High-conversion polymerization. I. Theory and application to methyl methacrylate

The concept of polymer entanglements has been applied in conjunction with classical free-radical kinetics to describe vinyl polymerizations carried to high conversion. A kinetic model has been developed on the assumption that two populations of radicals exist in a high-conversion polymerization system: those radicals whose chain lengths are long enough to become entangled with neighboring molecules and have, therefore, a restricted mobility; and those shorter radicals whose mobilities are not strongly affected by diffusional effects. It has also been assumed that the kinetic rate constant for the termination step between entangled radicals is inversely proportional to the mean entanglement density. The model contains only two parameters in addition to the kinetic rate constants required to describe low-conversion polymerizations. One of these parameters can be determined, at least in principle, from measurements of solution properties of the polymer-monomer mixtures. The model so developed has been tested against experimental data obtained from the literature on the bulk polymerization of methyl methacrylate. The agreement between predicted and experimental monomer conversions and molecular weight averages is found to be satisfactory.     

Kinetics and mechanisms of emulsion polymerization initiated by oil-soluble initiators. IV. Kinetic modeling of unseeded emulsion polymerization of styrene initiated by 2,2′-azobisisobutyronitrile

To explain the kinetic features of particle formation and growth in unseeded emulsion polymerization initiated by oil-soluble initiators, a mathematical kinetic model is proposed, based on the assumption that when initiator radicals or monomer radicals in the water phase enter monomer-solubilized emulsifier micelles, initiate polymerization, and propagate to a chain length which is long enough not to desorb from the micelles, the micelles are regarded to be transformed into polymer particles. It is demonstrated by comparing the experimental results obtained in the emulsion polymerization of styrene initiated by the oil-soluble initiator, 2,2'-azobisisobutyronitrile, with sodium lauryl sulfate as emulsifier that the proposed kinetic model satisfactorily explains the kinetic features such as the effects of initial emulsifier, initiator, and monomer concentrations on both the number of polymer particles produced and the monomer conversion versus time histories. © 1993 John Wiley & Sons, Inc.     

Modelling free-radical copolymerization kinetics, 3. Molecular weight calculations for copolymers with crosslinking

A comprehensive model for molecular weight calculations of free-radical crosslinking copolymerizations was developed using the pseudo-kinetic rate constants and the method of moments. The moments of copolymer chain distributions are defined in such a way so that the molecular weight averages of crosslinking copolymers can be calculated using the moments. The present model is based on a general crosslinking copolymerization scheme, accounting for chain transfer to small molecules and polymer, bimolecular termination, and crosslinking reactions. The influence of crosslinking reactions on molecular weight development is discussed. The effects of the reactivity of pendant double bonds on the moments development were further demonstrated using model simulations. The simulations results suggest that the higher-order molecular weight averages are very sensitive to the reactivity of pendant double bonds. It was found that chain transfer to polymer affects the gelation point significantly. The radical fractions must be calculated accounting for chain transfer reactions in addition to propagations in order to properly evaluate pseudo-kinetic rate constants. The present model was used to predict kinetic behavior and molecular weight development of styrene/m-divinylbenzene and styrene/ethylene dimethacrylate free-radical crosslinking copolymerizations in benzene solution at 60°C. It was found that the present model is in excellent agreement with the experimental data published in the literature. Model predictions and experimental data show that the reactivity of pendant double bonds is much lower than that of vinyl and divinyl monomers. The simulation results suggest that the assumption of the same reactivity of functional groups is likely not valid for many free-radical crosslinking copolymerizations. The present model based on a kinetics approach can be used to predict molecular weight development for vinyl/divinyl free-radical crosslinking copolymerizations and to estimate kinetic parameters in the pre-gelation period.     

Molecular weight distribution in free radical polymerization with long-chain branching

A new theory to predict the molecular weight distribution in free radical polymerization that includes chain transfer to polymer is proposed. This theory is based on the branching density distribution of the primary polymer molecules. The branching density distribution provides the information on how each chain is connected to other chains, and therefore, a full molecular weight distribution can be calculated by application of the Monte Carlo simulation. The present theory accounts for the history of the generated branched structure and can be applied to various reaction systems that involve branching and crosslinking regardless of the reactor types used. The present simulation confirmed the validity of the method of moments in a batch polymerization proposed earlier. It was shown clearly why gelation never occurs by chain transfer to polymer without the assistance of other interlinking reaction such as bimolecular termination by combination. © 1993 John Wiley & Sons, Inc.     

Molecular weight distribution in nonlinear emulsion polymerization

A modelistic study of the molecular weight distribution (MWD) formed in emulsion polymerization that involves chain transfer to polymer is conducted, by focusing our attention to the effect of very small reaction volume on the formed MWD. In emulsion polymerization, a polymer radical that causes polymer transfer reaction must choose the partner only within the same particle, which makes the expected size of the polymer molecule to be chosen smaller compared with the corresponding polymerization system that involves an infinitely large number of polymeric species. The usual assumption for homogeneous polymerization that the rate of chain transfer to a particular polymer molecule is proportional to its chain length cannot be used, except when branching frequency is low and particle size is large enough. This fact invalidates the direct use of models developed for homogeneous nonlinear polymerizations to emulsion polymerizations. Model equations that could be used to assess the significance of the limited space effects on the MWD under a given polymerization condition are also proposed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1515–1532, 1997     

The free radical distribution in emulsion polymerization using oil-soluble initiators

A new approach is presented to calculate both the distribution of particles with iradicals and the average number of radicals per particle in emulsion polymerizations carried out using oil-soluble initiators. The convergence and accuracy of the approach were examined. It was found that, in agreement with previously published experimental results, the present approach predicts a kinetic behavior similar to that found for water-soluble initiators. This effect is primarily due to the desorption of initiator radicals from the polymer particles rather than the contribution of the fraction of oil-soluble initiator dissolved in the aqueous phase.     

Polymerization in nonuniform latex particles: Distribution of free radicals

Previous kinetic studies in emulsion polymerization have almost always involved an assumption of uniform distribution of free radicals in the latex particle. Such an assumption is not likely to reflect reality in many systems that employ water-soluble initiators because the hydrophilic end-group of the oligomeric free radical will preferentially stay in the surface layer of the particle. This constrained end-group location would result in nonuniform distribution of free radicals in the polymerizing latex particles. A Monte Carlo simulation of the growth of a single polymer chain within the latex particle supports this hypothesis. Such a nonuniform distribution of free radicals in the latex particle is expected to have an influence on reaction kinetics and product properties. The mechanism for transport of free radicals out of polymerizing latex particles is reexamined based on the proposed concept, and a modified expression for the desorption rate constant is presented.     

Chain transfer to polymer in emulsion polymerization

Chain transfer to polymer in emulsion polymerizations of acrylate monomers and vinyl acetate has been studied using ¹³C NMR spectroscopy to elucidate the chemistry by which chain transfer occurs and to quantify the mol% branches resulting from the reaction. In emulsion polymerizations of n-butyl acrylate, ethyl acrylate and methyl acrylate, chain transfer to polymer proceeds via abstraction of hydrogen atoms from backbone tertiary C-H bonds and typically gives rise to 2-4 mol% branches in the polymers obtained at complete conversion, the level of branching increasing with reaction temperature. For these acrylates, there is no evidence for a significant difference between the extent of chain transfer to polymer. In emulsion polymerizations of vinyl acetate, chain transfer to polymer proceeds mainly via H-abstraction from methyl side-groups, though there is a small contribution from abstraction at backbone tertiary C-H bonds. The levels of branching that result are substantially lower than in acrylate emulsion polymerizations, typically being in the range 0.6-0.8 mol% in the polymers obtained at complete conversion. The level of branching increases with temperature and as the degree of monomer starving (and hence instantaneous conversion) increases. Emulsion copolymerization of vinyl acetate with a small amount (5-20 wt%) of n-butyl acrylate gives rise to a significant increase in the level of branching (to values around 1.3-1.6 mol%), which results predominantly from H-abstraction of backbone tertiary C-H bonds in n-butyl acrylate repeat units by propagating radicals with vinyl acetate end units.     

Molecular weight distribution in emulsion polymerizations

A mathematical formulation is given which describes the evolution of the number distribution of the molecular weight (MWD) of linear polymer chains that grow in emulsion polymerization systems. The resulting set of coupled ordinary differential equations takes into account the microscopic events of free radical entry, exit, chain annihilation, bimolecular termination (by combination and disproportionation), and chain transfer in a mono- or polydisperse system. Simple analytic solutions are presented for systems in which the number of particles, as well as the average number of free radicals per particle, is constant and in which the rate coefficients are size independent. These solutions indicate that compartmentalization of the free radicals in the latex particles results in a significant increase in the polydispersity of the polymer produced by emulsion polymerization, compared with that in bulk systems. The theory shows that significant mechanistic information may be obtained from experimental MWDs and that, in principle, experimental conditions may be prescribed to grow a desired MWD. The MWDs are presented in a novel manner that facilitates the comparison of theory with experiment.     

EFFECTS OF VINYL ETHERS UPON RADICAL POLYMERIZATIONS

Various vinyl ethers have been examined as additives during radical polymerizations initiated by azobisisobutyronitrile at 60°C; the monomers were methyl methacrylate (MMA), styrene (STY) and acrylonitrile (AN). For MMA and STY, the vinyl ethers were incorporated to only small extents but they caused reductions in rate of polymerization and chain length of the resulting polymer; the effects can be attributed to the low reactivities in growth reactions of radicals to which a vinyl ether unit was last added. Copolymerization of the vinyl ethers with AN was more evident but, in many cases, it was accompanied by increased rate of consumption of AN and increased chain length of the polymer. These changes can be explained in terms of a physical effect which can be likened to that believed to be responsible for the gel effect. It is considered that polymer radicals are rather tightly coiled in an indifferent solvent so that the normal bimolecular termination is impeded.     

Simultaneous long‐chain branching and random scission: I. Monte Carlo simulation

In free‐radical olefin polymerizations, the polymer transfer reactions could lead to chain scission as well as forming long‐chain branches. For the random scission of branched polymers, it is virtually impossible to apply usual differential population balance equations because the number of possible scission points is dependent on the complex molecular architecture. On the other hand, the present problem can be solved on the basis of the probability theory by considering the history of each primary polymer molecule in a straightforward manner. The random sampling technique is used to solve this problem and a Monte Carlo simulation method is proposed. In this simulation method, one can observe the structure of each polymer molecule formed in this complex reaction system, and virtually any structural information can be obtained. In the illustrative calculations, the full molecular weight distribution development, the gel point determination, and examples of two‐ and three‐dimensional polymer structure are shown. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 391–403, 2001     

Recent progress in nitroxide-mediated polymerizations in miniemulsion

Recent developments in nitroxide-mediated polymerizations conducted in emulsion and miniemulsion have advanced the field across a range of both experimental and theoretical fronts. This article reviews progress in bicomponent initiating systems (including use of camphorsulfonic acid to enhance rate), unimolecular initiating systems, miniemulsions not requiring the use of volatile costabilizers, polymerization of acrylates, mathematical modeling and simulation, and theoretical understanding with regards to issues such as compartmentalization, preservation of polymer chain livingness, the role of aqueous phase kinetics and phase partitioning. These topics are discussed and analyzed to present an integrated portrait of the current status of nitroxide-mediated polymerizations in emulsion/miniemulsion and to identify the most pressing concerns, issues, and opportunities. To cite this article: M.F. Cunningham, C. R. Chimie 6 (2003).     

Application of Molecular Weight and Particle Growth Measurements in Continuously Uniform Latices to Kinetic Studies of Styrene Emulsion Polymerization

It is possible to generate, in specially formulated styrene emulsion polymerizations, latices in which the monomer—polymer particles are uniform through all stages of growth. These latices are kinetically similar to their polydispersed counterparts and can therefore be used as model systems in generalized kinetic studies of emulsion polymerization. The most important feature of these systems is the fact that the particles are uniform throughout the reaction with regard to all intrinsic properties and rate processes, and the particles can be characterized by this complete, continuous uniformity. Certain remarkably simple, but precise, relationships exist between the overall, measurable kinetic parameters and the individual particle kinetic parameters, thereby resulting in a heretofore unrealized analytic accessibility. Molecular weight kinetic analyses are an order of magnitude more accurate than in non-uniform systems. Application of these continuously uniform systems in actual kinetic studies indicates an inconsistency in the current concepts of emulsion polymerization, i.e., the generation of polymer at a constant molecular weight is predicted while an increase of several fold is observed. Before the situation can be clarified, further studies with continuously uniform systems are needed to evaluate molecular weight development, molecular weight distribution, and molecular structure and also to re-evaluate the rate and diffusion processes which control these structural features.     

Determination of Monomer Transfer Constants in Emulsion Polymerization

The monomer transfer constant, C_m can be determined from the chain length distribution (CLD) under conditions in which the monomer transfer reaction rate is much larger than the other chain termination processes. Such reaction conditions are feasible in emulsion polymerization where bimolecular termination reactions are relatively less important. We conducted theoretical investigations aimed at finding the necessary reaction conditions to apply the CLD method to emulsion polymerization. The number of polymer chains per polymer particle needs to be large enough in order to keep the effects of unknown chain lengths to a minimum, i.e., the unknown chains formed during the nucleation period and those which stop growing when the polymerization is stopped for sampling. In emulsion polymerization, the polymer concentration at the polymerization locus is higher than the corresponding bulk polymerization as long as monomer droplets exist, and the polymer transfer reaction may possess significant effects under conditions where monomer transfer reactions are important. The Monte Carlo (MC) simulation results have shown that although the CLD profile becomes broader due to the polymer transfer reactions, they do not significantly change the slope, from which C_m is determined. According to the present simulation results, the CLD method is considered applicable even when the polymer transfer reaction cannot be neglected. The MC simulation method can be used to find the experimental conditions where the CLD method is applicable.     

The quenched instationary polymerization system, 1. Derivation of the radical and polymer chain length distributions for the case of δ‐pulse like initiation

A new instationary polymerization system is presented including, as an essential element, the complete deactivation of all active radicals by reaction with an inhibitor at a certain time after chain initiation. The complete kinetic scheme, the set of differential equations, as well as the analytical solutions are presented. A proof is presented that the reaction with the inhibitor during the quench period dominates any other possible reaction such as propagation and bimolecular termination. As a result, the radical spectrum present at the beginning of the quench period is converted (almost) completely unchanged and instantaneously into a polymer chain length distribution. The quenched radical spectrum appears as a single additional peak in the experimentally observable total chain length distribution. In the case of δ‐pulse initiation the analytical solutions of the differential equations reduce to a simple poisson distribution for the radical concentrations as a function of time. Theoretical expressions for the maximum and the points of inflections (low and high molecular weight side) were derived and their applicability for the direct determination of k_p was tested. All of them turned out to be equally well suited for this purpose.     

Modeling molecular weight distribution in emulsion polymerization reactions with transfer to polymer

A mathematical model was developed for the computation of the dynamic evolution of molecular weight distributions (MWDs) during nonlinear emulsion polymerization reactions. To allow the direct computation of the whole MWD, an adaptive orthogonal collocation technique was applied. The model was validated with experimental methyl methacrylate/butylacrylate (BuA) semicontinuous and vinyl acrylate (VA)/Veova10 continuous emulsion polymerization results. Both systems considered introduce significant chain‐transfer reactions to polymer chains as a result of the presence of BuA and VA, respectively. The model developed was able to represent quite properly the kinetics and MWD of polymer samples during emulsion polymerizations. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3513–3528, 2001     

Dye distribution in fluorescent-labeled latex prepared by emulsion polymerization

Emulsion polymerizations were used for preparing fluorescent-labeled polymers. The labeled polymers were analyzed by gel permeation chromatography (GPC) using both fluorescence (FL) and refractive index (RI) as detectors. The uniformity of polymer labeling was measured by the ratio between FL and RI signals, calculated by a computer software, on the basis of each GPC chromatogram. It was found that in emulsion polymerizations, the semicontinuous process can produce a more homogenous dye distribution in the host polymer molecules than the batch method. Uniform labeling of a polymer with various dyes can be achieved by the semi-continuous process. However, experimental conditions for polymerization, such as initiator concentration and the presence of surfactant or chain transfer agent, may influence the uniformity of dye distribution. © 1994 John Wiley & Sons, Inc.     

Free radical entry in emulsion polymerizations

Measurements of the rate coefficients characterising the entry of free radicals into seed particles in styrene emulsion polymerizations has allowed the rate determining step for entry to be identified. This was found to be the rate of production of oligomeric species in the aqueous phase by monomer addition to the primary free radicals. Once formed the subsequent diffusion of these species to the latex particles (and their incorporation within these particles) is relatively fast, contrary to the assumptions of the previous diffusion controlled theories. The experimental results imply that the entering free radicals contain only two or three monomer units. Thermodynamic considerations show that such species should be both water soluble and surface active. Similar conclusions have been reached for other sparingly water soluble monomers, such as butyl acrylate and butyl methacrylate.     

Bimolecular radical termination: New perspectives and insights

The reversible addition‐fragmentation chain transfer‐chain length dependent termination (RAFT‐CLD‐T) method has allowed us to answer a number of fundamental questions regarding the mechanism of diffusion‐controlled bimolecular termination in free‐radical polymerization (FRP). We carried out RAFT‐mediated polymerizations of methyl acrylate (MA) in the presence of a star matrix to develop an understanding of the effect of polymer matrix architecture on the termination of linear polyMA radicals and compared this to polystyrene, polymethyl methacrylate, and polyvinyl acetate systems. It was found that the matrix architecture had little or no influence on termination in the dilute regime. However, due to the smaller hydrodynamic volumes of the stars in solution compared to linear polymer of the same molecular weight, the gel onset point occurred at greater conversions, and supported the postulate that chain overlap (or c*) is the main cause for the observed autoacceleration observed in FRP. Other theories based on “short–long” termination or free‐volume should be disregarded. Additionally, since our systems are well below the entanglement molecular weight, entanglements should also be disregarded as the cause of the gel onset. The semidilute regime occurs over a small conversion range and is difficult to quantify. However, we obtain accurate dependencies for termination in the concentrated regime, and observed that the star polymers (through the tethering of the arms) provided constriction points in the matrix that significantly slow the diffusion of linear polymeric radicals. Although, this could at first sight be postulated to be due to reptation, the dependencies showed that reptation could be considered only at very high conversions (close to the glass transition regime). In general, we find from our data that the polymer matrix is much more mobile than what is expected if reptation were to dominate. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3155–3173, 2008     

Kinetics of redox polymerizations of acrylic acid in inverse dispersion and in aqueous solution

Redox polymerizations of acrylic acid in inverse dispersion and in aqueous solution (with surfactant) were conducted by using sodium metabisulphite/potassium bromate initiators. The monomer conversions were determined by using high‐performance liquid chromatography, and the polymer particles in the final lattices were examined using a scanning electron microscope with freeze‐fracture equipment. Experimental rate expressions implied that complex reactions are involved in the redox polymerizations. A chemical reaction scheme was proposed, and kinetic models were developed for the redox polymerization in aqueous solution. Comparison between the experimental rate expressions and the kinetic models suggested a combination of bimolecular and monomolecular termination modes, a chain transfer function of the surfactant, and an oxidizing role of the oxygen molecules. The differences in the experimental rate expressions between the redox polymerization in inverse dispersion and that in aqueous solution are in good agreement with the kinetic model predictions. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 313–324, 1999