Free Radical Copolymerization Kinetics Research Articles

Modeling of the Free Radical Copolymerization Kinetics of n-Butyl Acrylate, Methyl Methacrylate and 2-Ethylhexyl Acrylate Using PREDICI®

Kinetic modeling of the bulk free radical copolymerizations of n-butyl acrylate (BA) and 2-ethylhexyl acrylate (EHA); methyl methacrylate (MMA) and EHA; as well as BA, MMA and EHA was performed using the software PREDICI®. Predicted results of conversion versus time, composition versus conversion, and molecular weight development are compared against experimental data at different feed compositions. Diffusion-controlled effects and backbiting for BA were incorporated into the model as they proved to be significant in these polymerizations. The set of estimated global parameters allows one to assess the performance of these copolymerization systems over a wide range of monomer compositions.

Copolymerization Kinetics of Polyetyhylenglycol Allylether Type Polycarboxylate Superplasticizer

The free radical copolymerization kinetics of polyethylenglycol allylether (APEG) with acrylic acid (AA) had been studied in aqueous solution through using ammonium persulfate (APS) and 30% hydrogen peroxide (H2O2) as initiators. The structure of polycarboxylate superplasticizer had been characterized by IR and 1H-NMR. The rate of copolymerization was proportional to the molar ratio of monomers (AA:APEG) to the power of 0.4405, and to the amount of initiator (1.5%APS-2%H2O2, mass ratio to monomers) to the power of 0.7819, respectively. The overall observed activation energy of copolymerization was 45.048 kJ/mol. The kinetic relationship of copolymerization reaction of APEG with AA had been established as follow: Rp∝[APEG/AA]0.4405[APS-30%H2O2]0.7819e-5418/T. The temperature and initiator were main influencing factors on polymerization reaction.

On Single Compartment Pharmacokinetic Model Systems that Obey Free Radical Copolymerization Kinetics and Multiplicity

This study examines the issues in development of pharmacokinetic single compartment model for systems that obey free radical copolymerization kinetics. Copolymer composition as a function of reactivity ratios of comonomers for well mixed case was derived. For some cases, such as DEF-AN, diethyl fumarate and acrylonitrile system multiplicity in composition were found. The analysis is extended to n monomers. State space model expressions are used and the QSSA assumption is stated in state space equation form. Conditions when damped oscillations can be expected are noted. In addition to multiplicity in product composition, an account of reactivity ratios and other instances of multi- plicity were found during the pharmacodynamics of the free radical polymerization reactions. A careful study of initiated case, thermal case, 1 CSTR and 2 CSTRS was undertaken and results were presented. Numerical integration techniques were employed on the desktop computer. Steady state and transient state conversion for initiated case and thermal case for 1 CSTR and 2 CSTRs were calculated and plotted in Figures 7-9 and 12. No multiplicity was found in the thermal case for 1 CSTR in the dynamics of transient monomer conversion. Multiplicity was found in the initiated case for 1 CSTR in the dynamics of transient conversion of monomer. The multiplicity was found in the second CSTR for the case of 2 CSTRs in series. No multiplicity was found in the case of initiator decay.

A quantum chemistry study of the free‐radical copolymerization propagation kinetics of styrene and 2‐hydroxyethyl acrylate

AbstractSeveral difficulties are reported in literature about the experimental analysis of polymerizations involving 2‐hydroxyethyl acrylate (HEA), mainly due to transfer reactions that characterize the system. In particular, major problems are emerged in the study of free radical copolymerization kinetics of HEA. In this work, free‐radical copolymerization propagation kinetics of HEA and styrene (ST) are investigated through a computational approach based on density functional theory. Monomer reactivity ratios for HEA/ST copolymerization are calculated at 50°C and 125°C, obtaining values that exhibit a weak dependence on temperature. In particular, HEA reactivity ratio, rHEA, equal to 0.14 and ST reactivity ratio, rST, equal to 0.31 at 50°C, whereas rHEA = 0.17 and rST = 0.29 at 125°C. Moreover, the reliability of such parameters has been tested by analyzing copolymer composition data as a function of monomer feed composition, at the same temperatures indicated above. Experimental values proposed in literature are well predicted by the terminal copolymerization model using the kinetic parameters computationally determined. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers

Free Radical Copolymerization Kinetics of γ-Methyl-α-methylene-γ-butyrolactone (MeMBL)

The propagation kinetics and copolymerization behavior of the biorenewable monomer γ-methyl-α-methylene-γ-butyrolactone (MeMBL) are studied using the pulsed laser polymerization (PLP)/size exclusion chromatography (SEC) technique. The propagation rate coefficient for MeMBL is 15% higher than that of its structural analogue, methyl methacrylate (MMA), with a similar activation energy of 21.8 kJ·mol(-1). When compared to MMA, MeMBL is preferentially incorporated into copolymers when reacted with styrene (ST), MMA, and n-butyl acrylate (BA); the monomer reactivity ratios fit from bulk MeMBL/ST, MeMBL/MMA, and MeMBL/BA copolymerizations are r(MeMBL) = 0.80 ± 0.04 and r(ST) = 0.34 ± 0.04, r(MeMBL) = 3.0 ± 0.3 and r(MMA) = 0.33 ± 0.01, and r(MeMBL) = 7.0 ± 2.0 and r(BA) = 0.16 ± 0.03, respectively. In all cases, no significant variation with temperature was found between 50 and 90 °C. The implicit penultimate unit effect (IPUE) model was found to adequately fit the composition-averaged copolymerization propagation rate coefficient, k(p,cop), for the three systems.

Development of a Continuous Emulsion Copolymerization Process in a Tubular Reactor

This contribution describes the development of a continuous emulsion copolymerization processs for vinyl acetate and n-butyl acrylate in a tubular reactor. Special features of this reactor include the use of oscillatory (pulsed) flow and internals (sieve plates) to prevent polymer fouling and promote good radial mixing, along with a controlled amount of axial mixing. The copolymer system studied (vinyl acetate and butyl acrylate) is strongly prone to composition drift due to very different reactivity ratios. An axially dispersed plug flow model, based on classical free radical copolymerization kinetics, was developed for this process and used successfully to optimize the lateral feeding profile to reduce compositional drift. An energy balance was included in the model equations to predict the effect of temperature variations on the process. The model predictions were validated with experimental data for monomer conversion, copolymer composition, average particle size, and temperature measured along the reactor length.

An Investigation of Free Radical Copolymerization Kinetics of the Bio‐renewable Monomer γ‐Methyl‐α‐methylene‐γ‐butyrolactone with Methyl methacrylate and Styrene

AbstractThe free‐radical copolymerization propagation kinetics of the bio‐renewable monomer γ‐methyl‐α‐methylene‐γ‐butyrolactone (MeMBL) with styrene (ST) and with methyl methacrylate (MMA) have been investigated by the pulsed laser polymerization (PLP)—size exclusion chromatography (SEC) technique, in addition to DSC and proton NMR measurements. Monomer reactivity ratios for bulk MeMBL/ST and MeMBL/MMA copolymerizations are rMeMBL = 0.80 ± 0.04 and rST = 0.34 ± 0.04 and rMeMBL = 3.0 ± 0.3 and rMMA = 0.33 ± 0.01, respectively, with no significant variation with temperature found between 22 and 90 °C. The implicit penultimate unit effect (IPUE) model best represents the composition‐averaged copolymerization propagation rate coefficient, kp,cop for the MeMBL/ST system. Arrhenius parameters were estimated for MeMBL homopolymerization and found to be quite similar to those of MMA. DSC results show that copolymers of well controlled composition can be produced to suit specific Tg requirements over a much higher temperature range than possible with current acrylic glasses.magnified image

Evaluation of the Performance of a Kinetic Model for Free‐Radical Copolymerization of Vinyl/Divinyl Monomers in Supercritical Carbon Dioxide

AbstractThe performance of a mathematical model for free radical copolymerization kinetics with crosslinking of vinyl/divinyl monomers in supercritical carbon dioxide previously developed in our group is evaluated using experimental data of conversion versus time and gel fraction versus conversion for copolymerization of styrene and divinylbenzene. The effects of process conditions, type of stabilizer and initial divinyl monomer composition were also assessed. Reasonable agreement between model predictions and experimental data was obtained.

Modeling of the Free-Radical Copolymerization Kinetics with Cross Linking of Vinyl/Divinyl Monomers in Supercritical Carbon Dioxide

A mathematical model for free-radical copolymerization kinetics with cross linking of vinyl/divinyl monomers in carbon dioxide at supercritical conditions was developed. The copolymerization of styrene and divinylbenzene is analyzed as a case study. The effects of the kinetic and physical parameters on monomer conversion, molecular-weight development, copolymer composition, appearance of the gelation point, gel fraction, and average cross-link density are studied. Model predictions show the expected trends, although the system is quite sensitive to pressure, which provides an interesting and promising way to tailor some of the polymer properties.

Determination of reactivity ratios and kinetics of free radical copolymerization of linalool with styrene

AbstractCopolymerization of acyclic monoterpenoid, namely linalool (LIN), with styrene (STY) initiated by benzoyl peroxide (BPO) p‐acetyl benzylidene triphenyl arsonium ylide (p‐ABTAY) in xylene separately at 80°C for 180 min under inert atmosphere of nitrogen was performed. The results give a nearly alternating copolymer as evidenced from reactivity ratios (r1 = 0.016, r2 = 0.057) w.r.t. BPO; (r1 = 0.017, r2 = 0.052) w.r.t. p‐ABTAY (i.e. r1 = 0.0165 ± 0.0005 and r2 = 0.0545 ± 0.0025 per initiator set) using Kelen–Tudos method. The FT‐IR spectrum shows a band at 3026 cm−1 due to the aromatic ring of polystyrene and an alcoholic band of linalool at 3408 cm−1. 1H‐NMR spectrum shows peaks at δ 7.0–7.7 ppm of OH protons and peaks at δ 7.5–8.0 ppm due to phenyl protons of styrene. The system follows ideal kinetics i.e. Rp ∝ [LIN]1.0[STY]1.0[BPO]0.5/[p‐ABTAY]0.5. The overall energy of activation in the temperature range 75–85°C is 77.0 kJ mol−1 and 90.0 kJ mol−1, respectively. The values for Mark–Houwink constants for the functional copolymer has been evaluated as a = 0.40 and K = 1.60 × 10−4 with the help of gel permeation chromatography (GPC). Alfrey–Price, Q and e parameters for linalool have been evaluated as Q2 = 0.80; e2 = 1.25 w.r.t. BPO and Q2 = 0.90; e2 = 1.54 w.r.t. p‐ABTAY. Thermal properties of copolymers were investigated by thermogravimetric analysis (TGA) techniques. Copyright © 2004 John Wiley & Sons, Ltd.

Synthesis of Comblike Poly(butyl methacrylate) Using Reversible Addition−Fragmentation Chain Transfer and an Activated Ester

Comblike polymers of poly(n-butyl methacrylate) were prepared using an activated ester-type comonomer (N-acryloxysuccinimide, NAS) to generate branch points. The conventional solution free-radical copolymerization kinetics of n-butyl methacrylate (BMA) and NAS were first investigated by following individual monomer consumption rates by H-1 NMR spectrometry and reactivity ratios of BMA and NAS determined using the terminal model. The reactivity ratios so obtained are both close to 0.2; the joint confidence interval is also determined. Reversible addition-fragmentation chain transfer (RAFT) was then used to grow polymers with controlled backbone and branch chain length. Because both reactivity ratios have similar values, this implies that the copolymer will have a random distribution of NAS and hence of branch points. RAFT-mediated polymerization was first used to synthesize linear poly(BMA-co-NAS) chains. Primary hydroxy-functionalized RAFT agents were then immobilized on this linear poly(BMA-co-NAS) through nucleophilic substitution on the activated ester units of the NAS. From these immobilized RAFT agents, branches were grown upon addition of a further aliquot of monomer (BMA) and initiator (AIBN). The amount of NAS in the starting BMA/NAS composition was varied without adversely affecting the uniformity of the NAS distribution along the resulting linear poly(BMA-co-NAS) backbone. This results in branched polymers whose molecular weight, branching density, and degree of polymerization of branches are all relatively narrow and controlled.

On the inverse miniemulsion copolymerization and terpolymerization of acrylamide, N, N′-methylenebis(acrylamide) and methacrylic acid

AbstractThe kinetics of free-radical copolymerization and terpolymerization of acrylamide (AAm), N, N′-methylenebis(acrylamide) (MBA) and methacrylic acid (MA) in the inverse water/monomer/cyclohexane/Tween 85 miniemulsion was investigated. Polymerizable sterically-stable miniemulsions were formulated in cyclohexane as a continuous medium. Polymerizations are very fast and reach the final conversion within several minutes. The dependence of the polymerization rate vs. conversion is described by a curve with two nonstationary rate intervals. The maximum rate of polymerization slightly increases with increasing concentration of crosslinking monomer (MBA) and strongly decreases by the addition of MA. The rate of polymerization is inversely proportional to the 0.9th and 1.8th power of the particle concentration without and with MA, respectively. The number of polymer particles is inversely proportional to the 0.18th and 0.13th power of MBA concentration. The kinetic and colloidal parameters of the miniemulsion polymerization are discussed in terms of microemulsion polymerization model.

The mechanism of propagation in free-radical copolymerization

A brief overview of free-radical copolymerization kinetics is presented. Recent developments have highlighted the shortcomings of the terminal (or Mayo–Lewis) model. However, for many practical reasons, approximate models are useful for assisting our understanding of any given copolymerization reaction and allowing comparisons with the vast database on copolymerization reactions. Terminal model reactivity ratios have limited meaning, so it may be imprudent to use these values as a quantitative measurement of radical reactivity. Presently, experimental limitations restrict the amount of information that can be obtained by models being fitted to composition or propagation rate data; therefore, the direct measurement of radical reactivity is required together with high-level quantum calculations. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 597–603, 2001

Penultimate Unit Effect in Free-Radical Copolymerization

Based upon new insights into the dynamics of propagation reactions, a theoretical justification of the penultimate model in free-radical copolymerization kinetics is proposed. It is suggested that the penultimate unit effect may contain a large steric contribution (a different penultimate unit may affect the frequency factor for propagation by a factor typically between 1 and 10) and that the effect on activation energies is generally small. This implies that the stabilization energy model, where only differences in activation energies play a significant role, is valid only under unusual circumstances. Furthermore, a possible explanation is given for the occurrence of both the implicit and explicit penultimate unit effects. It is shown that mainly systems in which there is a large difference in the sizes of the substituents of both monomers are expected to exhibit an explicit penultimate unit effect. Finally, it is shown that neither a purely enthalpic effect, nor the steric effect proposed here, provides an adequate explanation why, experimentally, mainly radical reactivity ratios less than unity are found.

Emulsion co- and terpolymerization of styrene, methyl methacrylate, and methyl acrylate. I. Experimental determination and model prediction of composition drift and microstructure in batch reactions

In Part I of this series the reactivity ratios of the comonomer pair methyl acrylate-methyl methacrylate were determined with low-conversion bulk polymerizations. It was shown that the binary reactivity ratios of the systems styrene-methyl acrylate, styrene-methyl methacrylate, and methyl acrylate-methyl methacrylate describe composition drift in low-coversion bulk terpolymerizations with these monomers reasonably well. A computer model was developed to simulate the composition drift in emulsion co- and terpolymerizations. The composition drift in two batch emulsion copolymerization systems (styrene-methyl acrylate and methyl acrylate-methyl methacrylate) and one emulsion terpolymerization system (styrene-methyl acrylate-methyl methacrylate) was investigated both experimentally and with the model. Experimental results were compared with model calculations. The copolymer chemical composition distributions (CCD) were determined with gradient polymer elution chromatography (GPEC®). This technique was also used for the first time to obtain information about the extent of composition drift in emulsion terpolymerizations. Cumulative terpolymer compositions were determined with 3H-NMR as a function of conversion and with this information the three-dimensional CCD was obtained. The composition drift was analyzed with respect to free radical copolymerization kinetics (reactivity ratios) and monomer partitioning. It was shown that in most emulsion copolymerizations the composition drift is mainly determined by the reactivity of the monomers and to a lesser extent by monomer partitioning, except in systems where there is a large difference in water solubility. The model predictions for cumulative terpolymer composition as a function of conversion and the three-dimensional terpolymer CCD showed excellent agreement with the experiments. The GPEC® elution chromatogram of the terpolymer was found to be in accordance with the predicted CCD and the experimentally determined CCD. © 1996 John Wiley & Sons, Inc.

Batch Reactor Modelling of the Free Radical Copolymerization Kinetics of Styrene/Divinylbenzene Up to High Conversions

An effective model for the bulk, solution and suspension copolymerization of styrene/divinylbenzene has been developed. Experimental data from different sources and model predictions are in very good agreement in most cases for pre and post-gelation periods. The effects of solvent, chain transfer agent, inhibitor, type and concentration of crosslinker (m-DVB, p-DVB or a mixture of both), type and concentration of initiator, and temperature are accounted for by the present model.

高分子科学最近の進歩 ラジカル共重合理論

高分子科学最近の進歩 ラジカル共重合理論

Kinetics of free-radical copolymerization: the pseudo-kinetic rate constant method

The pseudo-kinetic rate constant method in which the kinetic treatment of a multicomponent polymerization reduces to that of a homopolymerization is a useful tool to analyse the kinetics of copolymerization. This method is applicable not only for the systems described by the terminal model for copolymerization but also for those described by the higher order Markov chain statistics such as the penultimate model. It has also been clarified that this method can practically be applicable even when the effect of the chain length dependent bimolecular termination reaction is significant.

Kinetics of the free-radical copolymerization of methyl methacrylate/ethylene glycol dimethacrylate: 2. Analysis of gelation and the pregel region

A kinetic model based on the pseudo-kinetic rate constant method is used to investigate the kinetics of the bulk free-radical copolymerization of methyl methacrylate (MMA) and the divinyl monomer ethylene glycol dimethacrylate (EGDMA) initiated with AIBN, with and without chain transfer agent (CBr 4) during the pregel region. Most of the kinetic parameters were estimated from experimental data. The agreement of predicted with measured onset of gelation is found to be satisfactory.

Kinetics of the free-radical copolymerization of methyl methacrylate/ethylene glycol dimethacrylate: 1. Experimental investigation

An experimental investigation was made of the kinetics of the bulk free-radical copolymerization of methyl methacrylate (MMA) and the divinyl monomer ethylene glycol dimethacrylate (EGDMA) initiated with AIBN at 70°C for levels of EGDMA of 0–25 wt% and chain transfer agent (CBr 4) levels of 0–1 wt%. The conversion of monomers to sol and crosslinked gel was measured by gravimetry using Soxhlet extraction. This provided measurements of monomer conversion at the gelation point as a function of EGDMA and CBr 4 levels and the weights of sol and gel as a function of time and monomer conversion. The experimental data are interpreted in terms of the pseudo-kinetic rate constant method in Part 2 of this series.