The Role of a Metallocene Additive in Radically Initiated Polymerization when Solving Direct and Inverse Kinetic Problems

Polymerization of methyl methacrylate, initiated by benzoyl peroxide in the presence of titanocene dichloride, is considered from the point of view of formal kinetics. Based on the kinetic scheme of the process (which includes the reactions of classical radical polymerization, the reaction of benzoyl peroxide with titanocene dichloride, the reactions of the controlled radical polymerization of organometallic mediated radical polymerization (OMRP) and atom transfer radical polymerization (ATRP), the reaction of the formation of a coordinating active site and the coordinating chain propagation on a mathematical model of the kinetics of the process is created. This model also makes it possible to calculate the molecular-mass characteristics of poly(methyl methacrylate). As a result of the solution of the inverse kinetic problem at a temperature of 343 K, the values of the reaction rate constants of the kinetic scheme are found under which the discrepancy between the calculated models and experimental data is minimal. Using the developed model of the kinetics of the process, a numerical experiment is performed (i.e., a direct kinetic problem is solved). This problem revealed the following regularities of the process. (1) An increase in the initial concentration of titanocene dichloride at a constant initial concentration of benzoyl peroxide leads to an increase in the rate of consumption of benzoyl peroxide but not to an increase in the initial rate of the process compared to classical radical polymerization. (2) With an increase in the initial concentration of titanocene dichloride, the lifetime of the macroradicals at the initial stage of the process is reduced, and hence the molecular weight of the resulting polymethyl methacrylate is less than that of the polymethyl methacrylate obtained in the absence of titanocene dichloride, and it will increase during the process of approaching the final values. (3) During the polymerization of methyl methacrylate, initiated by benzoyl peroxide in the presence of titanocene dichloride, a smoothing gel effect (as in the case of the polymerization of methyl methacrylate initiated by benzoyl peroxide in the presence of ferrocene) does not occur since titanocene dichloride forms stable complexes with methyl methacrylate and, consequently, it participates in reactions consuming macroradicals to a lesser degree than ferrocene.     

Modeling of elementary reactions and kinetics of radical‐initiated methyl methacrylate polymerization in the presence of ferrocene

On the basis of quantum chemical modeling, a kinetic scheme of methyl methacrylate polymerization initiated by benzoyl peroxide in the presence of ferrocene was proposed. The process runs by mechanism, which includes the reactions of free radical polymerization, and the reactions leading to formation and operability of two type coordination active sites that are capable of converting into each other. On the basis of the proposed scheme, a kinetic model was developed. This model quantitatively described the following: the experimentally determined time dependences of the methyl methacrylate conversion, the conversion dependencies of the number‐average and weight‐average molar masses of poly(methyl methacrylate), the stereoregularity values of poly(methyl methacrylate), and the time dependencies of the methyl methacrylate conversion upon its polymerization on poly(methyl methacrylate) macroinitiators obtained in radical‐initiated polymerization in the presence of ferrocene. As a result of solving the inverse kinetic problem, the parameters of temperature dependences of the reaction rate coefficients of the proposed kinetic scheme were found.     

Kinetic scheme and rate constants for methyl methacrylate synthesis occurring via the radical–coordination mechanism

Two kinetic schemes of the bulk radical–coordination polymerization of methyl methacrylate initiated by the benzoyl peroxide–ferrocene system are considered from the standpoint of formal kinetics. The most likely kinetic scheme is the one that includes the reactions characteristic of classical radical polymerization and, additionally, reactions of controlled radical polymerization proceeding via the Organometallic Mediated Radical Polymerization mechanism, a reaction generating a coordination active site, and a chain propagation reaction in the coordination sphere of the metal. The temperature dependences of the rate constants for the reactions of this kinetic scheme at temperatures typical of commercial poly(methyl methacrylate) production (313–353 K) have been determined by solving the inverse kinetic problem.     

Quantum Chemistry: A Powerful Tool in Polymer Reaction Engineering

Summary: The potentials of computational techniques based on quantum mechanics, to support and complement the experimental analysis, are examined. Mechanisms and reaction paths involved in the free radical polymerization of widely used monomers are studied through a computational approach based on Density Functional Theory (DFT). First, the attention is focused on the initiation kinetics in order to evaluate the role of the initiators in the polymerization process. Methyl acrylate, methyl methacrylate, acrylonitrile, and styrene homopolymerization using different initiators are studied. Then, propagation kinetics is investigated. In particular, the propagation kinetic rate constants for different kinds of acrylates, methacrylates and acetates are calculated and compared with experimental data reported in the literature. The same computational approach is applied to the study of secondary reactions (backbiting, beta-scission) occurring during free radical polymerizations. Finally, the same methodologies are applied to copolymer systems, with emphasis on the evaluation of the role of penultimate effect. The copolymers vinyl acetate/methyl methacrylate and styrene/methyl methacrylate are investigated as system characterized by weak and strong penultimate effect, respectively.     

Stochastic Simulation of Imperfect Mixing in Free Radical Polymerization

A modified algorithm for the stochastic simulation of chemical reactions subject to mass transfer limitation (imperfect mixing) is presented. This algorithm takes into account the mixing by diffusion of the reacting species between two consecutive reactions. The method is used to simulate the effect of mass transfer limitation in free-radical polymerization. Since this is a stiff reaction network, a hybrid stochastic-deterministic approach is considered. The hybrid stochastic algorithm under imperfect mixing (HSSA-IM) is applied to the bulk polymerization of methyl methacrylate up to high conversions. The accuracy of the algorithm relies on the precise determination of diffusion coefficients during the reaction.     

Computer simulation for the cooligomerization system

In order to clarify the kinetic features of the styrene (A)–methyl methacrylate (B)–CCl₄(S) cooligomerization system, a computer simulation was carried out. The experimental data on the degree of polymerization and the deviation of the cooligomer composition from the statistical steady-state composition were comparatively well explained by calculations based on the kinetic equations derived from the assumed reaction scheme and the values of the velocity coefficients, although the values of the four velocity coefficients in the initiation step and the velocity coefficient of the termination by the coupling of two solvent radicals were estimated. The results of the calculation of the rate of each component reaction show that the following two reactions are the most important in the initiation and in the transfer and termination steps when the [S]/([A] + [B]) ratio is large: where, A, A*, and P are styrene, polystyryl radical, and the cooligomer, respectively. Moreover, it was concluded that the deviation of the cooligomer composition from the statistical steady-state composition was caused by these two reactions.     

Efficient stochastic simulations of complex reaction networks on surfaces

Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations, which are based on the mean-field approximation. However, in case that the surface is partitioned into a large number of disconnected microscopic domains, the number of reactants in each domain becomes small and it strongly fluctuates. This is, in fact, the situation in the interstellar medium, where some crucial reactions take place on the surfaces of microscopic dust grains. In this case rate equations fail and the simulation of surface reactions requires stochastic methods such as the master equation. However, in the case of complex reaction networks, the master equation becomes infeasible because the number of equations proliferates exponentially. To solve this problem, we introduce a stochastic method based on moment equations. In this method the number of equations is dramatically reduced to just one equation for each reactive species and one equation for each reaction. Moreover, the equations can be easily constructed using a diagrammatic approach. We demonstrate the method for a set of astrophysically relevant networks of increasing complexity. It is expected to be applicable in many other contexts in which problems that exhibit analogous structure appear, such as surface catalysis in nanoscale systems, aerosol chemistry in stratospheric clouds, and genetic networks in cells.     

Stochastic simulation of catalytic surface reactions in the fast diffusion limit

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit. This derivation justifies the widely used assumption that the adlayer is in equilibrium for the current coverages and temperature when all reactants are highly mobile. Given the reduced master equation, two novel and efficient simulation methods of lattice gas reactions in the infinite diffusion limit are derived. The first method involves solving the reduced master equation directly for small lattices, which is intractable in configuration space. The second method involves reducing the master equation further in the large lattice limit to a set of differential equations that tracks only the species coverages. Solution of the reduced master equation and differential equations requires information that can be obtained through short, diffusion-only kinetic Monte Carlo simulation runs at each coverage. These simulations need to be run only once because the data can be stored and used for simulations with any set of kinetic parameters, gas-phase concentrations, and initial conditions. An idealized CO oxidation reaction mechanism with strong lateral interactions is used as an example system for demonstrating the reduced master equation and deterministic simulation techniques.     

Diene-functional macromonomers by a single-step free radical addition–fragmentation reaction. Syntheses and kinetics

A new chain transfer agent, 5-tert-butylthio-1,3-pentadiene (TBPD or 7, 7-dimethyl-6-thia-1,3-octadiene) was used in the free radical polymerization of methyl methacrylate and styrene to produce conjugated diene-end capped macromonomers by a free radical addition–fragmentation mechanism. The chain transfer was found to be degradative. A new kinetic model was proposed to describe the retarded polymerization. The kinetic parameters per-taining to transfer, reinitiation, primary radical termination, and mutual termination of the primary radicals were evaluated at different temperatures permitting precise theoretical prediction of the functionalities. The chain transfer constants, calculated using a modified Mayo's equation revealed better transfer properties for MMA. The macromonomers were synthesized by high conversion polymerization. Characterizations of the macromonomers revealed that copolymerization predominated over the fragmentation following 1,4-addition, although the former reaction is not detrimental for the chain-end functionalization. © 1995 John Wiley & Sons, Inc.     

On the origins of approximations for stochastic chemical kinetics

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.     

甲基丙烯酸甲酯聚合动力学和分子量模型及仿真

考虑甲基丙烯酸甲酯聚合过程中体积收缩，反应物和生成物的浓度变化，以及由于凝胶、玻璃化和笼闭等效应对各速率常数和物性参数的影响，从基元反应和物料平衡出发，推导了半间歇，有链转移剂参与情况下的聚合动力学和分子量模型。用模型仿真计算了聚合温度、引发剂、溶剂和链转移剂的种类和浓度等对甲基丙烯酸甲酯聚合动力学和聚合过程中分子量变化的影响规律，并与实验和文献数据进行比较。     

聚羧酸铜/亚硫酸钠体系引发甲基丙烯酸甲酯聚合的研究

以杨梅型(聚丙烯接枝)聚羧酸铜/亚硫酸钠体系引发甲基丙烯酸甲酯水溶液聚合,测得表现聚合速率 R_p=1.2×10~(14)e~(-21,400/RT)[MMA]~(1.3)[Na_2SO_3]~(0.5)[P-Cu]~0 聚合按自由基机理进行。聚羧酸铜/亚硫酸钠/甲基丙烯酸甲酯之间通过“络合-氢转移”过程产生初级自由基。     

Evaluation of polymerization rate by chain length dependence on polymer–polymer termination and primary radical termination in radical polymerization

In order to analyze the polymerization rate at high initiation rate and/or low monomer concentration, the rate equations are derived by a rate formulated previously for polymer–polymer termination and another rate for primary radical termination, which is formulated here (both rates depend on chain length of polymer radical). Such equations would be applicable to the kinetic data in the polymerizations of styrene and methyl methacrylate. This shows that the assumption that both rates are independent of chain length overestimates the rate of primary radical termination.     

Free radical exit in emulsion polymerization. I. Theoretical model

The exit or desorption of free radicals from latex particles is an important kinetic process in an emulsion polymerization. This article unites a successful theory of radical absorption (i.e., initiator efficiency), based on propagation in the aqueous phase being the rate determining step for entry of charged free radicals, with a detailed model of radical desorption. The result is a kinetic scheme applicable to true “zero-one” systems (i.e., where entry of a radical into a latex particle already containing a radical results in instantaneous termination), which is still, with a number of generally applicable assumptions, relatively simple. Indeed, in many physically reasonable limits, the kinetic representation reduces to a single rate equation. Specific experimental techniques of particular significance and methods of analysis of kinetic data are detailed and discussed. A methodology for both assessing the applicability of the model and its more probable limits, via use of known rate coefficients and theoretical predictions, is outlined and then applied to the representative monomers, styrene and methyl methacrylate. A detailed application of the theory and illustration of the methodology of model discrimination via experiment is contained in the second article of this series. © 1994 John Wiley & Sons, Inc.     

Applications of esr techniques to the study of free radical processes and kinetics in acrylic polymerizations

Electron spin resonance (ESR) techniques have been applied to a detailed study of batch and semicontinuous emulsion polymerization of methyl methacrylate; butyl acrylate and styrene have been briefly studied. Quenching of samples from the polymerization reactor followed by ESR analysis are useful, but we have developed continuous flow techniques which are preferable in many cases. ESR techniques can provide valuable information relating to the nature of free radical reactions, the concentration of propagating free radicals, and the kinetic processes in these reactions. Direct ESR analysis is most valuable but is not applicable to all systems. Spin trapping techniques can be useful for systems not accessible by direct analysis.     

Free-radical polymerization of methyl methacrylate in the presence of dithiobenzoates as reversible addition-fragmentation chain transfer agents

The pseudoliving radical polymerization of methyl methacrylate in bulk mediated by dithiobenzoates with various leaving groups as reversible addition-fragmentation chain-transfer agents has been studied. It has been shown that polymerization proceeds under conditions of the low steady-state concentration of radical intermediates; as a result, the steady-state of the process is rapidly achieved even at low conversions. Retardation of polymerization observed at high concentrations of reversible addition-fragmentation chain-transfer agents is apparently associated with the occurrence of chain termination reactions involving intermediates, as evidenced by the model reaction. The autoacceleration of polymerization is suppressed with an increase in the concentration of reversible addition-fragmentation chain-transfer agents. An efficient approach to the synthesis of a narrow-dispersed PMMA with the controlled molecular mass has been suggested.     

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.     

A versatile method for tuning the chemistry and size of nanoscopic features by living free radical polymerization

A novel approach is presented for manipulating the size and chemistry of nanoscopic features using a combination of contact molding and living free radical polymerization. In this approach a highly cross-linked photopolymer, based on a methacrylate/acrylate mixture, was patterned into submicrometer-sized features on a silicon wafer using a contact-molding technique. A critical component of the monomer mixture was the incorporation of an initiator containing monomer into the network structure, which provides sites for functional group amplification. Features ranging in size from 5 microm to <60 nm were accurately replicated by this process and living free radical polymerizations, both atom transfer radical and nitroxide-mediated polymerization (NMP), could be conducted from these initiating sites to yield polymer brushes which represent a grafted layer of linear chains attached to the original network polymer. Grafts consisting of polystyrene, poly(methyl methacrylate), and poly(2-hydroxyethyl)methacrylate were grown with controlled thicknesses ranging from 10 to 143 nm and graft molecular weights of between 18 000 to 290 000 amu. As a result of this secondary graft process, feature sizes could be tuned from the original 100 nm down to 20 nm, and the surface chemistry varied from hydrophilic to hydrophobic starting from the same initial master pattern. The thin films and patterned features were characterized by contact angle, ellipsometry, optical, and atomic force microscopies.     

Kinetic study of the alternating copolymerization of butadiene and methyl methacrylate

A kinetic investigation of the alternating copolymerization of butadiene and methyl methacrylate with the use of a system of ethylaluminum dichloride and vanadyl chloride as a catalyst was undertaken. The relation between the polymer yield and the molar fraction of methyl methacrylate in the feed was examined by continuous variation of butadiene and methyl methacrylate, the concentrations of total monomer, ethylaluminum dichloride, and vanadyl chloride being kept constant. This continuous variation method revealed that the polymer yield attains its maximum value with a monomer feed containing less than the 0.5 molar fraction of methyl methacrylate. This value of the molar fraction of methyl methacrylate affording the maximum polymer yield decreased on increasing the total monomer concentration but was not changed on varying the concentration of ethylaluminum dichloride. The number of active species estimated from the relation between yield and molecular weight of the polymer was almost constant, regardless of the molar fraction of methyl methacrylate in the feed. Consequently, it can be said that the maximum polymer yield depends mainly on the propagation reaction, not on the initiation reaction or the termination reaction. Three types of the mechanism have been discussed for this alternating copolymerization: polymerization via alternating addition of butadiene and methyl methacrylate complexed with ethylaluminum dichloride by the Lewis-Mayo scheme; polymerization via the ternary intermediate of butadiene, methyl methacrylate, and ethylaluminum dichloride; polymerization via the complex formation of butadiene and methyl methacrylate complexed with ethylaluminum dichloride occurring only at the growing polymer radical. From the kinetic results obtained, it was shown that the first and third schemes are excluded, and polymerization by way of the ternary intermediate is compatible with the data.