Propagation Rate Constants Research Articles

Investigation of the Peak Width of Polystyrene Prepared by Rotating‐Sector Polymerization in Microemulsion

AbstractStyrene was polymerized by intermittent photoinitiation (at a constant sector speed and a light to dark ratio of 1:5) in microemulsion. The molecular weight distribution was measured by size‐exclusion chromatography and turned out to be extremely well structured. When the points of inflection were used for the calculation of the rate constant of propagation in analogy to pulsed‐laser polymerization/size‐exclusion chromatography (PLP‐SEC), values were obtained which were lower than those accepted for bulk polymerization but good agreement was achieved with a slightly modified equation. The absolute peak width (introduced as the difference between two successive points of inflection) turned out to be an invariant quantity no matter which type of distribution curve (number, molar mass, or hyper distribution) was analyzed, thus demonstrating the Poissonian character of the peaks. Furthermore, the relative peak widths (defined as the ratio of two successive points of inflection) for the first peak scattered between 1.35–1.45, those for the second peak between 1.26–1.30. After subtracting the respective value for the theoretical peak width, the same value for the first and second peaks was obtained for all experiments over a broad range of experimental parameters. As the appearing peaks are well resolved and narrow, the influence of axial dispersion on the results is, therefore, conclusively demonstrated. A simple procedure for the direct determination of axial dispersion is presented based on the relative peak widths and the additivity of the peak variances. The invariance of the peak widths is an easily verifiable theoretical and experimental prerequisite for this procedure. Comparison of GPC traces of a microemulsion polymerization of styrene (t0 = 1.4 s, [M] = 4.326 mol · l−1; light‐to‐dark ratio 1:5; full line) and of a standard mixture (styrene, peak masses: 1 950, 89 400, 993 000; dashed line).imageComparison of GPC traces of a microemulsion polymerization of styrene (t0 = 1.4 s, [M] = 4.326 mol · l−1; light‐to‐dark ratio 1:5; full line) and of a standard mixture (styrene, peak masses: 1 950, 89 400, 993 000; dashed line).

Synthesis and photopolymerization kinetics of new flexible diacrylate and dimethacrylate crosslinkers based on C18 diacid

A series of new di(meth)acrylate monomers was synthesized from the reactions of methyl α-hydroxymethylacrylate (MHMA), ethyl α-hydroxymethylacrylate (EHMA), hydroxyethyl acrylate (HEA) and hydroxyethylmethacrylate (HEMA) with α,ω-C18 diacid chloride. The photopolymerization behavior and reaction kinetics of the synthesized monomers were investigated using photoinitiation with differential scanning calorimetry. The polymerization rates, conversions and kinetic constants for propagation and termination were determined for each of the monomers. The maximum rate of polymerizations of the diacrylate monomers was higher than that of the dimethacrylate monomers and followed the order: HDDA (1,6-hexanediol diacrylate)>HEA-C18>EHMA-C18∼HEMA-C18>MHMA-C18. The total conversions obtained were 78, 75, 72, 64 and 69% for MHMA-C18, EHMA-C18, HEMA-C18, HEA-C18 and HDDA, respectively, indicating comparable or higher conversions for methacrylates despite their lower rates of polymerization. Propagation and termination mechanisms of the monomers were investigated by plotting propagation and termination rate constants as a function of conversion.

Effect of minor additives of arenes on chain termination in low-temperature cationic polymerization of isobutylene in aliphatic solvents

The influence of small concentrations (1—8 mmol L–1) of arenes (viz., hexafluorobenzene, chlorobenzene, benzene, toluene, and mesitylene) on the molecular weight, molecular weight distribution, and degree of functionalization by terminal olefin groups was studied for polymers prepared by low-temperature (–78 °C) isobutylene polymerization in n-hexane initiated by the MeOH—AlBr3 and ButCl—AlBr3 systems. The criteria “extent of livingness” kel/kp were calculated, where kel and kp are the rate constants of proton elimination and chain propagation, respectively. It was established that arenes can be involved in proton elimination from the growing carbocation, and their activity in this process increases with an increase in the basicity. Arenonium ions formed by the interaction of arenes with the components of the initiating system or with the growing ionic active centers can form complexes with counteranions, thus retarding proton elimination with the transfer to the counterion.

Photo-DSC cure kinetics of vinyl ester resins II: influence of diluent concentration

The photopolymerization kinetics of two commercial vinyl ester resins (VERs) and a model VER photoinitiated by the camphorquinone/amine photoinitiator system were monitored using isothermal DSC. A decrease in styrene concentration in model VERs was found to raise the rate of photopolymerization. In contrast, when the styrene was replaced by a monomethacrylate diluent, the photopolymerization rate passed through a maximum near 70 wt% diluent monomer. This difference in the variation of the rate of polymerization with decreased monomer concentration was attributed to the competition of the effects of the higher reactivity of the methacrylyl radical relative to the styryl radical and the lower termination rate for divinyl-rich systems (both of which tend to raise the maximum polymerization rate) and the effects of the reduction in the initiation efficiency and decrease in k p due to increased fraction of pendant double bonds (which lower the polymerization rate) when the concentration of diluent monomer was reduced. Subsequent dark polymerization was observed during a temperature ramp and the onset of polymerization was independent of resin composition due to vitrification effects during the isothermal photocuring stage. The kinetics during the dark polymerization stage was discussed in terms of the radical concentration and the propagation rate constant. Increases in the concentration of either diluent monomer raised the extent of isothermal cure during the isothermal polymerization because vitrification was delayed by the lower crosslink density and the plasticizing effect of the diluent. Higher levels of diluent also raised the maximally attainable conversion due to reduced topological restrictions for reaction in networks of lower crosslink density.

Polymerization of neat 2‐ethylhexyl acrylate induced by a pulsed electron beam

AbstractThe bulk polymerization of 2‐ethylhexyl acrylate (2‐EHA), induced by a pulsed electron beam, was investigated with pulse radiolysis, gravimetry, and Fourier transform infrared spectroscopy. The roles of the dose rate, pulse frequency, and added acrylic acid (AA) in the polymerization of 2‐EHA were examined at ambient temperature. In the range of 12.6–71.2 Gy/pulse, the polymerization of 2‐EHA was dose‐rate‐dependent: at the same total dose, a lower dose rate yielded a higher conversion. Also, a lower pulse rate gave a higher conversion at the same total dose. The addition of up to 10 wt % AA showed no increase in the conversion of 2‐EHA at a low conversion (8 kGy), but at a higher conversion (16 kGy), a 20 wt % increase in the conversion of 2‐EHA was observed. The estimated values (1.6 ± 0.3) × 10−3 (dm3 s)3/2 mol−1 s−1/2 for kp(G/2kt)1/2 and 2.6 ± 0.8 dm3 s J−1 for 2ktG (where kp is the rate constant of propagation, kt is the rate constant of bimolecular termination, and G is the yield of free radicals) were obtained at relatively low conversions. The reaction rate constant of the addition of 2‐EHA· free radicals to the monomer was measured by pulse radiolysis and found to be 2.8 × 102 mol−1 dm3 s−1. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 196–203, 2003

Molecular Weight Distribution in Living Polymerization Proceeding with Reshuffling of Polymer Segments due to Chain Transfer to Polymer with Chain Scission, 2. Monte Carlo Simulation of Polymer Reshuffling Proceeding with Disproportionation of Chain Functionalities

The method for analyzing the reshuffling of polymer segments developed previously has been extended to systems involving the disproportionation of chain functionalities. The effect of interchain exchange reactions of this type, leading to the redistribution of chain lengths and of the chain functionalities (redistribution of living and dead chain ends), was analyzed by means of the Monte Carlo simulations. In the systems, in which no propagation occurs (monomer concentration equal to zero), a set of polymer chains containing one living and one dead end was taken as an initial material. A series of simulations were performed for systems with differing molecular weight distributions of the starting macromolecules. Uniform (no chain length distribution polymer – all chains are of the same length), Poisson, and the most probable (geometric) distributions were taken into consideration. Although the molecular weight distributions (MWDs) of functionally different chains of the same polymer were different apart from the eventual equilibrium conditions, the overall MWD was very close to that observed in analogous systems without disproportionation. The same was observed concerning MWDs in modeled polymerization systems, in which reshuffling and disproportionation accompanied propagation. Consequently, a method of estimating the ratio of rate constants of propagation and reshuffling (i. e. kp /k tr) in the relevant polymerization systems, using the observed polydispersity indexes, was proposed. The extent of disproportionation can be evaluated from the determined relationships of the polydispersity index and of the monofunctional chains fraction as functions of the average number of chain transformations.

Radical polymerization behavior of ethyl ortho‐(4‐phenyl‐1,3‐dioxolan‐2‐yl)phenyl fumarate

AbstractThe polymerization of ethyl ortho‐(4‐phenyl‐1,3‐dioxolan‐2‐yl)phenyl fumarate (EPDPF) with dimethyl 2,2′‐azobisisobutyrate (MAIB) was kinetically investigated in benzene. The polymerization rate (Rp) at 60 °C was presented by Rp = k[MAIB]1.1[EPDPF]0.8. The number‐average molecular weight of poly(EPDPF) was in the range of 2500–3500. Analysis of 1H and 13C NMR spectra of the resulting polymers suggested that the radical polymerization of EPDPF proceeds in a complicated manner involving vinyl addition, intramolecular hydrogen abstraction, and ring opening of the cyclic acetal. The polymerization system involved electron spin resonance (ESR)‐observable poly(EPDPF) radicals under the practical polymerization conditions. ESR‐determined apparent rate constants (2.0–8.5 L/mol s) of propagation increased with increasing initiator concentration and decreasing monomer concentration. The apparent rate constants (0.68–6.6 × l06 L/mol s) of termination decreased with the monomer concentration and slightly increased with the initiator concentration. The activation energies of initiation (Ei), propagation (Ep), and termination (Et) were calculated as Ei = 158, Ep = 41, and Et = 30 kJ/mol, respectively. Radical copolymerization of EPDPF with styrene was also examined at 70 °C in benzene. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2945–2955, 2002

Solvent effect on radical homo- and copolymerization of di-2-[2-(2-methoxyethoxy)ethoxy]ethyl itaconate

Solvent effect on homo- and copolymerization of di-2-[2-(methoxyethoxy)ethoxy]ethyl itaconate (DMEI) was studied at 50 °C using dimethyl 2,2 ′-azobisisobutyrate as radical initiator. The polymerization rate ( R p) highly depended on the kind of solvent; 19 solvents were used. The highest R p (in 1-tetradecanol) is 13 times the smallest (in chloroform). On the other hand, the solvents did not exert as great an effect on the molecular weight of the resulting polymers. The propagation rate constant ( k p) was determined in 15 different solvents by means of ESR spectroscopy. The highest k p (4.5 l/mol s in toluene) is 5.6 times the lowest (0.8 l/mol s in chloroform). A noticeable solvent effect was also observed in the copolymerization of DMEI ( M 1) and styrene ( M 2), where nine solvents were used. The highest r 1 (0.46 in 1-butanol) is about 6 times the lowest (0.08 in methanol). The r 2 value falls in the range of 0.2 (dimethyl sulfoxide) and 0.52 (benzene). The solvent effects thus observed were analyzed according to the linear solvation energy relationship proposed by Taft and co workers.

Tacticity dependence of reactivity of stereoregular poly(methyl methacrylate) macromonomers having a methacryloyl function in radical polymerization

Radical polymerizations of highly isotactic (it-) and highly syndiotactic (st-) poly(methyl methacrylate) (PMMA) macromonomers having a methacryloyl function were studied in benzene-d 6 at 60°C with 2,2′-azobisisobutyronitrile (AIBN). Rate of polymerization (R p) was determined from the consumption of the macromonomer by means of 1H NMR spectroscopy. The R p of the it-PMMA macromonomer was larger than that of the st-PMMA macromonomer. Concentrations of propagating radicals, [M·] , were estimated for the polymerization with di-t-butyl peroxide in benzene under irradiation of light at 30°C. The value of [M · ] for the polymerization of the st-PMMA macromonomer was larger than that for the polymerization of the it-PMMA macromonomer. The results indicated that rate constant of propagation (k p) for the it-PMMA macromonomer was larger than that for the st-PMMA macromonomer.

About propagation rate constants in carbocationic polymerizations

Published carbocationic propagation rate constants vary between 2 103 and 5 109 L·mol−1·s−1, e.g. for kp± with styrene in CH2Cl2. The low values were deduced from an evaluation of [Pn±], the high values from competitive experiments assuming diffusion-controlled termination. Recent kinetic and spectrophotometric studies of indene living polymerization have given intermediate values (5 104 to 5 105 L·mol−1·sec−1). An explanation of the high values obtained by the competition method is suggested.

On the propagation rate constants of cationic polymerizations

AbstractThe concepts employed to explain polymerizations by ionizing radiations are used for a critical examination of the concepts involved in interpreting the kinetics of chemically initiated cationic polymerizations. It is explained how the interactions of the propagating carbenium ions with the solvent, monomer, and anion can result in the formation of up to six distinct unpaired species and several kinds of ion pairs; therefore, the consumption of the monomer can be governed simultaneously by many rate constants. Only one of these can have any general theoretical use, and suggestions are made for how it can be measured. For the first time, it is shown that the ion‐pairing process must involve a ligand displacement and so resembles the amination of the Ag+ ion, for example, in an aqueous solution by NH3, rather than an association of inert ions of unchanging identity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2537–2544, 2002

Initiation and Propagation Rate Constants for the Cationic Polymerization of N-Vinylcarbazole

The kinetics of the reactions of benzhydryl cations with N-vinylcarbazole (1) and of the reactions of the N-ethylidenecarbazolium ion (6) with π-nucleophiles have been investigated to determine the nucleophilicity parameters N and s for 1 and the electrophilicity parameter E for 6. These values were employed to predict potential initiators for the cationic polymerization of N-vinylcarbazole (1) and to calculate the propagation rate constant for this process.

Development of a Comprehensive Model for Diffusion-Controlled Free-Radical Copolymerization Reactions

In the present study a comprehensive mathematical model for diffusion-controlled free-radical copolymerization reactions is developed. Termination and propagation rate constants as well as initiator efficiency are expressed in terms of a reaction-limited term and a diffusion-limited one. The contribution of the latter term to the apparent rate constants is described in terms of the diffusion coefficients of the corresponding species (e.g., polymer chains, monomers, primary radicals), calculated using the generalized free-volume theory of Vrentas and Duda for a ternary system, and an effective reaction radius. The predictive capabilities of the present model are demonstrated by simulating three free-radical polymerization systems, namely, the bulk copolymerizations of styrene−methyl methacrylate, styrene−acrylonitrile, and p-methylstyrene−methyl methacrylate. It is shown that the model predictions are in excellent agreement with experimental data on monomer conversion, average molecular weights, and copolymer composition, reported in the open literature under various experimental conditions.

Mechanistic comparison of cyclic ester polymerizations by novel iron(III)-alkoxide complexes: single vs multiple site catalysis.

The complexes Fe2(OCHPh2)6 and L2FeOR (R = Et or CHPh2, L = N,N'-bis(trimethylsilyl)benzamidinate) were structurally characterized, and comparative studies of the behavior of those compounds comprising the same alkoxide (Ph2HCO-) in polymerizations of -caprolactone (CL) and D,L-lactide (LA) were performed. Both Fe2(OCHPh2)6 and L2FeOCHPh2 are effective polymerization catalysts, as reflected by molecular weight control, polydispersities, and end group analysis, but the diiron complex generally exhibits greater polymerization control, particularly for CL. Kinetic investigations of the polymerization of CL revealed the same first-order dependence on [CL] for both catalysts, but different orders in [catalyst] that signified a distinct contrast in mechanism. Analysis that invoked the presence of a termination-causing impurity at low concentration yielded a first-order dependence on [Fe2(OCHPh2)6], but the order in [L2FeOCHPh2] was found to be one-half. This fractional dependence was interpreted by using a model of active chain aggregation. Comparison of the derived propagation rate constants (k(prop)) revealed a approximately 50-fold greater value for the diiron complex compared to the single site mononuclear compound. Implications of these findings for understanding cyclic ester polymerization mechanisms and catalyst design are discussed.

Radical Polymerization of Isomeric Methacrylic Monomers: cis- and trans-(2-Phenyl-1,3-dioxan-5-yl) Methacrylate

Two new monomers, cis-(2-phenyl-1,3-dioxan-5-yl) methacrylate (CPDM) and trans-(2-phenyl-1,3-dioxan-5-yl) methacrylate (TPDM), have been synthesized. The stereochemical configuration in both monomers was unequivocally assigned by correlation 1H−13C NMR experiments. The radical polymerization reactions of both monomers were studied by ultraviolet spectroscopy and electron paramagnetic resonance spectroscopy to determine the polymerization rate parameter kp/kt1/2 and the absolute propagation and termination rate constants (kp and kt) at different temperatures. The values of kp/kt1/2 lie in the range 0.40−0.55 L1/2/(mol1/2 s1/2) for CPDM and 0.29−0.37 L1/2/(mol1/2 s1/2) for TPDM at temperatures between 45 and 70 °C, showing that the polymerization rate of the cis monomer with the substituents in equatorial−axial positions on the dioxane ring is higher than that of its trans counterpart with the phenyl and ester residue in equatorial positions on the dioxane ring. Using EPR measurements of the polymer radical...

ESR study on radical polymerization and its application to microemulsion systems

Well-resolved electron spin resonance (ESR) spectra of propagating radicals of vinyl and diene compounds were observed in a single scan by a conventional CW-ESR spectrometry without the aid of computer accumulation and the specially designed cavity and cells Although solvents which could be used for ESR measurements were restricted to nonpolar solvents, such as benzene, toluene, and hexane, new information on dynamic behavior and reactivity of the propagating radicals in the radical polymerization of vinyl and diene compounds were obtained. Thus, values of propagation rate constants (k p ) for vinyl and diene compounds were determined by an ESR method. Some of the k p values were in a fair agreement with those obtained by a pulsed laser polymerization (PLP) method. Furthermore, polymer chain effect on apparent k p was clearly observed in the radical polymerization of macromonomers and in the microemulsion polymerization. In ESR measurement on inclusion polymerization system, important information on the origin of the 9-line spectrum observed in the radical polymerization of methacrylate propagating radicals was obtained.

Kinetic investigation of the anionic polymerization of MMA using sparteine as σ-ligand

The kinetics of the anionic polymerization of methyl methacrylate using THF as solvent, 1,1-diphenylhexyllithium as initiator and sparteine as ligand has been investigated in a flow-tube reactor for initiator concentrations higher than 1×10 −3 mol l −1 and a temperature range between −10 and 20 °C. Addition of sparteine induced a decrease in both the reactivity of the growing enolates and the extent of termination reactions. While a fractional kinetic order relative to the active centres was obtained in the presence of sparteine, this additive shifted the equilibrium between aggregated and unimeric species toward the formation of unimeric-ligated enolates as indicated by entropic and enthalpic parameters of the aggregation equilibrium. The rate constants of propagation and termination of these growing species were also determined.

The Quenched Instationary Polymerization System, 5. The Peak Broadness as an Invariant Quantity of the Number, Molar Mass and Hyper Distributions

The total number, molar mass and hyper distributions generated by quenched instationary polymerization techniques are dominated by the radical chain length distribution (RCLD) whereas the contribution from the polymer chain length distribution (PCLD) is in most cases negligible. For the determination of the rate constant of propagation (k p ) the location of different extraordinary points of the distribution curves is determined by the use of the first and second derivatives. For the number, molar mass and hyper distributions these points are related in an unambiguous way to k p [M]tx and can be used to extract k p . The choice of t x (duration of the dark period, or an initiation period. or the sum of different periods) depends on the experimental conditions (δ-pulse, incomplete preeffect, combination of periods differing in initiation extent) and is essential for the proper determination of k p . The broadness of appearing peaks (introduced as the difference between two succesive points of inflections) turned out to remain the same inespective which type of distribution curve was analyzed. Analytical expressions for the peak broadness were derived for different types of quenched instationary polymerization conditions. For δ-pulse initiation the broadness of the Poisson peak depends simply on the number of propagation steps that occurred whereas for non-δ-pulse initiation conditions the peak broadness is governed by the corresponding duration of the initiation period.

Search for highly resolved electron spin resonance spectra of the transient radical in radical polymerization

AbstractThe detection of highly resolved spectra in electron spin resonance (ESR) measurements of radical polymerization is presented. Well‐resolved ESR spectra of the propagating radical were detected in the radical polymerization of several vinyl monomers with a specially designed cavity and cell. More highly resolved ESR spectra of the propagating radicals of vinyl and diene compounds were observed with aconventional spectrometer without the specially designed cavity and cell. On the basis of the ESR spectra, propagation rate constants and dynamic behavior of propagating radicals are discussed. Moreover, the application of time‐resolved ESR spectroscopy to research on the initiation process in radical polymerization is shown. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 269–285, 2002

Synthesis and characterization of a new fluorogenic probe molecule N-(1-pyrene)methacrylamide for monitoring radiation-induced polymerization

This paper introduces the fluorogenic probe label N-(1-pyrene)methacrylamide (PyMA) used for monitoring radiation-induced polymerization in situ. The synthesis of the probe is given in addition to the experimentally determined relative reactivity of the probe during the radical polymerization of methyl methacrylate (MMA). The ratio between propagation rate constants for the reaction in which an MMA radical chain-end reacts with PyMA relative to the reaction with TaMMA is found to be 0.85±0.07. The results are compared with those for the commercially available fluorogenic probe N-(1-pyrene)maleimide (MPy).