which is largely responsible for the versatility in silica polymorphs. The model describes the assembly of polymerized silica structures starting from a solution of silicic acid in water at a given concentration and pH. This model can simulate related materials-chalcogenides and clays-by assigning energy penalties to particular ring geometries in the polymerized structures. The simplicity of this approach makes it possible to study the polymerization process to higher degrees of polymerization and larger system sizes than has been possible with previous atomistic models. We have performed Monte Carlo simulations of the model at two concentrations: a low density state similar to that used in the clear solution synthesis of silicalite-1, and a high density state relevant to experiments on silica gel synthesis. For the high concentration system where there are NMR data on the temporal evolution of the Q(n) distribution, we find that the model gives good agreement with the experimental data. The model captures the basic mechanism of silica polymerization and provides quantitative structural predictions on ring-size distributions in good agreement with x-ray and neutron diffraction data.     

Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results

Bulk atom transfer radical polymerization (ATRP) of styrene was carried out at 110 °C using benzal bromide as bifunctional initiator and 1-bromoethyl benzene as monofunctional initiator. CuBr/2,2′-bipyridyl was used as the ATRP catalyst. The polymerization kinetic data for styrene with both initiators was measured and compared with a mathematical model based on the method of moments and another one using Monte Carlo simulation. An empirical correlation was incorporated into the model to account for diffusion-controlled termination reactions. Both models can predict monomer conversion, polymer molecular weight averages, and polydispersity index. In addition, the Monte Carlo model can also predict the full molecular weight distribution of the polymer. Our experimental results agree with our model predictions that bifunctional initiators can produce polymers with higher molecular weights and narrower molecular weight distributions than monofunctional initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2212–2224, 2007