Radical polymerization of vinyl acetate with primary radical termination

Vinyl acetate was polymerized at high initiation rate with 2,2′-azobis(2,4-dimethyl valeronitrile) as initiator at 50°C. In this polymerization, the power dependence of polymerization rate on the initiation rate is smaller than at lower concentration of monomer. This dependence was kinetically analyzed at each given concentration of monomer. Average degree of polymerization of polymer formed depends on the concentration of initiator. This dependence was explained by considering chain and primary radical terminations and transfer to monomer of polymer radical, and the initiator efficiency (=0.503) was deduced. It was found that the chain termination is inversely proportional to solvent viscosity, but the primary radical termination is not inversely proportional to solvent viscosity. Further, the value of the primary radical termination rate constant (=1.4 × 10⁹l./mole-sec) was estimated.     

Kinetics of polymerization rate based on the dependence of termination rate on chain length

When the structure of a primary radical resembles that of the chain end of the polymer radical, the rate of the primary radical termination is approximately the same as the termination rate between the oligomer radical and the polymer radical. The rate constant of termination between polymer radicals of chain length n and s, which involve the primary radicals, is k_t,ns = const.(ns)^?a. In the polymerization of methacrylonitrile initiated by 2,2′-azobisisobutyronitrile in dimethylformamide at 60.0°C, the value of a is found to be 0.091. From data obtained previously in the bulk polymerization of styrene initiated by 1-azobis-2-phenylethane at 60.0°C, the value of a is found to be 0.167. Because such a values are so large that they are not estimated by the excluded volume, the termination rates are discussed by adding the dependence of the diffusion of the segments to that for chain length.     

Analysis of polymerization rates in radical polymerization with primary radical termination of some methacrylates

Polymerization rates in polymerizations with primary radical termination of ethyl methacrylate, β-phenylethyl methacrylate, β-methoxyethyl methacrylate, and phenyl methacrylate initiated by 2,2'-azobis-(2,4-dimethylvaleronitrile) at 60°C were analyzed by using a simple linear equation. The values obtained of k_ti/k_ik_p (where k_ti is the primary radical termination rate constant, k_i is the rate constant of addition on to monomer of primary radical, and k_p is the propagation rate constant) on these analyses are discussed on the theoretical base.     

A new method for evaluation of the characteristic constant for primary radical termination in free radical polymerization

A new model has been proposed for estimation of the characteristic rate constant for primary radical termination, using the radical life time, rate of polymerization, and rate of initiation. The model can be used to estimate the characteristic rate constant for primary radical termination under most conditions of free radical polymerization. By applying this model to high conversion polymerization data, it is possible to compare the conversion dependence of the characteristic rate constant for primary radical termination and initiation rate as well as the conversion dependence of the termination rate constant.The model has applied to various published experimental data and the results compared with literature values.     

Analysis of polymerization rates in radical polymerization with primary radical termination of methyl methacrylate initiated by 2,2′-azobis(2,4-dimethyl valeronitrile)

Polymerization rates in radical polymerization of methyl methacrylate initiated by 2,2′-azobis(2,4-dimethyl valeronitrile) under various conditions were analyzed by using a previously derived simple equation. The results obtained are discussed on the basis of the relation of solvent viscosity and temperature. It is concluded that chain termination rate constant is inversely proportional to the solvent viscosity, but primary radical termination rate constant can not be related immediately to solvent viscosity.     

Kinetics of polymerization reactions with reversible-chain termination

General kinetic features of radical and ionic polymerization processes accompanied by reversible chain termination reactions are considered. Special attention is paid to the conditions of applicability of the steady-state approximation usually employed to analyze the kinetics of radical polymerization. It is shown that the steady-state concentration of radicals is attained at practically the very beginning of the reaction, while the steady-state concentration of a reversible termination agent is reached with a certain delay. A kinetic explanation of the reversible termination reaction effect on the pattern of the molecular-mass distribution is suggested. Conditions providing the obtainment of a polymer with a narrow molecular-mass distribution in processes with reversible termination are formulated.     

Primary radical termination rate constant at high conversion in radical polymerization

A primary radical termination rate constant given by: k_ti = A_1iD_i, where A_1i is a constant and D_i is the diffusion constant of the primary radical, was examined on the basis of the variation of conversion. It was proved that this rate constant is correct at high conversion. A relationship between primary radical termination rate constant and conversion was derived. The effect of variation of conversion on the gel effect is discussed.     

Initiation,propagation and termination in fluid phase free‐radical polymerization

Free‐radical polymerizations are carried out in extended ranges of temperature, pressure, and conversion. The precise knowledge of individual rate coefficients of initiation, propagation, termination, and chain‐transfer is essential for the modelling and optimization of monomer conversion and of polymer microstructure in technical polymerizations. In addition to the application‐oriented interest, this data is of fundamental importance for the detailed understanding of reaction mechanisms of such free‐radical‐molecule, free‐radical‐free‐radical, and unimolecular decomposition processes. Even for the polymerization of rather common monomers at moderate temperatures and ambient pressure such information is scarce. The present paper illustrates some recent advances in measuring, within wide ranges of pressure and temperature, propagation and termination rate coefficients of free‐radical homo‐ and copolymerizations and also peroxyester decomposition rate coefficients.     

Studies in vinyl chloride polymerization. Determination of primary radical termination by initiator fragment method

The rate of vinyl chloride polymerization initiated by doubly labelled benzoyl peroxide in dichloroethane at 60° was measured dilatometrically. The extent of primary radical termination, evaluated from the assay of the polymer samples recovered at 10% conversion, is compared with values deduced from analysis of the kinetic data.     

Relationship between radical polymerization rate and initiator concentration in various solvents

Methyl methacrylate and styrene were polymerized by using 2,2′-azobis(2,4-dimethyl valeronitrile) as initiator in various solvents. When a poor solvent is used, the dependence of polymerization rate R_p on initiator concentration [C] is small and can be treated by equations for the analysis of the polymerization with primary radical termination. With a good solvent, the dependence of R_p on [C] is so large that such equations are not applicable. Thus, the [C] dependence in a good solvent is explained qualitatively through the molecular weight dependence of rate for termination between polymer radicals, based on the excluded volume effect.     

Average termination rate coefficients in emulsion polymerization: Effect of compartmentalization on free‐radical lifetimes

A method is presented by which the time‐dependent average termination rate coefficient in an emulsion polymerization may be calculated as an appropriate average of the chain‐length‐dependent termination rate coefficients. The method takes advantage of the fact that the overall termination rate is dominated by terminations between rapidly moving short radicals and much slower long ones. This termination rate coefficient is suitable for use in the Smith–Ewart equations describing the compartmentalization of radicals in an emulsion polymerization. Rate data in emulsion polymerizations can be quantitatively interpreted if the kinetics fall into one of two categories: zero–one (showing compartmentalization; intraparticle termination is not rate‐determining) or pseudo‐bulk (no compartmentalization; intraparticle termination is rate‐determining). The new method can be used to interpret rate data for systems falling between these categories and also can be used to find termination rate coefficients from Monte Carlo simulations of termination kinetics. The latter is especially useful for predicting and understanding kinetics in controlled radical polymerizations in disperse media. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1076–1089, 2005     

Termination rate constant in radical polymerization

On the basis of the assumption that the primary radical immerses into a polymeric radical, the rate constant of primary radical termination was derived. By applying and developing further the same treatment, the rate constant of chain termination was derived. This rate constant was experimentally confirmed. It was found that the rate constant of chain termination for the polymerization of some methacrylates depends on the distance of translation of radical chain end per collision, solvent viscosity, and the Taft polar constant for ester group.     

Modeling of molecular weight development in atom transfer radical polymerization

A kinetic model has been developed for atom transfer radical polymerization processes using the method of moments. This model predicts monomer conversion, number‐average molecular weight and polydispersity of molecular weight distribution. It takes into account the effects of side reactions including bimolecular radical termination and chain transfers. The determining parameters include the ratios of the initiator, catalyst and monomer concentrations, as well as the ratios of the rate constants of propagation, termination, transfer and the equilibrium constant between radicals and their dormant species. The effects of these parameters on polymer chain properties are systematically simulated. The results show that an ideal living radical polymerization exhibiting a linear relationship between number‐average molecular weight versus conversion and polydispersity approaching unity is only achievable under the limiting condition of slow monomer propagation and free of radical termination and transfers. Improving polymerization rate usually accompanies a loss of this linearity and small polydispersity. For polymerization systems having a slow initiation, the dormant species exercise a retention effect on chain growing and tend to narrow the molecular weight distribution. Increasing catalyst concentration accelerates the initiation rate and thus decreases the polydispersities. It is also shown that for a slow initiation system, delaying monomer addition helps to reduce the polydispersities. Radical termination and transfers not only slow down the monomer conversion rates but also broaden polymer molecular weight distributions. Under the limiting conditions of fast propagation and termination and slow initiation, the model predicts the conventional free radical polymerization behaviors.     

Effect of primary radical termination on chain length and initiator efficiency

In polymerization with primary radical termination, when reaction between primary radicals, which escape from solvent cage, is not negligible, a relation between chain length and polymerization rate is found regardless of tractable approximate procedures. Such a relation is applied to the kinetic data obtained in the polymerizations of methyl methacrylate (MMA) and vinyl acetate (VA) initiated by 2,2′-azobis(2,4-valeronitrile) at 50.0°C. Further, when the primary radical termination is high, an initiator efficiency can not be approximated to a ratio of the primary radicals escaping from the cage to the total primary radicals formed in the cage. In the polymerization of MMA, after the primary radicals escapes from the cage, they immediately react with the monomer. Thus, the reaction between the primary radicals is not significant. However, in the polymerization of VA, the rate of reaction between the primary radical and the monomer might be comparable to the rate of reaction between the primary radicals when the initiator concentration is quite high.     

The kinetics of free radical polymerizing systems at low conversion, 1. On the rate determining step of the bimolecular termination reaction

Using a styrene bulk system as a model, this paper examines rates of termination at very low conversions in bulk and solution polymerizations. No definitive answer to the question of what determines such rates of termination is arrived at. Indeed, it is argued that on the basis of existing kinetic information, no such definitive answer is possible. However several things may be said with conviction. To begin with, it is rigorously shown that low conversion rates of termination cannot be explained by assuming that all radical chain end encounters result in termination, and then using center-of-mass diffusion coefficients of polymer in free solution to calculate rates of chain end encounter. However this does not mean that rates of center-of-mass diffusion do not determine rates of low conversion termination, as is shown; the idea that it may be the case that not all chain end encounters result in termination, this a manifestation of a spin multiplicity effect, is especially worthy of mention. It is also possible to explain low conversion rates of termination, as has traditionally been done, in terms of chain end motions being hindered by the presence of another polymer chain. However in concentrating on interactions between overlapping long chain macroradical coils, this traditional picture is certainly inaccurate, for it is shown that most termination interactions must involve at least one radical of shorter than expected degree of polymerization. This has the important consequence that an understanding of overall rates of dilute solution termination must be founded on an understanding of the diffusional behavior of the ends of short and intermediate length polymer chains.     

Diffusion-controlled rate constant of termination reaction in radical polymerization

Smoluchowski's theory has been modified and the improved theory was applied to diffusion-controlled polymerization. This application proved that the rate-controlling process is not transrational diffusion but the segmental diffusion. The segmental diffusion-controlled rate constant was derived by the collision theory. This rate constant explains the experimental fact that the diffusion-controlled rate constant of bimolecular termination in radical polymerization of alkyl methacrylate is inversely proportional to solution viscosity and independent of the molecular weight of the polymeric free radical.     

Initiator concentration dependence of the autoacceleration of polymerization rate

The dependence of the polymerization rate on initiator concentration over a wide range of conversion is analyzed by an equation derived on the assumption that the primary radical termination is important and another equation derived on the assumption of the chain length dependence of the termination. The analytical result by the former equation, is nearly equivalent to the result by the later when transfer predominates. Fujita-Doolittle theory is applicable to both results. In the apparent termination, small polymer radicals not exceeding the size of the segment play an important role.     

Gamma radiation-initiated polymerization of styrene at high pressure. II. Chain termination

The pressure dependence of the termination rate constant k_t for the free radical polymerization of monomers such as styrene is a function of polymer chain length, chain stiffness, and monomer viscosity, all of which influence the rate of segmental diffusion of an active radical chain end out of the coiled polymer chain to a position in which it can react with a proximate radical. Although k_t is not sensitive to changes in chain length, the large increase in molecular weight is responsible for a significant reduction in k_t at high pressures. For most of the common vinyl polymers, which exhibit some degree of chain stiffness, k_t is inversely proportional to a fractional power of the monomer viscosity because it depends in part on the resistance of chain segments to movement and in part on the influence of viscosity in controlling diffusion of the chain ends. The fractional exponent appears to increase with pressure and this is interpreted as evidence that the polymer chains become more flexible in a more viscous solvent. Because the fractional exponent is higher for more flexible chains, the value of the activation volume for chain termination is an indication of the degree of flexibility of the polymer chains, provided that the monomer is a good solvent for the polymer and that chain transfer is negligible.     

Effects of poly(2-vinylpyridine) as a template for the radical polymerization of methacrylic acid—II: Influence of initiator concentration

The polymerization of methacrylic acid along an atactic poly(2-vinylpyridine) template was studied by varying the initiator concentration, [I]₀. The concentrations of monomer and template were 0.4 M, the temperature 30°. Reaction rates were determined calorimetrically. The experimental results could be well described by a template polymerization model based on a modified mechanism omitting the requirement of a critical chain length of the oligomer radical prior to its association with the template. This view is in line with the existence of preferential adsorption of monomer by the template. In addition, the different ways of termination were also considered. By applying this kinetic model, the various radical concentrations and rate coefficients could be estimated. The termination rate coefficients for template associated polymer radicals appeared to be about 1000 times smaller than termination rate coefficient for non-associated radicals. Moreover, it was found that the initial polymerization rate has 0.26 order with respect to initiator, signifying a predominance of termination between template associated radicals over that between template associated and non-associated radicals (cross termination).