Propagation Rate Constants Research Articles

Reexamination of the Pyrolysis of Polyethylene: Data Needs, Free-Radical Mechanistic Considerations, and Thermochemical Kinetic Simulation of Initial Product-Forming Pathways

Gaps in the voluminous data on pyrolysis of polyethylene that impede mechanistic understanding are highlighted, especially for H:C material balances, product distributions at varying conversions in isothermal closed systems, and inconsistencies between GC and FIMS analyses of products with lower volatility. Thermochemical kinetic estimates are made for the rates of various initiation processes; these suggest that molecular disproportionation contributes to chain initiation, along with homolysis, at lower Mn. Simulations indicate that the standard statistical test for random scission, a linear relationship between log Nc and c for volatile products, is not generally valid in open systems, and its empirical observation implies restrictions on the dependence of the rate of volatilization on c. Simulations of the initial distributions of volatile products and residue functionalities were performed based on propagation rate constants estimated by thermochemical kinetic procedures. The practice of deducing the ...

Synthesis of Bimodal Methacrylic Acid Oligomers by Template Polymerization

A multivinyl template monomer with 20.4 methacryloyl groups was synthesized with β-cyclodextrin by esterification of hydroxyl groups with methacrylic anhydride. Copper-mediated atom transfer radical polymerization of the template monomer was carried out with methyl 2-bromopropionate, 2,2‘-dipyridyl, and CuBr as an initiator, a ligand, and a catalyst, respectively. The effects of solvent and polymerization temperature on the degree of polymerization in the template monomer were investigated by kinetic analysis of conversion and the molecular weight of methacrylic acid oligomers obtained by hydrolysis of the polymerized products by GPC. Poly(methacrylate) oligomers with 7 and 14 degrees of polymerization were synthesized along the rims of the template monomer-3 by ATRP in a methanol/water mixture (water 10 vol %) at 50 °C. The observed propagation rate constant, kobs, of the methacryloyl group in the methanol/water mixture (water 10 vol %) at 50 °C was 11.3 × 10-5/s.

N-(2-Anthracene)methacrylamide: a new fluorogenic probe molecule for monitoring in situ the radiation-induced polymerization of methyl methacrylate in bulk and in solution

This paper introduces the fluorogenic molecule N-(2-anthracene)methacrylamide, AnMA, employed as a probe for monitoring radiation-induced polymerization in situ. The relative reactivity of AnMA during free radical polymerization of methyl methacrylate (MMA) has been determined via fluorescence techniques. The ratio between propagation rate constants for the reaction of an MMA free radical chain-end with AnMA relative to the reaction with MMA is found to be 0.96. It is demonstrated that AnMA can be used for monitoring MMA polymerization quantitatively throughout the entire course of the reaction including the gel effect region. Results are also provided which demonstrate that AnMA can be used for sensitive monitoring of MMA polymerization both in bulk and in solution.

Effect of Temperature, Solvent Polarity, and Nature of Lewis Acid on the Rate Constants in the Carbocationic Polymerization of Isobutylene

The absolute rate constant of propagation for ion pairs (kp±) was determined by the diffusion clock method in the living carbocationic polymerization of isobutylene at different solvent polarity and temperature in conjunction with TiCl4, Me2AlCl, and BCl3 as Lewis acids. The kp± ((3.6−5.7) × 108 L mol-1 s-1 in hexanes/MeCl 60/40, v/v) was independent of temperature and nature of Lewis acid and increased moderately with increasing solvent polarity to a nearly diffusion-limited value (∼1.7 × 109 L mol-1 s-1) in pure MeCl. A similar kp± (∼(5−6) × 108 L mol-1 s-1) value was obtained in the nonliving polymerization of isobutylene in conjunction with EtAlCl2 in hexanes/MeCl 60/40 (v/v) at −80 °C, indicating that living and nonliving polymerizations proceed on identical propagating centers. The apparent equilibrium constant of ionization (activation) Kiapp (= KiKD0, where Ki is the absolute equilibrium constant of ionization and KD0 is the equilibrium constant of TiCl4 dimerization) was calculated from the apparent and absolute rate constant of propagation. The rate constant of deactivation, k-i was determined from the conversion vs polydispersity plots. From Kiapp and k-i, the apparent values of ki (kiapp = kiKD0, where ki is the absolute rate constant of ionization) were also calculated. On the basis of the results, the observed large differences in the overall polymerization rates with different solvent polarity and temperature can be attributed solely to the changes in the active center concentration, which decreases with decreasing solvent polarity and increasing temperature. From the temperature dependence of Kiapp, the apparent standard enthalpy (= ΔHi° + ΔHD0°) and entropy (= ΔSi° + ΔSD0°) of ionization, and from the temperature dependence of kiapp and k-i, the apparent activation enthalpy and entropy of the activation/deactivation process were calculated.

First Nitroxide-Mediated Controlled Free-Radical Polymerization of Acrylic Acid

Controlled poly(acrylic acid) homopolymers were synthesized for the first time by direct nitroxide-mediated polymerization of acrylic acid. The polymerizations were performed in 1,4-dioxane solution at 120 °C, using an alkoxyamine initiator based on the N-tert-butyl-N-(1-diethyl phosphono-2,2-dimethyl propyl) nitroxide, SG1. The kinetics were controlled by the addition of free nitroxide at the beginning of the polymerization and the optimal amount was 9 mol % with respect to the initiator. In this case, whatever the initiator concentration, all polymerizations exhibited the same rate and conversion reached 85−90% within 5 h. Although the rate constant of propagation of acrylic acid is very large, its reactivity is moderated by a low activation−deactivation equilibrium constant between active macroradicals and SG1-capped dormant chains. Various alkoxyamine concentrations were investigated to target different molar masses. At high initiator concentrations, the number-average molar mass, Mn, increased linear...

Living polymerization of cyclic esters – a route to (bio)degradable polymers. Influence of chain transfer to polymer on livingness

AbstractPolymerization of cyclic esters leads to (bio)degradable polymers of the increasing industrial importance. These polymerizations are of the living nature, although chain transfer to polymer with chain scission may cause deviations from the livingness and introduce structural differences (e.g. in end‐groups), important for physical properties. Two different systems are discussed. In the first one two living macromolecules react one with another and reproduce two living macromolecules, retaining the same reactivities and the same end‐groups. Polymerizations of ϵ‐caprolactone and lactide belong to this category. On the other hand, polymerization of cyclic carbonates proceeds with chain transfer, in which disproportionation of the living chains takes place: from two living macromolecules one “dead” and one “doubly active” can be formed. Conditions of retaining the livingness in terms of the ratios of the rate constants of transfer, reinitiation, and propagation are discussed.

Influence of π-complexing agents on the anionic polymerization of styrene with lithium as counterion in cyclohexane 1. Effect of durene

The propagation reaction in the anionic polymerization of styrene with lithium as counter ion in cyclohexane has been investigated for six different concentrations of 1,2,4,5-tetramethylbenzene (durene) in the range of living ends concentration between 10 −5 and 10 −3 M at 20 °C. The values of the apparent dissociation constant of PStLi dimer and the weighted rate constants of all unassociated species were obtained for all six investigated concentrations of durene. The apparent dissociation constant increases several orders and the weighted rate constants of all unassociated species decreases one or two orders depending on the concentration of durene. A new mechanism was proposed and the values of the relevant absolute propagation rate constants of the three reactive monomeric species have been for the first time derived from the kinetic results. The absolute propagation rate constants of PStLi·D and PStLi·2D are comparable but much lower than that of PStLi. The complexation constant of PStLi with one molecule of durene is much larger than that of PStLi with a second molecule of durene.

Nonuniformity of Chain-Length Distributions in Photopolymerized Layers

For free-radical photopolymerization with a photobleaching initiator, constant chain propagation and termination rate constants kp and kt, and termination occurring only by recombination, we account for Beer−Lambert attenuation and initiator consumption to predict how spatial variation of the final chain length distribution (CLD) depends on kp, kt, incident light intensity Io, layer thickness L, photoinitiator absorption coefficient αA and initial concentration CA,0, and quantum yield of photoinitiator consumption φ, for a typical value (10-4) of the initial ratio of initiator and monomer concentrations CA,0/CM,0. We show how spatial variation of the final CLD depends on initial absorbance γ = αACA,0L and a parameter β = kp[fCA,0/(φαAIokt)]1/2, where f primary radicals are produced per photoinitiator molecule consumed. For small γ, the number-averaged mean chain length increases with depth at each β and with β at each depth. The chain length at which the CLD achieves its maximum value, along with a measure of polydispersity (half the CLD width at half-maximum, divided by the number-averaged mean), increase with depth at small β and decrease with depth at large β, with the CLD having its minimum nonuniformity at intermediate β. Front-to-rear CLD variation increases as γ increases. At small β, nonuniformity is confined to a progressively smaller portion of the front of the layer as γ increases, while for large β, spatial variation is more evenly distributed. The results are discussed in terms of spatiotemporal variation of initiation and monomer conversion. Examples from the literature are used to illustrate the degree of CLD nonuniformity that can be expected in experiments.

A Comprehensive Kinetic Model for the Combined Chemical and Thermal Polymerization of Styrene up to High Conversions

AbstractIn the present study, a comprehensive mathematical model is developed for the free‐radical polymerization of styrene to predict the polymerization rate and the molecular‐weight distribution of the polymer. The kinetic model accounts for both chemical and thermal radical generation and, thus, can be employed over an extended range of polymerization temperatures (e.g., 60–200 °C). The thermal initiation mechanism includes the reversible Diels‐Alder dimerization of styrene, radical formation via the reaction of the Diels‐Alder adduct with monomer, the formation of dead trimers, and the initiation of new polymer chains. Moreover, a comprehensive free‐volume model is employed to describe the variation of termination and propagation rate constants as well as of the initiator efficiency with respect to the monomer conversion. The cumulative molecular‐weight distribution of the polystyrene is calculated by the weighted sum of all the ‘instantaneous’ weight chain‐length distributions formed during the batch run. The capabilities of the present model are demonstrated by a direct comparison of model predictions with experimental data on monomer conversion, number‐ and weight‐average molecular weights, and molecular‐weight distribution. It should be noted that previously published kinetic models cannot describe the combined thermal and chemical free‐radical polymerization of styrene in terms of a unified, fundamental, kinetic model, which further underlines the significance of this study.Predicted and experimental weight‐average molecular weights with respect to monomer conversion (experimental conditions same as in Figure 1).magnified imagePredicted and experimental weight‐average molecular weights with respect to monomer conversion (experimental conditions same as in Figure 1).

Pulsed Laser Polymerization in an Ionic Liquid: Strong Solvent Effects on Propagation and Termination of Methyl Methacrylate

The rate constants of propagation and termination of methyl methacrylate (MMA) in the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate were measured using the pulsed laser polymerization technique across a range of temperatures, and Arrhenius parameters were calculated for the rate of propagation at ionic liquid concentrations of 0, 20, and 50% v/v. Point estimates for these values are A = 2.4 × 106 L mol-1 s-1 (0% v/v ionic liquid), 2.1 × 106 L mol-1 s-1 (20% v/v), and 2.5 × 106 L mol-1 s-1 (50% v/v) and EA = 22.1 kJ mol-1 (0% v/v), 21.0 kJ mol-1 (20% v/v), and 20.4 kJ mol-1 (50% v/v). The decrease in activation energy leads to large increases in the rate of propagation. In addition, the rate of termination decreases by an order of magnitude as the ionic liquid concentration is increased to 60% v/v. The increase in propagation rate was attributed to the increased polarity of the medium, while the decrease in the termination rate is due to its increased viscosity.

Effect of comonomer composition on the controlled free-radical copolymerization of styrene and maleic anhydride by reversible addition–fragmentation chain transfer (RAFT)

Controlled free-radical copolymerization of styrene and maleic anhydride was performed in 1,4-dioxane or tetrahydrofurane solution at 60 °C using the RAFT technique. The effect of monomer feed ratio on copolymerization kinetics and on control over molar mass distribution was examined. It was shown that polymerization was faster and quality of control was poorer when the proportion of maleic anhydride in the monomer feed was larger. These features were assigned to a decrease in the chain transfer constant of the polymeric RAFT agent, most probably due to an increase in the apparent rate constant of propagation with the proportion of maleic anhydride.

Effect of the Intramolecular Chain Transfer to Polymer on PLP/SEC Experiments of Alkyl Acrylates

AbstractPulsed‐laser polymerization (PLP) has been adopted by IUPAC as the method of choice for the determination of propagation rate constants (kp). However, the method has failed in the polymerization of alkyl acrylates at temperatures above 30 °C. In this work, the PLP experiments were analyzed by simulation using a Monte Carlo algorithm. It was found that the experimental difficulties encountered to accurately determine kp at temperatures above 30 °C were caused by extensive intramolecular chain transfer. This mechanism is not operative at lower temperatures because of its high activation energy.Pulsed‐laser polymerization of BA in bulk at temperatures between −41 and +40 °C: Simulated MWD trace.imagePulsed‐laser polymerization of BA in bulk at temperatures between −41 and +40 °C: Simulated MWD trace.

Kinetics of the ring‐opening metathesis polymerization of a 7‐oxanorbornene derivative by Grubbs' catalyst

AbstractThe kinetics of the initiation and propagation of the ring‐opening metathesis polymerization of exo,exo‐5,6‐bis(methoxycarbonyl)‐7‐oxabicyclo[2.2.1]hept‐2‐ene catalyzed by Grubbs' catalyst (Cl2(PCy3)2RuCHPh) were measured by ultraviolet–visible and 1H NMR spectroscopy, respectively. Activation parameters for these processes were also determined. Although the ratio of the rate constant of initiation to the rate constant of propagation was determined to be less than 1 for this system, this polymerization showed many of the characteristics of a living system, including low polydispersities. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2125–2131, 2003

Kinetic Gelation Modeling: Kinetics of Cross-Linking Polymerization

A kinetic gelation model that simulates free-radical network polymerization on a lattice with a stochastic kinetic approach to enable real time calculation was used to assess how initiation rate and primary cyclization affect the overall kinetics of polymerization of difunctional monomers. Changes that cause a more uniform distribution of reacted siteshigher initiation rate or less primary cyclizationincrease the accessibility of free radicals to functional groups, lower the fraction of trapped radicals, and consequently raise the apparent propagation rate constant. On the other hand, the final conversion, determined by kinetic chain length at a given initiator concentration, drops when termination becomes more severe such as under higher initiation rate or when radical trapping worsens such as under enhanced cyclization. In addition, the model simulates the contribution of pendant functional groups to the formation of different structures. The higher the radical concentration brought by higher initiation rate or by less preferred primary cyclization, the lower the fraction of pendant functional groups to form primary cycles and the higher the fractions of pendant functional groups to form cross-links and secondary cycles.

Elementary reaction analysis of the radical polymerization of α‐ethyl β‐N‐(α′‐methylbenzyl)itaconamates carrying (RS)‐ and (S)‐α‐methylbenzylaminocarbonyl groups

AbstractThe polymerizations of α‐ethyl β‐N‐(α′‐methylbenzyl)itaconamates carrying (RS)‐ and (S)‐α‐methylbenzylaminocarbonyl groups (RS‐EMBI and S‐EMBI) with dimethyl 2,2′‐azobisisobutyrate (MAIB) were studied in methanol (MeOH) and in benzene kinetically and with electron spin resonance (ESR) spectroscopy. The initial polymerization rate (Rp) at 60 °C was given by Rp = k[MAIB]0.58 ± 0.05[RS‐EMBI]2.4 ± 0.l and Rp = k[MAIB]0.61 ± 0.05[S‐EMBI]2.3 ± 0.l in MeOH and Rp = k[MAIB]0.54 ± 0.05[RS‐EMBI]1.7 ± 0.l in benzene. The rate constants of initiation (kdf), propagation (kp), and termination (kt) as elementary reactions were estimated by ESR, where kd is the rate constant of MAIB decomposition and f is the initiator efficiency. The kp values of RS‐EMBI (0.50–1.27 L/mol s) and S‐EMBI (0.42–1.32 L/mol s) in MeOH increased with increasing monomer concentrations, whereas the kt values (0.20−7.78 × 105 L/mol s for RS‐EMBI and 0.18−6.27 × 105 L/mol s for S‐EMBI) decreased with increasing monomer concentrations. Such relations of Rp with kp and kt were responsible for the unusually high dependence of Rp on the monomer concentration. The activation energies of the elementary reactions were also determined from the values of kdf, kp, and kt at different temperatures. Rp and kp of RS‐EMBI and S‐EMBI in benzene were considerably higher than those in MeOH. Rp of RS‐EMBI was somewhat higher than that of S‐EMBI in both MeOH and benzene. Such effects of the kinds of solvents and monomers on Rp were explicable in terms of the different monomer associations, as analyzed by 1H NMR. The copolymerization of RS‐EMBI with styrene was examined at 60 °C in benzene. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1819–1830, 2003

Kinetic studies of cationic photopolymerizations of phenyl glycidyl ether: termination/trapping rate constants for iodonium photoinitiators

In this contribution, we have performed a comprehensive investigation of cationic photopolymerizations of phenyl glycidyl ether using two iodonium photoinitiators: diaryliodonium hexafluoroantimonate (IHA), and (tolycumyl) iodonium tetrakis (pentafluorophenyl) borate (IPB). We characterized these reactions using dark-cure experiments in which the polymerization was monitored in the dark after illuminating it for a pre-determined period of time, and obtained profiles of the rate constant for termination/trapping as a function of time. Our studies reveal that though these photoinitiators result in similar reaction kinetics (reaction rate and conversion profiles that are nearly identical) for constant illumination with a Hg(Xe) arc lamp, they lead to very different results in the dark-cure experiments with the iodonium borate salt exhibiting a higher polymerization rate at a given time, and a higher limiting conversion (76%) than observed for the iodonium antimonate salt (62%). These dark-cure trends were explained by the fact that the rate constant for termination/trapping was approximately 50% higher for the iodonium antimonate photoinitiator (0.041 and 0.027min−1 for the IHA and IBP photoinitiators at 50°C, respectively). The active center concentrations and propagation rate constants were also characterized. Relative to the IPB, it was found that the IHA initiator leads to a higher active center concentration (due to the higher molar absorptivity of this initiator at the prominent emission wavelengths of the light source) but a lower propagation rate constant. Therefore, these two photoinitiators yield nearly identical kinetic profiles under constant illumination due to the fact that the IPB photoinitiator leads to a lower active center concentration, which is offset by a higher value of the propagation rate constant, and a lower value of the rate constant for termination/trapping.

Pseudostationary Pulsed Laser Polymerization: A Simple Method for the Direct Determination of Axial Dispersion as Occurring in Size Exclusion Chromatography

AbstractTheoretical distribution curves were calculated for several values of pulse separation t0 and concentrations of initiating radicals ρ formed by each pulse for both types of termination (disproportionation and combination). The absolute and relative peak widths of the additional peaks for the number, molar mass, and hyperdistribution were determined and compared. In all cases, the peak widths of these different distributions became the same with increasing values of C = ktρt0 and/or L0 = kp[M]t0, with [M] = monomer concentration and kt and kp are the rate constants of termination and propagation, respectively. This is similar to the behavior of Poisson distributions if only the degrees of polymerization are fairly high (P̄n ≥ 50). The analogy is further supported by the finding that under the same conditions the peak widths themselves approach the theoretical ones for Poisson distributions. Thus, the fulfilment of these two criteria suggests that the various peaks in multimodal distributions should be treated in the same formal way as Poissonian peaks although they clearly originate from a superposition of adjacent Poissonian peaks of different amplitude and, on the whole have a peak width somewhat in excess of the theoretical one of true Poisson peaks of the same P̄n. The point of inflection can be used as a measure of L0 without reservation only if the first criterion is not fulfilled. The influence of axial dispersion on the location of the extrema was calculated by use of standard deviations σad,k (0.05 and 0.025) to give “experimental curves” for which a pronounced increase in the absolute and relative peak widths was observed. Based on an assumed additivity of the peak variances, a simple procedure was tested for the direct determination of σad,k. The accuracy increased with increasing peak chain lengths and C values for those values determined from the first peak. The values determined from the second peak in the chain length region between 400–700 were closest to the input value.The points of inflection on the low and high molecular weight side of the additional first three peaks are given as a function of the peak maximum. The lower and upper lines were calculated with Equation (11) and (12), respectively.imageThe points of inflection on the low and high molecular weight side of the additional first three peaks are given as a function of the peak maximum. The lower and upper lines were calculated with Equation (11) and (12), respectively.

“Controlled” Synthesis and Characterization of Model Methyl Methacrylate/tert-Butyl Methacrylate Triblock Copolymers via ATRP

The heterogeneous atom transfer radical polymerization (ATRP) of tert-butyl methacrylate (tBMA) using CuX/N,N,N‘,N‘ ‘,N‘ ‘-pentamethyldiethylenetriamine (PMDETA) catalytic system with various initiators R−X (X = Br, Cl) was investigated. The importance of the structure of the initiator on the polymerization of tBMA was briefly examined. Polymerization of tBMA with ethyl 2-bromoisobutyrate resulted in uncontrolled polymerization due to slow initiation because of the low back strain effect and relatively high propagation rate constant of tBMA. Well-controlled polymers were obtained with p-toluenesulfonyl chloride and 2,2,2-trichloroethanol initiators. This can be explained by the fast initiation coupled with the rapid establishment of the equilibrium between the active and dormant species in the polymerization. Poly(methyl methacrylate) macroinitiators were used to synthesize poly(tBMA-b-MMA-b-tBMA) triblock copolymers in a range of tBMA compositions. The use of a mixed halogen system in the block copolymer...

The Quenched Instationary Polymerization Systems (QUIPS)

AbstractThe common element of quenched instationary polymerization systems is that at a given time all radicals present are deactivated by an efficient and fast quench reaction. Quenched instationary polymerizations can be carried out in a variety of ways distinguished by the way periods differing in their initiation characteristics are combined. The total chain length distribution of the resulting polymer is always the sum of the quenched radical and polymer chain length distribution. This distribution is either completely or at least partially dominated by the contribution of the quenched radical spectrum. Depending on the experimental conditions monomodal or multimodal distributions are obtained which can be characterized by their extrema (maximum, points of inflection) and peak widths (absolute, relative). The location of the extrema are related to the experimental parameters and can be used in an unambiguous way for the direct determination of the rate constant of propagation. Absolute peak widths (defined as the difference between two succeeding points of inflection) are invariant quantities with respect to the number, molar mass and hyper distribution which is only true for Poisson (and narrow Gauss) distributions. Relative peak widths are a valuable tool for the direct determination of axial dispersion which occurs in size exclusion chromatography. Comparison of experimental and ideal relative peak widths can be used for the direct determination of the axial dispersion. The influence of the type of termination and [R0] (termination by combination) on the total (number) chain length distribution for single δ‐pulse initiation.magnified imageThe influence of the type of termination and [R0] (termination by combination) on the total (number) chain length distribution for single δ‐pulse initiation.

Emulsion Polymerization of a Sugar Derivative–Kinetic Studies and Properties of the Sugar Latexes

AbstractFree‐radical batch‐emulsion polymerization of 3‐O‐methacryloyl‐1,2:5,6‐di‐O‐isopropylidene‐α‐D‐glucofuranose (3‐MDG) initiated by a water‐soluble initiator (potassium peroxodisulfate, KPS), in the presence of an ionic emulsifier (sodium dodecyl sulfate, SDS), was investigated at 60 °C. The effect of the emulsifier and initiator concentration on the reaction kinetics and on the colloidal and molecular properties of the sugar latexes was studied. It was found that the rate of polymerization over interval II is proportional to the concentration of the initiator and the emulsifier raised to the power of 0.40 and 0.68, respectively. The particle size decreased and the number of particles increased with increasing either SDS or KPS concentration. The average value of the propagation rate constants of polymerization (kp) for 3‐MDG was found to be 257 L · mol−1 · s−1. The weight‐average molecular weights also increased with increasing the emulsifier concentration. The sugar latexes exhibit a high glass transition temperature (Tg) of 167 °C.Effect of SDS concentration on the average number of particles (Np) and the weight‐average molecular weight (Mw).magnified imageEffect of SDS concentration on the average number of particles (Np) and the weight‐average molecular weight (Mw).