Non-ideal kinetics in vinyl polymerization primary radical termination and chain transfer to solvent in benzoyl peroxide initiated polymerization of vinyl acetate in benzene

The kinetics of vinyl acetate polymerization initiated by benzoyl peroxide in benzene at 60°C have been studied. Deviation of the rate of polymerization from kinetic orders of 0.5 in initiator and 1.0 in monomer is discussed in terms of primary radical termination and chain transfer to solvent.     

Contribution of primary radical termination to radical polymerization of diethyl fumarate estimated from absolute rate constants

Summary Diethyl fumarate was radically polymerized under UV irradiation and concentration of the propagating radical was determined to be of the order of 10^-5 mol/L by scavenge with a stable free radical. The absolute rate constant for propagation (k_p) was evaluated from the overall rate of polymerization at 30°C: K_p =(2.9 ± 0.3) × 10^-2 L/mol · s. The rate constant for mutual termination of the polymer radical (k_t) was calculated from the decreasing rate of the radical concentration in the dark: k_t=8.0 L/mol·s. The k_t value determined is one twentieth of that evaluated previously by a rotating sector method. This discrepancy is accounted for by contribution of much faster primary radical termination.     

Chain length dependent termination in radical cross-linking polymerization

The work presents an evidence in support of chain length dependent termination during cross-linking polymerization. It is based on the behavior of the ratio of the bimolecular termination coefficient to propagation rate coefficient k_p during the after-effect of a photo-induced polymerization. The chain-length dependence was manifested by a decrease of the ratio with the increase in dark reaction time faster than that resulting from the conversion increase. Two monomethacrylate/dimethacrylate and one dimethacrylate/dimethacrylate systems were chosen, which enabled to study the chain-length dependence as a function of cross-link density of the polymer being formed and physical properties of the initial composition. The ratios of the polymerization rate coefficients were calculated for various postpolymerization processes as a function of dark reaction conversion using the mixed termination model (concerning the bimolecular and monomolecular termination occurring parallel). A rapid drop of the ratio during the dark reaction was observed at the beginning of the after-effect and in slightly cross-linked systems suggesting a significant chain length dependence, but when the cross-link density increased with conversion or with cross-linking agent concentration in the feed, the drop of the ratio became much slower indicating that the chain length dependence decreased.     

Chain length dependence of termination rate constant: computer experiment of effects on the kinetics of radical polymerization of styrene

The kinetics of the radical polymerization of styrene, initiated by AIBN, have been studied by computer experiments. The models adopted assume a termination rate constant for polystyryl radicals with degrees of polymerization m and n, given by:

k_t,mn=km^-n^-

Deviations from simple kinetic rules have been found for 0.0. For example, the rate of polymerization is roughly proportional to the 0.45 power of initiator concentration for = 0.1. Conventional methods for the kinetic study of radical polymerizations are shown to come to erroneous conclusions if the effects of the chain length dependence of termination rate constant are not taken into account.     

On the modelling of continuous emulsion polymerization using a population balance with instantaneous radical termination

An analytical solution of a population balance is used to mathematically describe continuous emulsion polymerization. Steady state performance is examined. The assumption of instantaneous free radical termination within particles is made. The desorption mechanism is included. Particle size distribution information is obtained, and the effect of the desorption mechanism is noted. A desorption rate constant is calculated when the model is fit to data found in the literature.     

Probing the reaction kinetics of vinyl acetate free radical polymerization via living free radical polymerization (MADIX)

Living free radical polymerization technology (macromolecular design via the interchange of xanthates (MADIX)) was applied to give accesses to chain length and conversion dependent termination rate coefficients of vinyl acetate (VAc) at 80 °C using the MADIX agent 2-ethoxythiocarbonylsulfanyl-propionic acid methyl ester (EPAME). The kinetic data were verified and probed by simulations using the PREDICI^® modelling package. The reversible addition-fragmentation transfer (RAFT) chain length dependent termination (CLD-T) methodology can be applied using a monomer reaction order of unity, since VAc displays significantly lower monomer reaction orders than those observed in acrylate systems (ω(VAc, 80 °C)=1.17±0.05). The observed monomer reaction order for VAc is assigned to chain length dependent termination and a low presence of transfer reactions. The α value for the chain length regime of log(i)=1.25−3.25 (in the often employed expression ) reads 0.09±0.05 at low monomer to polymer conversion (10%) and increases significantly towards larger conversions (α=0.55±0.05 at 80%). Concomitantly with a lesser amount of midchain radicals, the chain length dependence of k_t is significantly less pronounced in the VAc system than in the corresponding acrylate systems under identical reaction conditions. The RAFT(MADIX)-CLD-T technique also allows for mapping of k_t as a function of conversion at constant chain lengths. Similar to observations made earlier with methyl acrylate, the decrease of k_t with conversion is more pronounced at increased chain lengths, with a strong decrease in k_t exceeding two logarithmic units from 10 to 80% conversion at chain lengths exceeding 1800.     

The influence of nanosilica on styrene free radical polymerization kinetics

A series of nanocomposites were prepared by in situ polymerization of styrene with different silica content (1, 3, and 5 wt%) with an average particle size of 7 nm. The influence of nanosilica content on the kinetics of styrene free radical bulk polymerization was studied by isothermal differential scanning calorimetry (DSC) at different temperatures (70, 80, and 90°C). Using appropriate kinetic model, describing two reactions observed during styrene polymerization (the first‐order reaction and autoacceleration), it was found that silica presence does not affect the apparent activation energies of both processes. The adsorption of styrene on the silica surface caused the formation of interfacial layer in the structure of hybrid materials. Using suggested equation, the thickness of the interfacial layer was determined to investigate its influence on the glass transition temperature of polystyrene (T_g), which was found not to be affected by silica addition. POLYM. COMPOS., 2012. © 2011 Society of Plastics Engineers     

Non-steady-state model for kinetics of free radical polymerization, 2. Redox initiation

This work deals with the non-steady-state kinetics of free radical polymerization with redox initiation. Rigorous expressions for the radical concentration, monomer conversion, molecular size distribution function, and number-average and weight-average molecular weights, etc., were derived. The molecular parameters of the resulting polymer were evaluated in relation to the polymerization conditions.     

Non-steady-state model for kinetics of free radical polymerization, 3. Direct photo-initiation

The non-steady-state kinetics of directly photo-initiated polymerization were studied theoretically. Taking account of the facts that the amount of monomer consumed in propagation is much more than that in initiation for a process producing high polymer and that the rate constant of chain termination is much larger than that of chain propagation or transfer, a few very close approximations were adopted to solve the set of kinetic differential equations of the polymerization under consideration. The inexplicit function method developed in a previous paper of this series for the derivation of the molecular weight distribution function is still valid in this work. Some numerical computation was implemented to show the tendency of free radical concentration decay and the plots of molecular size distribution.     

Chain-length-dependent termination in radical polymerization: Subtle revolution in tackling a long-standing challenge

Few would dispute that the study of the termination reaction has turned out to be the most difficult aspect of radical polymerization kinetics. However it is an aspect that may not be avoided, because without intimate knowledge of the associated rate coefficient, k_t, accurate control over and design of radical polymerization protocols are impossible. While there has been constant interest in the field since the first concepts were laid in the 1940s, for the most part progress has been stuttering. However the last two decades have seen a significant yet largely unnoticed revolution of gathering pace, as experimental and theoretical advances have enabled the main stumbling block to progress to be overcome: it is now routinely possible to obtain accurate values for , the termination rate coefficient as a function of the chain length, i, of the terminating macroradicals. Here we review this substantial progress. To begin with we explain some background concepts, emphasizing how the failure to appreciate these principles has led to misunderstanding. Then follows a section on experimental methods for determining . This forms the bulk of the review, because this is where recent advances have been most pronounced, in particular through three broad ways: (1) the emergence of powerful living radical polymerization protocols, such as reversible addition-fragmentation chain transfer (RAFT) chemistry, that can effectively correlate the growing macroradical length with monomer-to-polymer conversion; (2) the development of sophisticated spectroscopic approaches, including time-resolved electron paramagnetic resonance spectroscopy, to monitor the concentration of radicals after the application of a laser pulse; and (3) the attaining of a keener understanding of the kinetics of conventional steady-state polymerization. We then illustrate the remarkable progress that has been made by documenting how independent methods have arrived at almost identical values for a variety of monomers, including methyl methacrylate, styrene and butyl acrylate. As well as these case studies, we collate and critically evaluate all existing data at low conversion. In the final section of the review, we embed these results in currently available theoretical contexts. While this is certainly an area for future work of a deeper nature, it would seem that most current results can be understood at least qualitatively within a surprisingly simple theoretical framework.     

Nitroxide-mediated radical polymerization in nanoreactors: Factors influencing compartmentalization effects on bimolecular termination

Modeling and simulations of nitroxide-mediated radical polymerization (NMP) in dispersed systems have been performed to elucidate what factors dictate the magnitude of the segregation effect on bimolecular termination between propagating radicals generated from alkoxyamine activation. The reduction in termination rate due to segregation cannot be predicted merely based on the average number of propagating radicals per particle . This is because the magnitude of the segregation effect is also governed by the distribution of propagating radicals between particles, which is influenced by both the termination (k_t) and the deactivation (k_deact) rate coefficients. The results have implications with regards to improvement of livingness (end-functionality) in NMP by exploitation of particle size, and are expected to apply (qualitatively) to other controlled/living systems based on the persistent radical effect (e.g. atom transfer radical polymerization).     

Influence of centrifugal field on free‐radical polymerization kinetics

It has been observed that when a prepolymer mix of styrene, poly(styrene), toluene, and benzoyl peroxide is transferred from a conventional stirred tank reactor (STR) to a spinning disc reactor (SDR), the rate of polymerization is substantially increased. Furthermore, the molecular weight and the molecular weight distribution of the polymer formed at conversions up to about 80% in the SDR is virtually unchanged from that of the polymer formed at 60% conversion in the STR. These results seem to indicate that the increase in polymerization rate is not the result of the well‐known Trommsdorff–Norrish effect, which would be expected to lead to an increase in polydispersity. We believe that shear and centrifugal forces experienced by the film provide intense mixing and extension flow effects, which are responsible for the above‐described observations. In this report an explanation has been put forward to describe the observed effects. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2283–2286, 2002     

Non-steady-state model for kinetics of free radical polymerization, 4. Direct thermal initiation

This paper deals with the non-steady-state kinetics of direct thermal initiated polymerization. The initiation is assumed to be a bimolecular reaction of the monomer. The relationship between the radical concentration and the monomer conversion is rigorously derived. In further treatment a few very close approximations are introduced based on the fact that the number of monomer molecules reacting in the initiation step is much less than that consumed in the propagation step for a process producing high polymer, and the value of the rate constant for propagation or chain transfer is much lower than that for chain termination. Expressions for various molecular parameters, such as molecular weight distribution, number-average and weight-average degrees of polymerization, and dispersity, are given. Several numerical examples are provided.     

Free-radical propagation and termination kinetics of the butyl acrylate dimer studied by pulsed laser polymerization techniques

The propagation and termination rate coefficients for bulk polymerization of the butyl acrylate dimer (BA dimer) are determined by pulsed laser techniques. The rate coefficient for propagation, k_p, is deduced for temperatures from 20 to 90 °C via the pulsed laser polymerization-size exclusion chromatography (PLP-SEC) method at pulse repetition rates between 1 and 10 Hz. The Arrhenius parameters were found to be: E_A(k_p) = (34.2 ± 1.0) kJ mol⁻¹ and A(k_p)/L mol⁻¹ s⁻¹ = (1.08 ± 0.49) × 10⁷ L mol⁻¹ s⁻¹. The termination rate coefficient, k_t, has been measured via SP-PLP-ESR, single pulse-pulsed laser polymerization in conjunction with time-resolved electron spin resonance detection of radical concentration. The resulting Arrhenius parameters as deduced from the temperature range −15 to +30 °C are: E_A(〈k_t〉) = (22.8 ± 3.7) kJ mol⁻¹ and log(A/L mol⁻¹ s⁻¹) = 10.6 ± 1. The chain-length dependence of k_t was studied at 30 °C. For short chains a significant dependence was found which may be represented by an exponent α = 0.79 in the power-law expression k_t(i) = k_t⁰i^−α.     

Mechanism and kinetics of the free radical ring-opening polymerization of cyclic allylic sulfide lactones

The polymerization of 7-, 8- and 11-membered lactones, 6-methylene-1,4-oxathiepan-7-one, 3-methylene-1,5-oxathiocan-2-one and 3-methylene-1-oxa-5-thiacycloundecan-2-one in benzene at 70, 40–70 and 40–65 °C, respectively, is presented. All polymerizations proceeded with complete ring-opening up to approximately 25% conversion, where insoluble polymer was formed. Evidence is given attributing polymer double bond loss to crosslinking, although redistribution of the molecular weights via addition to polymer double bonds followed by β-fragmentation also appears to occur for polymerizations of the 8- and 11-membered lactones. Michael adducts of lactones with 2-methyl-2-propanethiol were prepared as models for chain-transfer products of hydrogen abstraction by carbon-centred radicals. Polymerization rates were found to increase marginally with ring size. Arrhenius parameters obtained for the polymerizations of the 8- and 11-membered lactones indicated that the addition step was more important than fragmentation in determining the rate of propagation.